levels 3 to 6 ebook - jebelalimaths.weebly.com€¦ · n1 n2 n3 n4 s1 s2 s3c1 c2 c3 c5 c6c4 s4 s5...
TRANSCRIPT
© Mathswatch Ltd
Levels 3 to 7eBook Answers
Level 3 Contents ................. (i)
Level 4 Contents ................. (ii)
Level 5 Contents ................. (iii)
Level 6 Contents ................. (iv)
Level 7 Contents ................. (v)
APP Record Sheet .............. (vi)
Level 3 Certificate ............... (vii)
Level 4 Certificate ............... (viii)
Level 5 Certificate ............... (ix)
Level 6 Certificate ............... (x)
Level 7 Certificate ............... (xi)
Worksheets ......................... 1A to 134
Extras - Weights .................. 135A to 135E
Extras - Balances ................ 136A to 136E
Extras - Congruent Halves .. 137A to 137E
Extras - Circles .................... 138A to 138E
M atchathsWM atchathsW
© Mathswatch Ltd
Number
N1..... Place Value .......................................................1A, 1BN2..... Negative Numbers.............................................2A, 2BN3..... Introduction to Fractions ....................................3A, 3BN4..... Money ...............................................................4A, 4B
Calculating
C1..... Mental Addition ..................................................5A, 5BC2..... Mental Subtraction ............................................6A, 6BC3..... Addition of Integers ...........................................7A, 7BC4..... Subtraction of Integers ......................................8A, 8BC5..... Multiplication by 2, 3, 4, 5 and 10 ......................9A, 9BC6..... Division by 2, 3, 4, 5 and 10 ..............................10A, 10B
Shape, Space and Measure
S1 ..... Reflective Symmetry of 2D Shapes ...................11A, 11BS2 ..... Recognising Nets ..............................................12A, 12BS3 ..... Reflecting Shapes .............................................13A, 13BS4 ..... Metric Units .......................................................14A, 14BS5 ..... Time ..................................................................15A, 15B
Handling Data
D1..... Reading Bar Charts and Pictograms .................16A, 16B, 16CD2..... Drawing Bar Charts and Pictograms .................17A, 17B
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
LEVEL 3
Page
Page (i)
© Mathswatch Ltd
Number
N5..... Number Patterns ...............................................18A, 18BN6..... Square Numbers ...............................................19A, 19BN7..... Multiples ............................................................20A, 20BN8..... Factors ..............................................................21A, 21BN9..... Multiplication and Division by 10 and 100 .........22A, 22BN10... Fractions and Percentages................................23A, 23BN11 ... Ordering Decimals .............................................24A, 24BN12... Basic Ratio ........................................................25A, 25B
Calculating
C7..... Addition .............................................................26A, 26BC8..... Subtraction ........................................................27A, 27BC9..... Short Multiplication ............................................28A, 28BC10... Short Division ....................................................29A, 29BC11 ... Multiplication of Decimals ..................................30A, 30BC12... Problems, Without a Calculator .........................31A, 31BC13... Problems, With a Calculator ..............................32A, 32B
Algebra
A1 ..... Formulae Expressed in Words ..........................33A, 33BA2 ..... Coordinates in First Quadrant ...........................34A, 34B
Shape, Space and Measure
S6 ..... Making 3D Models .............................................35A, 35B, 35C, 35DS7 ..... Reflection in Diagonal Lines ..............................36A, 36B, 36C, 36D, 36ES8 ..... Translation .........................................................37A, 37BS9 ..... Rotation .............................................................38A, 38BS10 ... Reading Scales .................................................39A, 39BS11 ... Perimeter ...........................................................40A, 40BS12 ... Areas .................................................................41A, 41B
Handling Data
D3..... Discrete Data.....................................................42A, 42BD4..... Grouping Data ...................................................43A, 43BD5..... Mode, Median and Range .................................44A, 44B
LEVEL 4
Level 4
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page
Page (ii)
© Mathswatch Ltd
Number
N13... Mult. and Div. of Decimals by 10 and 100 .........45A, 45BN14... Rounding ...........................................................46A, 46BN15... Ordering Negative Numbers ..............................47A, 47BN16... Ordering Fractions.............................................48A, 48BN17... Simplification of Fractions .................................49A, 49BN18... Understanding Ratios ........................................50A, 50B
Calculating
C14... Long Multiplication .............................................51A, 51BC15... Long Division .....................................................52A, 52BC16... BODMAS...........................................................53A, 53BC17... Fraction of an Amount .......................................54A, 54BC18... Directed Numbers .............................................55A, 55BC19... Ratio Questions in Context ................................56A, 56BC20... Direct Proportion ...............................................57A, 57BC21... Real Life Tables .................................................58A, 58B
Algebra
A3 ..... Algebraic Expressions .......................................59A, 59BA4 ..... Coordinates in Four Quadrants .........................60A, 60BA5 ..... Horizontal and Vertical Lines .............................61A, 61BA6 ..... Function Machines ............................................62A, 62B
Shape, Space and Measure
S13 ... Symmetries of 2D Shapes.................................63A, 63BS14 ... Measuring and Drawing Angles .........................64A, 64B, 64C, 64D, 64E, 64FS15 ... Angle Facts .......................................................65A, 65BS16 ... Area of Rectangles ............................................66A, 66B
Handling Data
D6..... Probability..........................................................67A, 67BD7..... The Mean Average ............................................68A, 68B
LEVEL 5
Level 5
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Page
Page (iii)
© Mathswatch Ltd
Number
N19... Fractions, Decimals and Percentages ................... 69N20... Improper Fractions and Mixed Numbers ............... 70N21... Prime Numbers, HCF and LCM ............................ 71
Calculating
C22... Percentage of an Amount ...................................... 72C23... Percentage Increase and Decrease ...................... 73C24... Addition and Subtraction of Fractions.................... 74C25... Multiplication & Division of Integers by Fractions .. 75
Algebra
A7 ..... Substitution............................................................ 76A8 ..... Trial and Improvement........................................... 77A9 ..... Algebraic Simplification ......................................... 78A10 ... Linear Equations ................................................... 79A11 ... Generate a Number Sequence ............................. 80A12 ... Finding the nth Term.............................................. 81A13 ... Straight Line Graphs.............................................. 82A14 ... Distance - Time Graphs ......................................... 83A15 ... Real Life Graphs ................................................... 84
Shape, Space and Measure
S17 ... Properties of Quadrilaterals ................................... 85S18 ... Nets of 3D Shapes ................................................ 86A, 86BS19 ... Constructions ........................................................ 87S20 ... Geometric Problems.............................................. 88S21 ... Corresponding and Alternate Angles ..................... 89S22 ... Enlargement .......................................................... 90A, 90BS23 ... Similar Shapes ...................................................... 91S24 ... Area of a Triangle .................................................. 92A, 92BS25 ... Area of a Parallelogram......................................... 93S26 ... Volume of a Cuboid ............................................... 94S27 ... Surface Area of a Cuboid ...................................... 95S28 ... Circumference of a Circle ...................................... 96S29 ... Area of a Circle...................................................... 97A, 97B
Handling Data
D8..... Bar Charts and Frequency Diagrams .................... 98D9..... Scatter Graphs ...................................................... 99D10... Pie Charts.............................................................. 100D11 ... Two-Way Tables .................................................... 101D12... Surveys ................................................................. 102D13... Further Probability ................................................. 103
LEVEL 6
Level 6
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page
Page (iv)
© Mathswatch Ltd
Number
N22... Rounding to 1 Significant Figure ........................... 104
Calculating
C26... Percentage Increase and Decrease ...................... 105C27... Addition and Subtraction of Fractions.................... 106C28... Multiplication and Division of Fractions ................. 107C29... Numbers Between 0 and 1 (Mult. & Div.) .............. 108C30... Estimating Answers ............................................... 109C31... Using a Calculator ................................................. 110
Algebra
A16 ... Further Algebraic Simplification ............................. 111A17 ... Expanding Brackets .............................................. 112A18 ... Factorisation .......................................................... 113A19 ... Solving Difficult Equations ..................................... 114A20 ... Rearranging a Formula ......................................... 115A21 ... Trial and Improvement........................................... 116A, 116BA22 ... Inequalities ............................................................ 117A23 ... Solving Inequalities ............................................... 118A24 ... Understanding Straight Line Graphs ..................... 119A25 ... Regions ................................................................. 120A26 ... Simultaneous Equations Graphically ..................... 121A27 ... Simultaneous Equations Algebraically ................... 122A28 ... nth Term of Quadratic Sequences ......................... 123A29 ... Graphs of Quadratic and Cubic Functions ............ 124A, 124B, 124C
Shape, Space and Measure
S30 ... Pythagoras’ Theorem ............................................ 125A, 125B, 125CS31 ... Areas of Compound Shapes ................................. 126A, 126B, 126CS32 ... Volumes of Prisms................................................. 127S33 ... Surface Area of Triangular Prisms ......................... 128S34 ... Loci ........................................................................ 129S35 ... Enlargement by a Negative Scale Factor .............. 130S36 ... Bounds .................................................................. 131S37 ... Compound Measures ............................................ 132
Handling Data
D14... Averages from Tables ............................................ 133A, 133BD15... Relative Frequency ............................................... 134
LEVEL 7
Page
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Level 7
Page (v)
© Mathswatch Ltd
Secure Level 3
Secure Level 3 withsome Level 4 features
Secure Level 4
Secure Level 4 withsome Level 5 features
Secure Level 5
Secure Level 5 withsome Level 6 features
Secure Level 6
Name: _________________________
Year: ______ Class: ______
Teacher: ________________
APP Record Card
Date
Page (vi)
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Level 4
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Level 5
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Level 6
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29S17 S18
D8 D9 D10 D11 D12 D13
Level 7
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Secure Level 6 withsome Level 7 features
Secure Level 7
© Mathswatch Ltd
LEVEL 7
LEVEL 6
LEVEL 5
LEVEL 4
LEVEL 3
MathematicsLevel 3
Certificate
This is to certify that _______________________
has successfully achieved Level 3 in Mathematics.
Class: ____________________
Date: ___________ Signed: ____________
Page (vii)
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
© Mathswatch LtdPage (viii)
MathematicsLevel 4
Certificate
This is to certify that _______________________
has successfully achieved Level 4 in Mathematics.
Class: ____________________
Date: ___________ Signed: ____________
Level 4
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
LEVEL 7
LEVEL 6
LEVEL 5
LEVEL 4
LEVEL 3
© Mathswatch LtdPage (ix)
MathematicsLevel 5
Certificate
This is to certify that _______________________
has successfully achieved Level 5 in Mathematics.
Class: ____________________
Date: ___________ Signed: ____________
Level 5
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
LEVEL 7
LEVEL 6
LEVEL 5
LEVEL 4
LEVEL 3
© Mathswatch LtdPage (x)
MathematicsLevel 6
Certificate
This is to certify that _______________________
has successfully achieved Level 6 in Mathematics.
Class: ____________________
Date: ___________ Signed: ____________
Level 6
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29S17 S18
D8 D9 D10 D11 D12 D13
LEVEL 7
LEVEL 6
LEVEL 5
LEVEL 4
LEVEL 3
© Mathswatch LtdPage (xi)
MathematicsLevel 7
Certificate
This is to certify that _______________________
has successfully achieved Level 7 in Mathematics.
Class: ____________________
Date: ___________ Signed: ____________
LEVEL 7
LEVEL 6
LEVEL 5
LEVEL 4
LEVEL 3
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Level 7
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
Put the following numbers in the place value table.
a) 2415
b) 607
c) 9380
d) 2004
N1Place Value
2 4 1 56 0 7
9 3 8 02 0 0 4
667
2156
914
4071
five thousand four hundred and thirty two
eight hundred and eleveneight hundred and eleven
three thousand six hundred and twenty
nine thousand and ninety
200
6000
1)
2) Write the following numbers in figures.
a) six hundred and sixty seven
b) two thousand one hundred and fifty six
c) nine hundred and fourteen
d) four thousand and seventy one
3) Write the following numbers in words.
a) 5432
b) 811
c) 3620
d) 9090
4) a) What is the value of the 2 in thenumber 1250?
b) What is the value of the 6 in thenumber 6924?
Page 1A
1000Thousands
100Hundreds
10Tens
1Units
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersN1Just For Fun
1) Match the words with the correct numbers.
2) Here are four number cards.
a) What is the biggest three digit numberyou can make with these cards?
b) What is the biggest even number youcan make with all four cards?
3) a) Write a whole number that is bigger thanone thousand but smaller than onethousand one hundred.
b) Write the number eleven thousand elevenhundred and eleven.
6 4 3
6 3 1 4
anything from 1001 to 1099
12 111
Page 1B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersN2Negative Numbers
-5-4-3-2-10123456789
101112C
-5-4-3-2-10123456789101112C
-5-4-3-2-10123456789
101112C
-5-4-3-2-10123456789101112C
-5-4-3-2-10123456789101112C
-5-4-3-2-10123456789
101112C
A B C D E F
A
B
C
D
E
F
-3 °C rises 8 °C 5 °C
5 °C falls 6 °C -1 °C
-5 °C rises 3 °C -2 °C
11 °C falls 15 °C -4 °C
-1 °C rises 8.5 °C 7.5 °C
2 °C falls 6.5 °C -4.5 °C
Thermometer Temperatureat 3.00 A.M
Temperaturechange over
next five hours
Temperature at8.00 A.M.
The thermometers A to F show the temperature at 3:00 A.M.in six different cities.Use them to fill in the table below.The first one has been done for you.
Page 2A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersN2Just For Fun
1) Place these numbers in order of size, smallest to largest.
a) -1, 2, 5, 6
b) -5, -2, 3, 4, 7
c) -4, -2, -1, 0, 3, 9
d) -9, -6, -4, -3, 1, 4, 8
e) -12, -10, -8, -7, -6, -4, -3
f) -5.5, -4, -3.5, -3, -2.5, 6, 7.5, 8.5
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
Player A Player B
Start point
3) Place a counter on 0.Player A and B take turns in rolling a dice.Whatever scores player A gets, he/she alwaysmoves this many squares to the left.Whatever scores player B gets, he/she alwaysmoves this many squares to the right.Player A wins if he/she needs to move to asquare which is less than -8.Player B wins if he/she needs to move to asquare which is more than 8.
2) a) What is special about the temperature 100 °C?
b) What is special about the temperature 0 °C?
Water boils
Water freezes
Page 2B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
Introduction to Fractions
1) Find three equivalent fractions to each of thefollowing:
a) b) c)
d) e) f)
2) Fill in the missing number in each of theseequivalent fractions.
a) = b) = c) =
d) = e) = f) =
g) = h) = i) =
13
3) Complete the following equivalent fraction series.
a) = = = = =
b) = = = = =
14
15
25
34
58
23
15
3119 20 22
13
5 27
10 49
8
25
57
910
814250
12
26
520
615
1250
30035
28
312
416
26
39
412
210
315
420
68
1216
2432
410
820
1640
5080
500800
50008000
6 4 6
15 35 18
20 30
90
4
3
10
10
100
10
9
20
30
500
50
These are a selectionof possible answers.
As long as you multipliedthe top and bottom
by the same numberyour answer is fine.
N3
Page 3A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
Just For Fun
Use the diagram below to help you fill in themissing numbers.
a)
b)
c)
d)
1) Here are six number cards.
a) Choose two of these six cards
to make a fraction that is
equivalent to .
b) Choose two of these six cards
to make a fraction that is
equivalent to .
2)
2 4 6 8 10 12
16
14
13
= +
1216
16
= –
212
16
+ =
16
13
+ =14
+
2
12
6
8
1
12
1
4
1
3
3
12
112
16
112
112
13 1
4
112
N3
Page 3B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
Money
1) Write the following amounts of money usinga £ sign and numbers.
a) Three pounds and thirty seven pence.
b) Twenty four pounds and fifty pence.
c) Two hundred and five pounds.
d) Nine pounds and sixty pence.
e) Nine pounds and six pence.
f) Forty eight pence.
2) Write the following amounts of money in words.
a) £2.78
b) £6.07
c) £5.40
d) £0.24
3) Work out the following on a calculator and write theanswers correctly:
a) £115.23 ÷ 23
b) £100.80 ÷ 14
c) 71p × 10
d) £6.40 – £3.83 + £2.10
e) £14.83 + £6.17
£3.37
£24.50
£205
£9.60
£9.06
£0.48
Two pounds and seventy eight pence
Six pounds and seven pence
Five pounds and forty pence
Twenty four pence
£5.01
£7.20
£7.10
£4.67
£21
N4
Page 4A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
Three men went into a second-hand shop to buy atelevision.
It was priced in the window at £30.
Each of them handed over £10 to the shop assistant.
As the assistant opened the till, the manager had a quietword with him, “that TV is in the sale and is only £25now, you will have to give them £5 back.”
The assistant was very lazy and couldn’t be bothered tocount out the right change for each man.
Instead, he took 5 £1 coins out of the till.
He put two of them in his own pocket and gave eachman £1 back.
Here’s the problem:
The men have now paid £9 each for the TV.
The assistant has kept £2 for himself.
3 × £9 = £27.
£27 + £2 = £29.
But £30 was handed over in the first place.
WHERE IS THE MISSING £1?
This is a very famous question and has puzzledmany generations of children.
The missing £1 is . . . . . please ask your teacher,your parents and/or your friends.
We’re just not allowed to tell you.
N4Just For Fun
Page 4B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC1Mental Addition
For each set of questions, time how long it takes to getthe answers.You must work out the answers in your head - you can’tdo any working on paper.
1) 23 + 35
2) 17 + 13
3) 45 + 46
4) 38 + 44
5) 71 + 54
6) 38 + 46
7) 27 + 68
8) 64 + 77
9) 64 + 99
10) 87 + 96
Set A
1) 42 + 56
2) 23 + 56
3) 37 + 25
4) 68 + 26
5) 83 + 65
6) 59 + 37
7) 42 + 39
8) 57 + 68
9) 99 + 48
10) 68 + 94
Set B
1) 62 + 24
2) 38 + 22
3) 17 + 34
4) 52 + 29
5) 82 + 63
6) 28 + 36
7) 88 + 17
8) 67 + 56
9) 42 + 98
10) 78 + 93
Set C
= 58
= 30
= 91
= 82
= 125
= 84
= 95
= 141
= 163
= 183
= 98
= 79
= 62
= 94
= 148
= 96
= 81
= 125
= 147
= 162
= 86
= 60
= 51
= 81
= 145
= 64
= 105
= 123
= 140
= 171
For any set of questions:45 seconds or less: Maths teacher standard46 to 89 seconds: Extremely fast90 to 149 seconds: Fast150 to 209 seconds: Reasonable210 seconds or more: A bit more practise needed
Page 5A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC1
How do you win every time?
You probably noticed that if you can get to 18 youdefinitely win.
But, if you get to 15 you can definitely get to 18and so 15 is a step on the way to victory.
And if you get to 12 you can get to 15.
To cut a long story short, just stick to the 3 timestable (or get on to it as soon as you can if you gofirst.)
So, if you go second, your numbers will always be:
3, 6, 9, 12, 15, 18, 21.
If you go first, start with a 1 or 2 and keep playinguntil you can say, 6, 9, 12, etc.
Just For Fun
Page 5B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC2Mental Subtraction
For each set of questions, time how long it takes to getthe answers.You must work out the answers in your head - you can’tdo any working on paper.
1) 75 – 71
2) 98 – 93
3) 84 – 32
4) 68 – 24
5) 79 – 47
6) 38 – 29
7) 67 – 48
8) 54 – 39
9) 94 – 36
10) 72 – 25
Set A
1) 57 – 52
2) 78 – 71
3) 56 – 13
4) 78 – 27
5) 66 – 31
6) 84 – 38
7) 76 – 29
8) 43 – 17
9) 62 – 26
10) 51 – 24
Set B
1) 39 – 34
2) 67 – 62
3) 83 – 42
4) 88 – 34
5) 76 – 25
6) 63 – 39
7) 46 – 28
8) 54 – 48
9) 72 – 27
10) 72 – 38
Set C
= 4
= 5
= 52
= 44
= 32
= 9
= 19
= 15
= 58
= 47
= 5
= 7
= 43
= 51
= 35
= 46
= 47
= 26
= 36
= 27
= 5
= 5
= 41
= 54
= 51
= 24
= 18
= 6
= 45
= 34
For any set of questions:45 seconds or less: Maths teacher standard46 to 89 seconds: Extremely fast90 to 149 seconds: Fast150 to 209 seconds: Reasonable210 seconds or more: A bit more practise needed
Page 6A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC2Just For Fun
This trick works by itself.On the piece of paper you must alwayswrite the number 1089.This number will always be the answer.Here are some examples to show you.
412214198891
–
+1089
913319594495
–
+1089
784487297792
–
+1089
543345198891
–
+1089
978879099990
–
+1089
310013297792
–
+1089
Page 6B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
1) 51 + 36
2) 41 + 27
3) 231 + 25
4) 446 + 38
5) 569 + 84
6) 316 + 262
7) 596 + 472
8) 657 + 847
9) 62 + 38 + 517
10) 216 + 32 + 518 + 74
=
=
=
=
=
=
=
=
=
=
87
68
256
484
653
578
1068
1504
617
840
C3Addition of Integers
Page 7A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
2 3
4
6 8
1) 5 8
2
8 4
2)
7 9
4
3) 3
8
4)
1 2 7 1 6 0
5) 2 6
3 5
6)
4
6 4
7) 6
4 6
8)
7 5 1 1 3 6 3
8
1 9 2
+ +
+ +
+ +
+ +
5 6
8 7
7
49
9
6
2
6 1 8
8 7
2
8 7
9
Work out whatthe must be.*
C3Just For Fun
Page 7B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
1) 35 – 12
2) 58 – 27
3) 93 – 46
4) 258 – 37
5) 681 – 79
6) 420 – 68
7) 743 – 471
8) 361 – 278
9) 800 – 692
10) 1450 – 785
C4
23
31
47
221
602
352
272
83
108
665
=
=
=
=
=
=
=
=
=
=
Page 8A
Subtraction of Integers
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
8)
5 9 6
9
6 3
7)
5) 6) 3 5
2 6
6 1
4)6 73)
7 9
5
3
2)4 5
2
2
1)
3 4
6
68
74
4
3
2 8
3
7 38
C4Just For Fun
4 1 2 5
5 6 5 1 8 7
6 3
– –
– –
– –
– –
8 21 6
2 4
2
Page 8B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC5
× 5 4 2
2
4 12
20
3
× 10 4 5 3
3
2 8
1 3
5 25
2) Work out
a) 2 × 17 = ____ b) 24 × 5 = ____
c) 10 × 9 = ____ d) 4 × 62 = ____
e) 37 × 3 = ____ f) 2 × 81 = ____
g) 5 × 32 = ____ h) 3 × 19 = ____
i) 26 × 4 = ____ j) 11 × 10 = ____
30 12 15 920 10 610 4 550 20 15
10 6 8 420 16 850 30 4015 9 12 6
3
10
34 120
90 248
111 162
160 57
104 110
Page 9A
1) Fill in the missing numbers in theminitables below.
a) b)
Multiplication by 2, 3, 4,5, and 10
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC5Just For Fun
1) a) Use the table to fill in the gaps below.
21 × 14 = ____
12 × ____ = 228
____ × 15 = 315
286 ÷ 22 = ____
b) Give two different pairs of numbers.
____ × ____ = 252
____ × ____ = 252
× 11 12 13 14 15
18 198 216 234 252 270
19 209 228 247 266 285
20 220 240 260 280 300
21 231 252 273 294 315
22 242 264 286 308 330
2) Julia says:
“Multiply any number by five. The answer must be an odd number.”
Is she correct?Circle Yes or No
Explain how you know.
_______________________________________
Yes / No
294
19
21
13
12 21
14 18
2 × 5 = 10 and 10 is an even number.Any example which shows this is wrong such as:
Page 9B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC6
2) Work out
a) 46 ÷ 2 = ____ b) 39 ÷ 3 = ____
c) 65 ÷ 5 = ____ d) 62 ÷ 4 = ____
e) 47 ÷ 3 = ____ f) 11 ÷ 10 = ____
g) 92 ÷ 4 = ____ h) 57 ÷ 3 = ____
i) 90 ÷ 5 = ____ j) 83 ÷ 10 = ____
1) Work out
a) 16 ÷ 2 = ____ b) 30 ÷ 5 = ____
c) 21 ÷ 3 = ____ d) 40 ÷ 4 = ____
e) 35 ÷ ____ = 7 f) 24 ÷ ____ = 8
23 13
13 15 r2
15 r2 1 r1
23 19
18 8 r3
8 6
7 10
5 3
Page 10A
Division by 2, 3, 4,5, and 10
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersC6Just For Fun
1) Here is part of the 45 times table.Use the table to help you fill inthe missing numbers.
a) 315 ÷ 7 = ____
b) 135 ÷ 45 = ____
c) 270 ÷ ____ = 45
d) ____ × 45 = 405
e) 495 ÷ 45 = ____
f) ____ × 45 = 900
g) 450 ÷ 30 = ____
2) Joe says:
“Divide any number by three. The answer must be an even number.”
Is he correct?Circle Yes or No
Explain how you know.
_______________________________________
Yes / No
45
3
6
9
20
11
15
15 ÷ 3 = 5 and 5 is an odd number.
1 × 45 = 45
2 × 45 = 90
3 × 45 = 135
4 × 45 = 180
5 × 45 = 225
6 × 45 = 270
7 × 45 = 315
8 × 45 = 360
9 × 45 = 405
10 × 45 = 450
Page 10B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
Look at each shape, read the descriptionand then draw in all the lines of symmetry.
S1Reflective Symmetry
of 2D Shapes
1) RectangleTwo lines of symmetry
2) SquareFour lines of symmetry
3) Isosceles triangleOne line of symmetry
4) Equilateral triangleThree lines of symmetry
5) Regular pentagonFive lines of symmetry
6) Regular hexagonSix lines of symmetry
Page 11A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersS1Just For Fun
1) Shade in five more littletriangles so that the figurehas one line of symmetry.
2) Shade in just three morelittle triangles so that thefigure has one line ofsymmetry.
Page 11B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersS2Recognising Nets
Cuboid
Triangle-basedpyramid
Square-basedpyramid
Cube
Draw two lines from each label.One line should go to the correct 3-Dshape.The other one should go to the net ofthe 3-D shape.
Page 12A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
There are exactly eleven different nets of a cube.
Below, you can see two of them.
See how many of the other nine you can find.
1) 2)
3) 4)
6) 7)
9) 10)
5)
8)
11)
S2Just For Fun
Page 12B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
In all four questions, reflect the shadedshape in the dotted mirror line.
1)
3)
2)
4)
S3Reflecting Shapes
Page 13A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
Answers
3)
2)1) Reflect every line in the dottedmirror line.
Use the grid to help you reflectRobbie Rabbit in the dotted mirrorline.
Reflect the shape in the verticalmirror line.Then, reflect both shapes in thehorizontal mirror line.
4) Reflect the shape in the verticalmirror line.Then, reflect both shapes in thehorizontal mirror line.
S3Just For Fun
Page 13B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersS4
1) a) How many millimetres are in a centimetre?
b) How many centimetres are in a metre?
c) How many metres are in a kilometre?
d) Work out how many millimetres are in a metre.
2) How many grams are in three kilograms?
3) How many millilitres are in a five litres?
4) In the table, work out what each item should bemeasured in.
Your choices are mm, cm, m, km, g, kg, ml or l.
Amount of lemonade in a bottle
Mass of a lemonade bottle
Width of a lemonade bottle
Distance to the moon
Mass of a wasp
Length of a wasp
Amount of blood in a human body
10
1000
1000
100
3000
5000
ml or l
g or kg
mm or cm
km
g
mm
l
Metric Units
Page 14A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersS4Just For Fun
Average capacity ofair breathed in a day
Blood vessels in a humanbody laid end-to-end
Mass of MountEverest
Length of airways in thelungs laid end-to-end
Mass ofthe Earth
Capacity of allwater on Earth
5 980 000 000 000 000 000 000 000 kg
1460 000 000 000 000 000 000 litres
2 400 km
11 000 litres
3 041 409 000 000 000 kg
100 000 km
A
B
C
D
E
F
U
V
W
X
Y
Z
Try to match up A to F with U to Z1)
The ship is in a harbour.
There are ten rungs visible on theship’s ladder and they are 30 cm apart.
The tide is coming in and the water isrising at the rate of 20 cm per minute.
How many rungs will be visible after 9minutes?
2)
All ten rungs will still be visiblebecause the ship floats.Try this question with your parents.
Page 14B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersS5 Time
121
2
3
4
567
8
9
1011
121
2
3
4
567
8
9
1011
121
2
3
4
567
8
9
1011
121
2
3
4
567
8
9
1011
1) Write these times as 24 hour clock times
a) b) c) d)
a.m. p.m. p.m. p.m.04:00 14:50 16:35 21:20
a) b) c) d)09:40 18:10 13:35 23:55
121
2
3
4
567
8
9
1011
121
2
3
4
567
8
9
1011
121
2
3
4
567
8
9
1011
2) Draw these times on the clock faces.Underneath the clocks write whether the time is a.m. or p.m.
a.m. p.m. p.m. p.m.
3) Peter wants to watch a programme which begins at 8.00 p.m.
It is now 4.30 p.m.
How much time will Peter have to wait?
4) Susie is going to watch a programme which begins at 20:30and lasts for one hour and forty five minutes.
What time will it finish?
Three and a half hours(3 hours 30 minutes)
22:15
121
2
3
4
567
8
9
1011
Page 15A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersS5Just For Fun
1) Here is a train timetable for trains going fromLondon Euston to Crewe.
a) How many trains stop at Tamworth?
b) If Tom gets to London Euston at 15:30 howlong will he have to wait for a train to take himto Crewe?
c) How many minutes does the 09:38London Euston train take to get to Northampton?
d) How many minutes does the 14:23 Lichfield traintake to get to Crewe?
e) How long does the 17:48 London Euston traintake to get to Crewe in hours and minutes?
2) This is the easiest way but you need 22 minutes:
4
16 mins
47 mins
46 mins
1 hour and 46 mins
Put the egg in theboiling water andset both timers off
11
0
7
0
after 7 mins
4
7
0
7
turn the 7 minutetimer over straight
away
4
7
7
0
after another 4mins
0
11
3
4
turn the 7 minute timer overand wait for it to finish.
You now have 15 minutes.
11
0
4
3
set them offtogether
11
0
7
0
after 7 mins put theegg in the boiling
water
0
7
4
7
11
0
after 4 mins turnthe 11 minute timer
over again
0
11
11 minutes lateryour egg will haveboiled for exactly
15 mins
This is a harder way but it only takes 15 minutes:
Page 15B
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersD1Reading Bar Charts
and Pictograms
Red
Blue
Yellow
Green
1234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901
1234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901
123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012
1234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901123456789011234567890112345678901
1
2
3
4
5
6
0
Favourite colour
Numberof
children
Bar chart to show favouritecolour of all pupils in class 5A
a) How many children chose green as their favourite colour?
b) Which was the least favourite colour in the class?
c) How many more children chose blue than red?
d) How many children are in class 5A?
5
Yellow
2
18
Page 16A
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersD1
An art gallery uses a pictogram to show the numberof paintings sold over a 5 week period.
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
Week 1123451234512345123451234512345
12345123451234512345123451234512345
12345123451234512345
1234512345123451234512345
Week 2
1234512345123451234512345
123451234512345123451234512345
12345123451234512345
1234512345123451234512345
Week 3
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
Week 4123451234512345123451234512345
12345123451234512345123451234512345
12345123451234512345
1234512345123451234512345
Week 5
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
123451234512345123451234512345
12345123451234512345123451234512345
12345123451234512345
1234512345123451234512345
1234512345123451234512345
123451234512345123451234512345
12345123451234512345
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
1234512345123451234512345
123456123456123456123456123456123456
123451234512345123451234512345123456
123456123456123456123456
1234512345123451234512345
123456123456123456123456123456123456123456123456123456123456
123451234512345123451234512345
12345612345612345612345612345612345612345
12345123451234512345
123456123456123456123456123456
123456123456123456123456123456
1234512345123451234512345
123456123456123456123456123456
1234512345123451234512345
1234512345123451234512345
123451234512345123451234512345
12345123451234512345
1234512345123451234512345
Key: = 4 paintings
a) How many paintings were sold in week 1?
b) In which week was the least number ofpaintings sold?
c) How many paintings were sold in week 3?
d) How many paintings were sold in week 4?
e) How many more paintings were sold in week 2compared with week 5?
f) How many paintings were sold altogether in thefive weeks?
12
Week 5
10
7
12
49
Page 16B
Reading Bar Chartsand Pictograms
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersD1Just For Fun
300
250
200
150
100
50
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
Ann Ben Jane Cara Dave Carl
Ma
rks
Science123456123456123456123456123456123456
Maths English
Six students sat exams in English, Maths and Science.Each exam was marked out of 100.Their teacher made a bar chart of their results.
a) Which student got the highest total mark?
b) Who got the highest English mark?
c) One student got the same mark for all threesubjects. Write down the name of this student.
d) What mark did Ann get for Maths?
e) One student had their lowest mark for English.Who was it?
Ben
Dave
Carl
75
Ann
Page 16C
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersD2
White Yellow Orange Green Blueo
1
2
3
4
5
6
7
8
9
Number of different colour belts in a Judo club
Colour of belt
Fre
quen
cy
1)
Red
Green
Black
Yellow
Blue
Number of different colour pencil cases
Key:
represents 4 pencilcases
2)
Page 17A
Drawing Bar Chartsand Pictograms
© Mathswatch Ltd
Level 3
N1 C1 C2 C3 C5 C6N2 N3 N4 S1 S2 S3C4 S4 S5 D1 D2
AnswersD2Just For Fun
1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567
123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678
1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567
1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567
Fish Curry Pizza Stewo
1
2
3
4
5
6
7
8
9
Meals bought by Class A and Class B
Meals bought
Fre
quen
cy
1234512345123451234512345
Class A Class BKey:
2)
1) a) Geography had the most grade A results.
b) Geography had 4 more grade D results comparedwith History.
Page 17B
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N5
Page 18A
1) For each number pattern:
a) Describe the pattern
b) Work out what the next three terms are
(i) 2, 4, 6, 8, 10, 12, 14, 16, 18
(ii) 1, 4, 7, 10, 13, 16, 19, 22, 25
(iii) 5, 12, 19, 26, 33, 40, 47, 54, 61
(iv) -2, 3, 8, 13, 18, 23, 28, 33, 38
(v) 36, 33, 30, 27, 24, 21, 18, 15, 12
(vi) -12, -8, -4, 0, 4, 8, 12, 16, 20
(vii) 100, 91, 82, 73, 64, 55, 46, 37, 28
(viii) 7, 8.5, 10, 11.5, 13, 14.5, 16, 17.5, 19
goes up in 2s
goes up in 3s
goes up in 7s
goes up in 5s
goes down in 3s
goes up in 4s
goes down in 9s
goes up in 1.5s
goes up by 3 then 5 then 7 etc ORsquare numbers (1 × 1), (2 × 2), (3 × 3), etc
goes up by 2 then 3 then 4 etc ORtriangle numbers
Number Patterns
2) For both of the following number patterns:
a) Describe the pattern
b) Work out what the next three terms are
(i) 1, 4, 9, 16, 25, 36, 49, 64, 81
(ii) 1, 3, 6, 10, 15, 21, 28, 36, 45
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N5
Page 18B
1) Work out the next two terms for each ofthe following number patterns:
a) 3, 8, 15, 24, 35, 48, 63
b) 4, 14, 36, 76, 140, 234, 364
2) Work out the next two terms for each ofthe following number patterns:
a) 1, 2, 4, 8, 16, 32, 64, 128
b) 2, 7, 22, 67, 202, 607, 1822
3) Work out the next two terms for each ofthe following number patterns:
a) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
b) 1, 2, 3, 6, 11, 20, 37, 68, 125, 230
4) Work out the next two terms for each ofthe following :
a) O, T, T, F, F, S, S, E, N
b) J, F, M, A, M, J, J, A, S
Each row describes the row above.In the first row we have one 1.The second row says this (1 1)The third row describes the secondrow.We have two 1s and it says this (2 1)We now have one 2 and one 1.The fourth row is therefore 1 2 1 1If you got this right you are one of aselect few.
6)
First letters of 1, 2, 3, 4, etc
First letters of Jan, Feb, Mar, etc
Yes, mathematiciansthink so.
It does eventually if you make no mistakes.
11 12 1
1 2 1 11 1 1 2 2 13 1 2 2 1 1
1 3 1 1 2 2 2 11 1 1 3 2 1 3 2 1 1
3 1 1 3 1 2 1 1 1 3 1 2 2 11 3 2 1 1 3 1 1 1 2 3 1 1 3 1 1 2 2 1 1
Just For Fun
5) Choose any number between 1 and 20.
If your number is even, halve it andwrite down the answer.If your number is odd, multiply it bythree and add one. Write down theanswer.
Look at your answer and follow thesame rules:If it is even you halve it and write downthe answer.If it is odd you multiply by three andadd one and write down the answer.
Only stop when you get to one.
Try more starting numbers (of any size).
Do they all go to one?
What about if you use 27 as thenumber to start with?
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N6
Page 19A
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81 82 83 84
85 86 87 88 89 90 91 92 93 94 95 96
97 98 99 100 101 102 103 104 105 106 107 108
109 110 111 112 113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128 129 130 131 132
133 134 135 136 137 138 139 140 141 142 143 144
Square Numbers
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunN6
Page 19B
a) The numbers1, 3, 6, 10, 15, . . . arecalled triangular numbers.You can see why, below.
1 3 6 10 15
b) The triangular numbers are1, 3, 6, 10, 15, . . . etc.If you choose any two of them which are next to eachother you will always get a square number.eg 1 + 3 = 4, 3 + 6 = 9, 6 + 10 = 16
If you look carefully at the shapes of the dots you cansee they fit together to make a square. Here’s anexample:
6 10
+ =
16
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N7
Page 20A
Multiples
1) a) Write down the first five multiples of 3.
b) Write down the first five multiples of 7.
c) Write down the first five multiples of 4.
2) 6, 12, 18, 24, 30 are the first five multiplesof which number?
3) What are the eighth, ninth and tenth multiples of 11?
4) Put the correct numbers in these circles.Be careful of the overlaps.
First eight multiplesof 3 in this circle
First eight multiplesof 4 in this circle
3, 6, 9, 12, 15
7, 14, 21, 28, 35
4, 8, 12, 16, 20
6
88, 99, 110
12
24
3 6
9 15
1821
4
8
1620
2832
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunN7
Page 20B
×××× ×× ××××× × ×× ×× ×
××× ×× ×× × ×× ×× ××× × ×× ××
××
×× × ×× ×
×
× × ×× ××× × ×× ×× ×
××× ×× ××××
× × ××××
×× × ×××1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
The sieve of Eratosthenes
Just follow these steps:
a) Cross out 1.
b) Shade in the square with 2 in it.Now cross out all other multiples of 2.
c) Shade in the 3 square.Cross out all other multiples of 3(some will already be crossed out).
d) Shade in the 5 square.Cross out all other multiples of 5.
e) Shade in the 7 square.There should be just threeother multiples of 7 whichhaven’t already been crossed out.Cross them out.
f) Shade in every square that hasn’tbeen crossed out.
g) Write out the numbers in everyshaded square.
h) Prime numbers
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N8
Page 21A
Factors
1) Write down all the factors of:
a) 6
b) 8
c) 10
d) 12
e) 20
f) 21
2) 100 has nine factors.
What are they?
3) The numbers 2, 3, 5 and 7all have exactly two factors.
Find the next four numberswith only two factors.
4) The numbers 1, 4, 9 and 16 allhave an odd number of factors.
Find the next three numberswhich have an odd number offactors.
Factors of 24 inthis circle
Factors of 40 inthis circle
5) Put the correct numbers in the circles.Be careful of the overlaps.
1 2 3 6
1 2 4 8
1 2 5 10
1 2 3 4 6 12
1 2 4 5 10 20
1 3 7 21
1 2 4 5 10 20 25 50 100
11 13 17 19
25 36 49
1
2
4
3
6
12
24
5
810
2040
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunN8
Page 21B
A
B
C
Place all the whole numbers from 1 to 60 in thediagram below.However, you must stick to these four rules:
1) In the rectangle you must have every wholenumber from 1 to 60
2) In circle A you must have all the factors of 60
3) In circle B you must have all the factors of 45
4) In circle C you must have all the factors of 36
13
515
9
2 46 12
10
20
30
60
45
18
36
Factors of 60
Factors of 45
Factors of 36
Numbers from 1 to 60
7 8
11 13
14 16
17 19
21
22 23
24
25
26
27
28
29
31 32 33
34
35
37
38
39
40
4142
43
4446
47 4849
50
51
52
53
54
5556
5758
59
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N9
Page 22A
1) 75 × 100
2) 102 × 10
3) 9 × 1000
4) 450 ÷ 10
5) 3800 ÷ 10
6) 9700 ÷ 100
7) 60 × 1000
8) 7000 ÷ 100
9) 210 × 1000
10) 1050000 ÷ 1000
7500
1020
9000
45
380
97
60000
70
210000
1050
=
=
=
=
=
=
=
=
=
Multiplication and Divisionby 10 and 100 (and 1000)
=
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunN9
Page 22B
7 000 000
700 000
70 000
7 000
700
Place Approximate population
London
Glasgow
Barnsley
Penkbridge
High Bickington
Penkbridge
London
100
Glasgow
High Bickington
10
The table shows the approximatepopulations of five different places.
Complete these sentences:The population of Barnsley is about 10 times
bigger than the population of .............................
The population of ............................. is about 100times bigger than the population of Barnsley.
The population of Glasgow is about ........ times
bigger than the population of Penkbridge.
The population of Barnsley is about 10 timessmaller than the population of .............................
The population of ............................. is about 100times smaller than the population of Barnsley.
The population of High Bickington is about ........times smaller than the population of Penkbridge.
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
1) What fractions of the following shapes are shaded?
a) b) c)
d) e) f)
2) Shade the shapes according to the given fractions.
a) b) c)57
13
25100
3) What percentage of the shapes below are shaded?
a) b) c)
24
12
or 56
39or
13
28
14
or 49
510or
12
1% 60% 75%
N10
Page 23A
Fractions and Percentages
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunN10
Page 23B
13
16
of this shape is shaded.
a) What fraction of this diagram is shaded?
b) What fraction of this diagram is shaded?
13
These are a selection of possible answers.As long as each of your four sections is comprised offour little squares, your answer is correct.
1)
2)
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N11
Page 24A
1) a) 0.47 b) 0.407 c) 7.04 d) 47.4 ____ ____ ____ ____
From the following list, match the correct way ofreading each of the above numbers.
A- seven point four F- seven zero fourB- zero point forty seven G- forty seven point fourC- zero point four zero seven H- four seven fourD- four seven point four I- four seven point zeroE- seven point zero four J- zero point four seven
2) Arrange the numbers in order of size, starting withthe smallest.
a) 1.8 0.8 8 8.1___ ___ ___ ___
b) 0.08 1.16 0.12 1.09___ ___ ___ ___
c) £4.04 £4.40 £4.14 £0.41___ ___ ___ ___
d) 3.11 3.1 3 3.011 3.001___ ___ ___ ___ ___
e) 0.2 0.022 0.202 0.222 0.22___ ___ ___ ___ ___
f) 6.06 60.06 6.606 66.06 6.066___ ___ ___ ___ ___
Ordering Decimals
J
0.8 1.8 8 8.1
C E G
0.08 0.12 1.09 1.16
£0.41 £4.04 £4.14 £4.40
3 3.001 3.011 3.1 3.11
0.022 0.2 0.202 0.22 0.222
6.06 6.066 6.606 60.06 66.06
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N11
Page 24B
Just For Fun
I am a decimal number.I have two figures before the decimal point andtwo figures after the decimal point.I read the same forwards as backwards.I have no zeros.My first digit is bigger than my second digit.The sum of my digits is 8.
What number am I?
4 7 3 1 .
1 . 3 4 7
7 4 3 . 1
9.92
31.13
1)
2)
3)
Here are some number cards.
a) What is the smallest number you canmake?
b) What is the largest number you canmake?
Each card can be used once, all cards must be used,the decimal point card cannot be at the end of a number.
The times, in seconds, for the seven runnersin a 100m race were:
9.96 10.03 9.92 10.26 10.37 9.99 10.00
What was the time of the winner?
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
N12
Page 25A
1) For each of the three grids below, write down theratio of shaded squares to unshaded squares.
Simplify the ratios if possible.
a) b) c)
2) Shade in squares for each grid to give the correct ratios.
Shaded Unshaded
5 : 7
Shaded Unshaded
1 : 2
Shaded Unshaded
5 : 1
a) b) c)
2 : 13 5 : 10 1 : 2 6 : 9 2 : 3
80 ml
50 ml
100 ml squash400 ml water
3) The instructions on a lemonsquash bottle are as follows:
a) If you put 20 ml of squash in a glass, how muchwater would you need?
b) If you had used 200 ml of water, how muchsquash should be in the drink?
c) If you want to make 500 ml of squash drink,how much squash should be used and howmuch water?
1 part squash to4 parts water
Basic Ratio
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunN12
Page 25B
DragianVesuvian
1) Here we have a fine exampleof a Vesuvian and a Dragian.
If you count carefully you cansee that the ratio of teeth is 5 : 7
a) What is the ratio of feet?
b) What is the ratio of eyes?
c) What is the ratio of fingers?
Check that you have given allratios in the simplest form.
2) Look at this picture ofVesuvians and Dragians andwork out the following:
a) The ratio of Vesuvians toDragians.
b) The ratio of Vesuvian feet inthe picture to Dragian feet inthe picture.
c) The ratio of Vesuvian eyes inthe picture to Dragian eyes inthe picture.
3) In another picture of Vesuvians and Dragians we onlyknow two things:
Firstly, there are more Vesuvians than Dragians.Secondly, there are 46 teeth altogether in the picture.
Work out how many Vesuvians and Dragians there arein the picture.
6 : 2, 3 : 1
4 : 1
6 : 6, 1 : 1
12 : 8, 3 : 2
72 : 16, 9 : 2
48 : 8, 6 : 1
5 Vesuvians3 Dragians
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C7
Page 26A
1) 1524 + 4273
2) 7452 + 216
3) 24578 + 1215
4) 591 + 372 + 85
5) 9876 + 55 + 1039
6) 59.1 + 37.2
7) 24.75 + 9.98
8) 94.78 + 104.9
9) 309 + 12.5 + 631.4
10) 105 + 7.32 + 51.8 + 2804
5797
7668
25793
1048
10970
96.3
34.73
199.68
952.9
2968.12
=
=
=
=
=
=
=
=
=
=
Addition
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunC7
Page 26B
a)
1)
2)
+ = 4.6
3.61
3.2
2.975
7.65
2.35
1.006
1.3
3.58
6.72
2.25
+ = 11.26b)
1 1 10 2 23 3 34 4 05 0 5 +
0 1 12 2 03 3 34 4 45 0 5 +
1 1 12 2 23 0 34 4 05 5 0 +
1 1 12 2 03 0 34 4 45 0 5 +
1141 3151 6261 3851
Choose a number from a box and a number from a
loop to make the totals in a) and b).
2.35 2.25
3.61 7.65
a) b) c) d)
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C8
Page 27A
1) 14562 – 1251
2) 6652 – 716
3) 42160 – 39215
4) 2300 – 934
5) 475.83 – 81.6
6) 68.1 – 27.3
7) 24.75 – 0.098
8) 94.78 – 36
9) 3564 – 1971.6
10) 800 – 237.62
13311
5936
2945
1366
394.23
40.8
24.652
58.78
1592.4
562.38
=
=
=
=
=
=
=
=
=
=
Subtraction
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For Fun
Page 27B
C8
Complete the boxes and the circles:
2010
– 135
– 1962
– 750
– 1179
– 806.5
– 216.2
– 21.65
– 26.261
– 1002– 347
– 38.1
1875
26.35
0.0891658.8
48
453.5
81
1260
661
1008969.9
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C9
Page 28A
=
=
=
=
=
=
=
=
=
=
39
220
576
460
609
2736
1248
2980
2023
1017
1) 3 × 13
2) 55 × 4
3) 9 × 64
4) 92 × 5
5) 7 × 87
6) 342 × 8
7) 6 × 208
8) 745 × 4
9) 289 × 7
10) 113 × 9
Short Multiplication
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For Fun
Page 28B
C9
20 3×27
1) Here are some items available from a
local shop:
Work out the cost of:
a) 5 jackets
b) 6 MP3 players
c) 4 pairs of trainers
d) 7 televisons
Jacket: £17 Trainers: £56 MP3 player: £32 Television: £499
2) Work out what the must be.
a) b)
*5
72
×
answer:
£85£192£224£3493
9 180
20793
6
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C10
Page 29A
1) 786 ÷ 2
2) 465 ÷ 5
3) 448 ÷ 8
4) 552 ÷ 6
5) 801 ÷ 9
6) 5976 ÷ 8
7) 9080 ÷ 5
8) 17801 ÷ 7
9) 18054 ÷ 6
10) 374877 ÷ 9
393
93
56
92
89
747
1816
2543
3009
41653
=
=
=
=
=
=
=
=
=
=
Short Division
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For Fun
Page 29B
C10
1) Here are some items available from a local
shop:
Work out the unit price of each item knowingthat:
7 watches cost £336,
5 cameras cost £380,
4 camcorders cost £1260,
6 laptops cost £7794.
2) a) If 3 chairs cost £17.40,
how much would one of them cost?
£_____
b) If 7 shirts cost £34.93,
how much would one of them cost?
£_____
Watch: £ ____ Camera: £ ____ Camcorder: £ ____ Laptop: £ _______48 76 315 1299
5.80
4.99
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C11
Page 30A
=
=
=
=
=
=
=
=
=
=
4.8
19.5
168.3
18
57.4
8.34
73.6
33.4
25.34
227.7
1) 4 × 1.2
2) 6.5 × 3
3) 9 × 18.7
4) 3.6 × 5
5) 7 × 8.2
6) 6 × 1.39
7) 9.2 × 8
8) 8.35 × 4
9) 3.62 × 7
10) 25.3 × 9
Multiplication of Decimals
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunC11
Page 30B
1) Here are some items available from alocal shop:
Work out the cost of:
a) 7 lollies,
b) 3 bottles of milk,
c) 2 loaves of bread,
d) 5 boxes of chocolates.
Milk: £1.20 Bread: £0.65 Lollies: £0.30 Chocolates: £3.99
2)
£2.10£3.60£1.30£19.95
Rulers cost £0.25 each.Pens cost £0.45 each.Kelly buys 3 rulers and 5 pens.
Work out how much she pays.
£3.00
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C12
Page 31A
1) Which four coins make a total of 77p?
2) Six bars of metal each weigh 2.75 kg.How much do they weigh altogether?
3) At a party for 171 people, 9 guestssat at each table.How many tables were there?
4) Coke cans cost 43p each.How many cans you buy with £6?
5) Olivia went to a cafe.She ordered:
2 sausagesBaked beans3 coffee1 juice
She paid with a £5 note.Work out how much change she got.
19 tables
MenuFried eggs 30pBaked beans 45pSausages 38p
Coffee 65pTea 72pJuice 50p
50p 20p 5p 2p
16.5 kg
13 cans
£1.34 change
Problems Withouta Calculator
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C12
Page 31B
Just For Fun
21
1.59 m
£1.25
£8.37
A bus starts at Birmingham and makes three stopsbefore reaching London.At Birmingham, 37 people get on.At Rugby, 13 people get off and 6 get on.At Willen, 9 people get off and 15 get on.At Luton, 24 people get off and 8 get on.How many people are on the bus when itreaches London?
A mug and a plate together cost £2.90.The mug cost 40p more than the plate.
How much does the plate cost?
1)
2)
3)
4)
(I hope you remembered tocount the driver)
Cheese is on offer at £3.26 per kilogram.Emma buys half a kilogram.
How much change does she receive froma £10 note?
A man is 27 cm taller than his son, who is8 cm shorter than his mother. The man was born42 years ago and is 1.78 m tall.
How tall is his wife?
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C13
Page 32A
£30.94
18 teams
£19.06
£6.00
7 Mars Bars
1) There are 7 people in a team.How many teams can you make from131 people?
2) A motorist bought 26 litres of petrol at£1.19 per litre.a) How much did it cost?b) What change did he get from £50?
3) A museum trip is organised for 57members of a youth club. They go inminibuses that can each seat up to15 people.It costs £42.50 for each minibus and £172for the group to access the museum.How much will the trip cost per person?
4) Mars Bars cost 35p. Skittles cost 45p.Gillian bought 5 bags of Skittles andsome Mars Bars.She paid with a £5 note and received30p change.How many Mars Bars did she buy?
Problems With a Calculator
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
C13
Page 32B
Just For Fun
34 35 36
81
8
1.1
18
6625
1) Three consecutive integers have a sum of 105.What are they?
2) Using the brackets keys of your calculator,
work out the following.
a) 164 – (27 + 56) =
b) 44.8 ÷ (15.4 – 9.8) =
c) (19.8 – 3.3) ÷ (31.2 – 16.2) =
d) (8 × 14.4) ÷ (11.1 – 4.7) =
3) If you start with 16 and press the square root key ofyour calculator ( ) twice, the answer given is 2.
If you start with 81 and press the square root key ofyour calculator ( ) twice, the answer given is 3.
Complete the following sentences:a) If you start with 1296 and press the square root
key of your calculator twice,the answer given is_____ .
b) If you start with _____ and press the square rootkey of your calculator twice, the answer given is 5 .
16
16
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
A1
Page 33A
Multiply by 2 Add 3Input Output
3) a) If Simon puts 7 into the number machine, what numbercomes out?
b) If 100 goes in, what comes out?
c) If 5½ goes in, what comes out?
d) If 2.25 goes in, what comes out?
e) If 25 comes out, what number was put in?
f) If 8 comes out, what number was put in?
g) If x goes in, what comes out?
17203147.5
112.5
x × 2 + 3 or 2 × x + 3 or 2x + 3
preferred
60p
48p
55 copies
£125£510
6 days
2) It costs 4p per copy on the school photocopier.
a) How much would it cost to make 15 single-sidedcopies?
b) Jane has to make 6 copies of a documentwhich is double-sided (writing on both sides).
How much will it cost?
c) Ted copies a single-sided document but forgetshow many copies he has made.
Rather than counting them he simply looks atthe bill and works it out from there.
The bill was for £2.20.
How many copies had he made?
Single-sidedcopies
4p each
1) A vintage car hire firm charges £70 for the first day’shire followed by £55 per day for all other days.
a) How much would it cost to hire a car for 2 days?
b) How much would it cost to hire a car for 9 days?
c) When Sue hires a car it costs her £345.
How many days did she hire the car for?
Formulae Expressed in Words
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunA1
Page 33B
1) Choose any number.
Add three to it.
Multiply your result by two.
Add six to it.
Halve your answer.
Subtract your original number.
You should be left with six.Try to find out why you are always left with six.
Input Output
1 __
4 __
10 __
2.5 __
-3 __
__ 30
__ 48
__ -18
x __
Input Output
3 __
10 __
-4 __
__ or __ 54
x __
4) Copy the table on the right.
Use this function machine to complete thetable.
Multiply byitself
Add 5Input Output
xx + 3
2x + 6
2x + 12x + 6
6
Input Output
1 __
4 __
10 __
2.5 __
-3 __
__ 30
__ 48
__ -18
x __
2) 3)
2
14
38
8
-14
8
12.5
-4
4x – 2
-4
8
32
2
-20
9.5
14
-2.5
4(x – 2)
14
105
21
-7 7
x2 + 5
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
A2
Page 34A
Coordinates in First Quadrant
×
×
0 1 2 3 4 5 6 7 80
1
2
3
4
5
6
7
8
×
×
×
×
×
×
××
A
B
C
D
E
F
G
H
I
J
x
y1) Write down the
coordinates of thecrosses labelledA to J.
0 1 2 3 4 5 6 7 80
1
2
3
4
5
6
7
8
x
y
2) Put crosses at the followingpoints and label them with thecorrect letters.
A (3, 7)
B (8, 4)
C (2, 5)
D (6, 0)
E (2.5, 3)
F (0, 6.5)
G (5.5, 7.5)
H (8, 8)
A (1, 6)
B (3, 4)
C (7, 3)
D (5, 0)
E (6, 7)
F (8, 1.5)
G (0, 3)
H (2, 7.5)
I (4, 5.5)
J (1.5, 2.5)
××
×
×
×
××
×A
B
C
D
E
F
G H
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunA2
Page 34B
a) From (2, 3) you have to go 4 squares to theright and 2 squares up to get to the ostrich.
4 + 2 = 6
b) From (4, 6) it is 2 to the right and 1 down.
2 + 1 = 3
c) From (8, 8) it is 2 to the left and 3 down.
2 + 3 = 5
d) (6, 4) is 1 away.
e) The guess which would be furthestaway is (0, 0). It is 11 away.
0 1 2 3 4 5 6 7 80
1
2
3
4
5
6
7
8
x
y
×O
×
1)
×
×
×
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 35A
Making 3D Models
Tetrahedron
S6
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 35B
Making 3D Models
Cube
S6
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 35C
Making 3D Models
Octahedron
S6
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 35D
Making 3D Models
Shapes put together tomake a tetrahedron
S6
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
S7
Page 36A
Reflecting in Diagonal Lines
In all four questions, reflect the shadedshape in the dotted mirror line.
1)
3)
2)
4)
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 36B
Just For FunS7
Six Rangoli Patterns Placed Together
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 36C
Just For FunS7
Six Rangoli patterns put together for you to colour
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 36D
Just For FunS7
Six Rangoli patterns put together for you to colour
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 36E
Just For FunS7
Six Rangoli patterns put together for you to colour
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
S8
Page 37A
Translate the shape 5 squaresto the right and 2 squares up.
1) Translate the shape 3 squaresto the left and 2 squares down.
2)
Translate the shape with vector3) -43
Translate the shape with vector4) 4-5
Translation
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Page 37B
A
C
D
E
F
GB
HI
Just For FunS8
A with vector
B with vector
C with vector
D with vector
E with vector
F with vector
G with vector
H with vector
I with vector
03
-20
5-1
20
-1-3
4-2
-3-2
23
1-4
Use tracing paper and translate the following shapes.
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
S9
Page 38A
Rotate the shape 90° about thecross.
1) 2)
3) 4)
Rotate the shape 90° about thecross.
Rotate the shape 180° aboutthe cross.
Rotate the shape 90° clockwiseabout the cross.
Rotation
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunS9
Page 38B
1
2
AC
B
180°
a) Rotate triangle A 90° clockwise about cross 1.Label your new triangle B.
b) Rotate triangle B 90° clockwise about cross 2.Label your new triangle C.
c) How many degrees would you need to rotate triangle A toget to triangle C?
d) Mark with a cross the centre of rotation to get from A to C.
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
S10
Page 39A
Reading Scales
ml.50
100
150
A
B
1)
2)
Miles
Kilometres0
0 10 20 30
10 20 30 40 50
Use the scale to convert
a) 10 miles to km.
b) 40 km to miles.
c) 16 miles to km.
d) 8 km to miles.
3)
1.25 L
About 3.8 L
125 ml
85 ml
C
16 km25 milesabout 25.6 km5 miles
a) If water comes up to arrow A, howmuch will there be in thecontainer?
b) About how much water will therebe if it comes up to arrow B?
a) If milk comes up to arrow A, howmuch milk will there be in thecontainer?
b) How much milk will there be ifit comes up to arrow B?
c) Draw arrow C to show 140ml ofliquid.
0.5L1L1.5L2L2.5L3L3.5L4L
A
B
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunS10
Page 39B
You have a 3 pint jug and a 5 pint jug and asmuch water from a tap as you like.How can you use the two jugs to measure outexactly 4 pints of water?
1)
2)
A
B
C
Split the coins into threesets of three.
Put set A into one panand B into the other.
If they balance, the fakeis in C.
If A is heavier than Bthen the fake is in B.
If B is heaviest, thefake is in A.
Take the set of three coinswith the fake in it and putone coin in one pan andanother coin in the otherpan.
If they balance, the othercoin is the fake.
If they don’t balance, theone that goes up is thefake.
Fill the 5 pint jug and pour it intothe 3 pint jug. This leaves 2 pints inthe 5 pint jug.
Empty the 3 pint jug and pour the 2pints from the 5 pint jug into the 3pint jug.
Fill the five pint jug and pour intothe 3 pint jug until it is full.
This will leave you exactly 4 pints inthe 5 pint jug.
5 Pints 3 Pints
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
S11
Page 40A
Perimeters
1) Find the perimeter of thisrectangle on the cm grid.
2) Find the perimeter of thisshape on the cm grid.
3) Find the perimeter of thisshape on the cm grid.
4) Find the perimeter of thisshape on the cm grid.
P = 20cm P = 22cm
P = 26cm P = 20cm
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunS11
Page 40B
A
Perimeter = 16Area = 7 squares
There is more than one answer for some of the shapes.
Here are some possible answers.
Area of8cm2
Area of9cm2
Area of10cm2
Area of11cm2
Area of12cm2
Area of13cm2
Area of14cm2
Area of15cm2
Area of16cm2
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
S12
Page 41A
Areas
1) Find the area of the rectangleon this centimetre grid.
2) Find the area of the rectangleon this centimetre grid.
3) Find the area of the rectangleon this centimetre grid.
Area = 20cm2
Area = 34cm2
Area = 61.75cm2
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunS12
Page 41B
1) Draw three different-shapedrectangles with an area of 12cm2
on the centimetre grid.
2) Find the area of thesquare on thiscentimetre grid.
3) Find the area of thesquare on thiscentimetre grid.
This is a difficult question
Area = 18cm2
Area = 20cm2
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
D3
Page 42A
Discrete Data
Blue
Green
Red
Yellow
Tally Total1)
1234
Tally Total2)
56
7
9
11
3
712
6411
DogCatHamsterGoldfish
Tally Total3)
Snake
11101382
Colour
No. of children
Pets
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For Fun
Page 42B
D3
MANY YEARS AGO IN A FAR-OFF LAND THERE LIVED AN
OGRE OF HUGE PROPORTIONS.
HIS FAVOURITE OCCUPATION WAS TO CAPTURE POOR
PEASANTS AND MAKE THEM WORK FOR FREE ON HIS LAND.
HE WASN’T VERY NICE.
THE NAME OF THE OGRE WAS LANCE.
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
D4
Page 43A
1) Here are the Maths test marks for two mixedability Year 7 classes.
Complete the frequency table to show all the results.
Mark Tally Frequency
20 and under
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
over 70
43 16 68 49 31 24 83 61 55 40 72 44 45 23 48 33 2081 63 58 41 50 59 46 35 24 13 66 99 53 47 66 48 5133 35 40 64 50 31 37 42 35 54 97 24 33 48 53 42
3
4
11
14
7
6
5
Class interval Tally Frequency
14 s < 16
16 s < 18
18 s < 20
20 s < 22
<
<
<
<
3
6
8
4
2) A group of students measured their hand span (s) inin centimetres. Here are their results:
Complete the frequency table to show all the results.
14.720.016.721.618.217.918.1
19.019.916.014.419.121.816.4
17.915.918.019.116.521.118.9
Grouping Data
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunD4
Page 43B
Sally, the organiser of a slimming club, keeps data on howmuch weight (w), in kg, her 60 members have lost over theprevious twelve months.
She organises the data in a two-way table.
a) Complete the two-way table.
b) How many members of the club were women?
c) How many women lost between 5 and 10 kg?
d) How many men lost less than 20 kg?
e) How many men lost 5 kg or more?
f) How many men and women lost 15 kg or more?
Men Women Total
0 < w < 5 2 4 6
5 < w < 10 4 10 14
10 < w < 15 7 9 16
15 < w < 20 2 8 10
20 < w < 25 3 11 14
Total 18 42 60
4210
1516
24
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
D5
Page 44A
Mode, Medianand Range
Tim Sue Ben Tom Dev Ned Kim
1) a) In this group of seven people, which one hasthe median average height?
b) What are the names of the people who arebelow the median average height?
c) To find the range of the heights you wouldneed to measure the height of two people.Which two?
2) A class of students were asked how many petsthey own.
The answers were as follows:
1, 0, 1, 2, 1, 5, 2, 0, 1, 2, 3, 1, 4
2, 3, 1, 2, 2, 0, 1, 1, 2, 1, 3, 2
a) Find the median average number of pets per student.
b) Which number of pets is the mode?
c) What is the range of the answers?
3) Twenty children were asked what their favourite colour was.
Their answers were:
Blue, Red, Yellow, Red, Green, Red, Green, Blue, Red, Blue
Green, Blue, Red, Blue, Yellow, Red, Blue, Orange, Red, Red
a) Which colour is the modal average?
b) Why can’t we find the median colour?
Tom
Tim, Sue and Ben
Kim and Tim
2
1
5 (5 – 0)
Red
The median can only be usedwith numerical values.
© Mathswatch Ltd
Level 4
Answers
N5 N6 N7 N8 N9 N10 N11 N12 C7 C8 C9 C10 C11 C12 C13A1 A2 S6 S7 S8 S9 S10 S11 S12 D3 D4 D5
Just For FunD5
Page 44B
1) The heights of 18 plants, to the nearest cm, are as follows:
15, 19, 16, 12, 13, 15, 20, 18, 16, 14, 12, 18, 16, 16, 17, 15, 15, 15
a) Find the modal height of the plants.
b) Find the median height of the plants.
c) Find the range of the heights.
87815
2) You are told that the median score onthese four cards is 9.5
Work out what the number is on thebottom card.
9123) We have six cards with numbers on
them and we know the following:
the modal average is 3
the median average is 5
the range is 11
Work out the numbers on the other four cards.
Score Frequency
1 2
2 3
3 3
4 4
5 4
6 7
4) Sue rolls a dice 23 times and puts herscores into a table.
a) What is Sue’s modal score?
b) What is Sue’s median score?
c) What is the range of Sue’s scores?
15 cm
15.5 cm
8 cm
11
1 3 3 7
6
4
5
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
N13
Page 45A
1) 3.6 × 10
2) 82.9 × 100
3) 0.5 × 1000
4) 47 ÷ 10
5) 106.4 ÷ 10
6) 9.9 ÷ 100
7) 6.2 × 1000
8) 70 ÷ 1000
9) 0.035 × 10000
10) 0.01 ÷ 100
36
8290
500
4.7
10.64
0.099
6200
0.07
350
0.0001
=
=
=
=
=
=
=
=
=
=
Multiplication and Divisionby 10 and 100
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For Fun
Page 45B
N13
1)
2) Using the fact below:
365 × 17 = 6205
Work out the following
a) 36.5 × 17 = ____ d) 3650 × 1.7 = ____
b) 36.5 × 1.7 = ____ e) 62.05 ÷ 17 = ____
c) 365 × 170 = _____ f) 6.205 ÷ 36.5 = ____
1200
0.75
×100
×1000
÷10
÷100
÷100
7370
0.018
0.104
620.5
62.05
62050
6205
3.65
0.17
Fill in the missing box in each case.
a) f)
b) g)
c) h)
d) i)
e) j)
1)
12 540 5.4
7.5 0.6 0.006
83.1 8310 73.7
0.9 900 ×10 0.18
662 66.2 ×1000 104
×100
÷10
÷100
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
N14
Page 46A
Rounding
4.2
53.4
31.6
8.8
0.7
578.5
79.0
3443.8
27.0
100.0
2) Round the following numbers to 1 decimal place.
a) 4.21 f) 578.48
b) 53.43 g) 79.035
c) 31.59 h) 3443.77052
d) 8.827 i) 26.9999
e) 0.653 j) 99.961
1) Using a calculator, work out the following.Give your answers to the nearest 10.
a) 24 × 14
b) 383 × 43
c) 4088 ÷ 56
d) 265364 ÷ 326
e) (42000 + 768) ÷ 54
340 to the nearest 10
16470 to the nearest 10
70 to the nearest 10
810 to the nearest 10
790 to the nearest 10
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For Fun
Page 46B
N14
Round each of the numbers on the calculators to(i) 1 d.p.(ii) 2 d.p.(iii) the nearest whole number.
4.762181)
(i) ___
(ii) ___
(iii) ___
0.5239872)
(i) ___
(ii) ___
(iii) ___
4870.10553)
(i) ___
(ii) ___
(iii) ___
4)(i) ___
(ii) ___
(iii) ___
1.6371285)
(i) ___
(ii) ___
(iii) ___
17.490386
6)(i) ___
(ii) ___
(iii) ___
4.8
4.76
5
0.5
0.52
1
4870.1
4870.11
4870
19800.0
19799.99
19800
1.6
1.64
2
17.5
17.49
17
19799.992
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
N15
Page 47A
Ordering Negative Numbers
1) Work out the value of each card and then place the cards inorder from lowest to highest.
2) Work out the value of each card and then place the cards inorder from lowest to highest.
C-3
D-2
B-1
A4.5
J-£5
G-£4.50
E-£4
I-£2.75
F-£2
H-£1.50
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunN15
Page 47B
5 21)
2)
3)
4)
1 4
12 83 10
5 9-2 4
12 7-5 8
2 + 1 = 34 + 1 = 55 + 2 = 75 + 4 = 9
8 + 3 = 1110 + 3 = 1312 + 8 = 2012 + 10 = 22
4 + (-2) = 29 + (-2) = 75 + 4 = 99 + 5 = 14
7 + (-5) = 28 + (-5) = 312 + 7 = 1912 + 8 = 20
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
N16
Page 48A
123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456123456
123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012
123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012
123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678
123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234
123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012
123456123456123456123456123456123456
123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678123456789012345678
123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012
123456789012123456789012123456789012123456789012123456789012
123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234123456789012345678901234
1234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567123456789012345671234567890123456712345678901234567
Ordering Fractions
1)
34
56
23
712
1320
35
34
710
9 squares 10 squares 8 squares 7 squares
34
56
23
712
The correct answer
The working
2) 710
34
1320
35
The correct answer
The working
13 squares 12 squares 15 squares 14 squares
3) 712
58
1324
12
The correct answer
4) 13
25
310
16
The correct answer
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunN16
Page 48B
1730 2
5
4760
1524
38
712
129
20
23
715
34
13
Smallest
Largest
Place the fractions on thecards in order of size fromsmallest to largest.
13
40120
38
45120
25
48120
920
54120
715
56120
12
60120
1730
68120
712
70120
1524
75120
23
80120
34
90120
4760
94120
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
N17
Page 49A
Simplification of Fractions
1) Cancel each of these fractions to theirsimplest form:
a) b) c)
d) e) f)
26
510
312
216
927
2080
2) Cancel each of these fractions to theirsimplest form:
a) b) c)
d) e) f)
414
3070
1634
2442
2745
2836
3) Cancel down fully each of these fractions:
a) b) c)
d) e) f)
3355
7296
4590
13
=12
=14
=
18
=13
=14
=
27
=37
=817
=
47
=35
=79
=
35
=34
=12
=
34
=29
=1729
=75100
40180
68116
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunN17
Page 49B
Here are six number cards.
a) Choose two of these six cards
to make a fraction that is
equal to .
b) Choose two of these six cards
to make a fraction that is
equal to .
c) Choose three of these six cards
to make a fraction that is
equal to .
d) Choose three of these six cards
to make the smallest
possible fraction.
11
7
9
2 5 9 7 4 11
4599
112144
28175
5
4
2 5
2
9 11
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
N18
Page 50A
Shaded : Unshaded
1 3
1 2
1 5
5 7
1 1
1 11
2 4
0.5 2.5
0.2 1
9 15
a
b
c
d
e
f
g
h
i
j
b
3) Find the missing numbers inthese ratios:
a) 1 : 4 = 2 :
b) 1 : 5 = 6 :
c) 2 : 7 = 8 :
d) 5 : 4 = 15 :
e) 2 : 3 = : 12
f) 9 : 5 = : 35
g) 3 : = 18 : 30
c d
e f g
h i j
2) Write the following ratios intheir simplest form:
a) 8 : 12
b) 6 : 10
c) 15 : 10
d) 16 : 4
e) 18 : 16
f) 25 : 15
g) 45 : 15
h) 18 : 27
i) 24 : 30
j) 36 : 48
2 : 3
3 : 5
3 : 2
4 : 1
9 : 8
5 : 3
3 : 1
2 : 3
4 : 5
3 : 4
8
30
28
12
8
63
5
1)
Understanding Ratios
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunN18
Page 50B
A
1
2
3
4
5
6
7
B
A B
A B
BA
A B
BA
A B
= water= orangeWhich is orangier: A or B?
You must give convincingreasons for each of youranswers
A is 1:1, B is 1:3A is orangier.
A is 2:1, B is 3:2A is 6:3, B is 6:4A is orangier.
A is 1:3, B is 2:5A is 2:6, B is 2:5B is orangier.
A is 1:2, B is 2:4A is 1:2, B is 1:2They are both the same
A is 5:4, B is 3:2A is 15:12, B is 15:10B is orangier.
A is 2:3, B is 3:4A is 6:9, B is 6:8B is orangier.
A is 6:3, B is 4:2A is 2:1, B is 2:1They are the same.
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C14
Page 51A
1) 17 × 32
2) 24 × 62
3) 13 × 156
4) 1.5 × 22
5) 7.6 × 2.1
6) 4.5 × 9.99
7) 528 × 16
8) 19.7 × 6.3
9) 34 × 466
10) 0.35 × 0.12
=
=
=
=
=
=
=
=
=
=
544
1488
2028
33
15.96
44.955
8448
124.11
15844
0.042
Long Multiplication
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC14
Page 51B
2)
312£374.40
A school organises a trip to a museum.
They set off in 13 minibuses, each minibus containing24 pupils who will each pay to go into the museum.
Entrance to the museum costs £1.20 per person.
a) How many people made the trip?
b) What was the total cost?
1) Work out what the must be.*a) 3
2
1 6 2
11 5
27 0
1 3 5 00
×3
4800
6120
80
answer:
×b) 60
240
5166
2
47
3 39 0
3
×c)
384
41
9 0
25450
40
answer: 13775
×
00
d)
36 200500
5
900010059
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C15
Page 52A
24
19
17
14
3.6
0.31
23.5
0.21
25.4
383.25
Long Division
=
=
=
=
=
=
=
=
=
=
1) 288 ÷ 12
2) 285 ÷ 15
3) 425 ÷ 25
4) 784 ÷ 56
5) 79.2 ÷ 22
6) 5.89 ÷ 19
7) 893 ÷ 38
8) 9.87 ÷ 47
9) 330.2 ÷ 13
10) 35259 ÷ 92
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC15
Page 52B
1)
2)
a) If 48 luxurious pens cost £768,how much would one of them cost?
b) If 25 tee shirts cost £77.50,how much would one of them cost?
c) If 53 mobile phones cost £2 119.47,how much would one of them cost?
Cans of juice cost 24p each.
Wendy has £8.65 to spend.
a) What is the maximum number of cans Wendycan buy?
b) How much change does she get?
3) Find the missing digits.
a) b)
£16
£3.10
£39.99
36
£0.01 or 1p
3 6514 0 4 2 2 2
21
15
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C16
Page 53A
BODMAS
1) Work out the following:
a) 3 × 6 – 2
b) 7 + 2 × 3
c) 5 + 3 × 4 – 1
d) (7 + 1) × 3
e) 5 – 3 × 2
f) 9 – 35 ÷ 5
g) 3 × 2 + 7 + 5 × 4
h) 20 – 9 ÷ 3 + 1
i) 2 × (15 – 10) ÷ 5
j) 7 + 2 – 3 × 4
k) 10 ÷ (2 + 3)
l) 10 ÷ 5 – 8 ÷ 2
m) 7 × (5 – 2) + 10
n) 48 ÷ (2 + 3 × 2)
o) 4 × 12 ÷ 8 – 6
2) Work out the following:
a) 32 – 23
b) 25 – (3 – 1)2
c) 8 × 7 – 16
d) 36 ÷ 22 – 3 × 3
e) 53 – (3 × 15 – 25)
f) ((9 + 1) × 4) ÷ 2
3) Place brackets in thefollowing questions tomake the answers correct.
a) 3 × 5 – 1 = 12
b) 10 + 2 × 3 = 36
c) 7 × 5 – 2 × 2 = 42
d) 24 ÷ 6 – 2 = 6
e) 3 + 2 × 6 ÷ 10 = 3
f) 5 × 5 – 3 ÷ 4 + 1 = 2
4) If x = 3 and y = 7, work out the following:
a) 2x – y
b) 3y + x2
c) y2 – x2
d) (x + y)2 – x3
e) 5(y – x) + (y + x) ÷ 2
f) 10xy – (2y – x)2
= 16
= 13
= 16
= 24
= -1
= 2
= 33
= 18
= 2
= -3
= 2
= -2
= 31
= 6
= 0
= 1
= 21
= 52
= 0
= 112
= 20
( )
( )
( )
( )
( )
( ) ( )
= -1
= 30
= 40
= 73
= 25
= 89
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC16
Page 53B
2) Use four 4s plus the operations +, –, ×, ÷ to make thenumbers 0 to 9.
All four 4s must be used. 4s cannot be put together as in 44.
Signs can be used as many times as you like. Brackets canbe used.
A possible answer for 0 could be 4 ÷ 4 – 4 ÷ 4
0 = 4 + 4 – 4 – 4 5 = (4 × 4 + 4) ÷ 4
1 = (4 + 4) ÷ (4 + 4) 6 = (4 + 4) ÷ 4 + 4
2 = 4 ÷ 4 + 4 ÷ 4 7 = (4 + 4) – (4 ÷ 4)
3 = (4 + 4 + 4) ÷ 4 8 = 4 × 4 – 4 – 4
4 = (4 – 4) × 4 + 4 9 = (4 + 4) + (4 ÷ 4)
These are just examples ofhow to get the answers.You may well havedifferent correct answers.
1) Use the numbers 6, 3, 2 and 1 plus the operations +, –, ×, ÷to make the numbers 0 to 9.
The numbers must be used in the specified order (6, 3, 2, 1).
They cannot be put together as in 63 for example.
Signs can be used as many times as you like. Brackets canalso be used.
0 = 6 – 3 – 2 – 1 5 = 6 ÷ 3 + 2 + 1
1 = 6 – 3 × 2 + 1 6 = 6 + 3 – 2 – 1
2 = 6 – 3 – 2 + 1 7 = 6 + 3 ÷ 2 + 1
3 = 6 + 3 ÷ 2 + 1 8 = 6 + 3 – 2 + 1
4 = 6 – 3 + 2 – 1 9 = 6 – 3 × 2 + 1
( ) ( )
( )
( ) ( )
These are just examples ofhow to get the answers.You may well havedifferent correct answers.
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C17
Page 54A
1) Find the following:
a) 13
of 24 b) 23
of 24
c) 15
of 30 d) 35
of 30
e) 18
of 40 f) 58
of 40
2) Work out:
a) 710
of £30 b) 37
of £84
c) 45
of £1.50 d) 1120
of £19
e) 29
of £10.98 f) 813
of £31.85
3) Julie has £4.50 pocket money every week.
If she spends of it on a magazine and ofit on a dance lesson, how much of the pocketmoney does she have left?
25
13
4) Paul has £7.80 pocket money each week.
He always saves of it.
With the remaining money he spends oncomics and the rest on sweets.
(i) How much does he save?
(ii) How much is spent on comics?
(iii) How much does he spend on sweets?
58
13
= 8
= 6
= 5
= 16
= 18
= 25
= £21
= £1.20
= £2.44
= £36
= £10.45
= £19.60
£1.20
£2.60
£3.25
£1.95
Fraction of an Amount
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC17
Page 54B
12
a)1) of 23( )of 60
34
b) of 12( )of 80
12
c) of 49
of 42of 34
2) If 34
a) of a number is 60, what is the number?
If 37
b) of a number is 21, what is the number?
If 49
c) of a number is 12.3, what is the number?
3) If 12
of 15
of a number is 6, what is the number?
4) If 12
of 13
of 14
of 15
of a number is 2.5, what is the number?
5) If 35
of 12
of 23
of a number is 3.8, what is the number?
= 20
= 30
= 7
80
49
27.675
60
300
19
Find
Find
Find
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C18
Page 55A
Directed Numbers
1) The temperature is 3°C at midnightand then falls 8 degrees by 6 a.m.
What is the temperature at 6 a.m?
2) Tim has only £8 in his bank accountbut writes a cheque for £15.
If the cheque is cashed, how muchwill Tim have in his account?
3) Sue owes £7 to one friend and £6 toanother friend.
She writes this in her diary as (-7) + (-6)
a) How much does she owe altogether?
b) What is (-7) + (-6)?
4) Sue still owes £7 to one friend and £6to another friend but her motherdecides to take away the £6 debt bypaying it off.
Sue writes this as (-7) + (-6) – (-6)
a) How much does Sue owe now?
b) What is (-7) + (-6) – (-6)?
5) Work out the answers to
a) 6 – 14
b) 2 – 12
c) -1 – 6
d) -3 – 5
e) -7 – 15
6) Work out the answers to
a) 2 – (-3)
b) 6 – (-5)
c) -3 – (-6)
d) -7 – (-2)
e) -20 – (-18)
7) Work out the answers to
a) 5 + (-2)
b) 8 + (-6)
c) 3 + (-8)
d) -4 + (-3)
e) -8 + (-4)
-5°C
-£7
£13-13
£7
-7
-8
-10
-7
-8
-22
5
11
3
-5
-2
3
2
-5
-7
-12
-1 0 1 2 3 4 5 6 7 8-2-3-4-5-6-7-8
8) Work out the answers to
a) 4 – (+1)
b) 7 – (+5)
c) 1 – (+3)
d) -6 – (+1)
e) -1 – (+6)
3
2
-2
-7
-7
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC18
Page 55B
1) Each magic square below has a magic number writtenabove it.
You must fill in the blank squares so that the rows,columns and diagonals add up to the magic number.
10-1 3
48 0
-25 9
12 12
515 -5
9-2 8
3-8 -22
-9-23 5
-214 -10
Magic Number is
12Magic Number is
15Magic Number is
-27
2) Work out which numbers should go in the squares tomake the sums correct.
a) 7 + = 9
b) 7 + = 5
c) 2 – = -6
d) 4 – = 7
e) -5 – = 4
f) + 6 = 4
g) – 9 = -12
h) – 14 = -30
a) b) c)
2
-2
8
-3
-9
-2
-3
-16
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C19
Page 56A
Ratio Questionsin Context
1) Share out £20 between Bill and Suein the ratio 3 : 2.
2) Divide £60 between Jack and Jillin the ratio 7 : 3.
3) Debbie and Dave share 200 Smartiesin the ratio 1 : 4. How many Smartiesdo they each get?
4) Alec, Tony and Sara share £720 inthe ratio 1 : 2 : 3. How much do theyeach get?
5) If Dave and Sue share £30 in theratio 2 : 3, how much more thanDave does Sue get?
6) Divide £12 between Mick andSharon in the ratio 5 : 3.
7) Pete and Sandra work part-time in arestaurant. They share the tips in theratio 3 : 5.If Pete gets £30 at the end of theweek, how much will Sandra get?
8) Vicky and John share some sweetsin the ratio 2 : 7.If Vicky ends up with 12 sweets, howmany will John have?
9) Len makes some concrete bymixing cement, sand and gravel in theratio 1 : 4 : 3.If he uses 8 bags of sand, how manybags of cement and gravel will he use?
10) An old television has a width and heightin the ratio 4 : 3. If the width is 48 cm,what is the height?
Bill gets £12, Suegets £8
Jack gets £42, Jillgets £18
Debbie gets 40,Dave gets 160
Alec £120, Tony £240Sara £360
£6 more
Mick £7.50,Sharon £4.50
£50
42 sweets
2 of cement and 6 of gravel
36 cm
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC19
Page 56B
1) Which one of these regularpolygons has the number ofdiagonals and the number ofsides in the ratio 2 : 1?
A B C D
2) Two numbers are in the ratio 7 : 3.If you take one of the numbers away from theother one you get an answer of 24.What are the two numbers?
3) In a class of 30 pupils the ratio of boys to girlsis 2 : 3.If 6 girls (but no boys) join the class what isthe new ratio of boys to girls?
C Heptagon has 14diagonals and 7 sides.
42 and 18
1 : 2
4) Sue, Ted and Ben all have theirbirthday on the 1st January.
In 2010, Sue, Ted and Ben haveages in the ratio 2 : 3 : 4.
a) If Ted is 15 years old, how oldare Sue and Ben?
b) When Sue, Ted and Ben are allfive years older, what will be theratio of their ages? Write theanswer in its simplest form.
c) In which year was the ratio ofSue, Ted and Ben’s age 1 : 2 : 3?
d) How old was Ben when the ratioof the three ages was 1 : 3 : 5?
e) On what date was the ratio ofSue and Ben’s age 1 : 41?
Sue is 10,Ben is 20
3 : 4 : 5
2005
12.5
1st April 2000
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C20
Page 57A
Direct Proportion
1) 4 litres of orange juice cost £3.20.
a) What is the cost of 8 litres?
b) How much would 20 litres cost?
c) How much would you pay for 6 litres?
d) What is the cost of 5 litres?
2) 15 voice minutes cost 45p.
What is the cost ofa) 30 voice minutes?
b) 150 voice minutes?
3) If £1 is worth 1.12 euros, how many euroswould you get for £150?
4) Use direct proportion to solve the followingproblems:
a) 5 litres of water cost £3.00.How much would 9 litres cost?
b) A recipe for two people uses 90 g of flour.How much flour is needed for 5 people?
c) 20 blank CD-Roms cost £3.20.How much do 75 CD-Roms cost?
d) A litre of water costs 62p.What is the cost of 2.5 litres of water?
e) 3 kg of cheese costs £7.50What is the cost of 6.5 kg of cheese?
f) 2 litres of smoothie contains 900 ml oforange juice.How much orange juice is in 8.5 litres ofsmoothie?
g) A 120 ml carton of yoghurt contains12 g of sugar.How much sugar would be in a 200 mlcarton of yoghurt?
£6.40
£16£4.80
£4
90p
£4.50
168 euros
£5.40
225 g
£12
£1.55
£16.25
3.825 litres
20 g
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC20
Page 57B
Miles Kilometres
5 8
10 16
15 24
20 32
50 80
1)a) Use direct proportion to complete
this conversion table.
b) The distance between London andBirmingham is 120 miles.Use the table to work out thisdistance in kilometres.
c) The distance between London andParis is 460 kilometres.Use the table to work out thisdistance in miles.
3) A jar has 200 sleeping flies in it and the lid is firmly on.
The weight of the jar, when empty is 1 kg.
The weight of the jar and sleeping flies is 1.9 kg (1900 g).
a) If all the flies are the same weight, what is the weightof one fly?
b) Tina shakes the jar so that all the flies are now awakeand flying around.What will the weight of the jar of flies be, now?
2) Here are three offers for voice minutes on a mobile phone.
In which of the offers are the numbers in direct proportion?In each case, explain your answer.
Minutes Cost
1 £0.04
5 £0.20
40 £1.60
A
Minutes Cost
2 £0.24
10 £1.00
100 £7.00
B
Minutes Cost
10 £0.70
50 £3.50
60 £4.20
C
A and C are in direct proportion.
For A the cost of 1 minute is 4p. 5minutes is 5 x 4p = 20p40 minutes is 40 x 4p = £1.60
For C the cost of 1 minute is 7p.50 minutes is 50 x 7p = £3.5060 minutes is 60 x 7p = £4.20
4.5 g
Still 1.9 kgTo stay in the air, each fly must flap its wings whichcreates a downthrust equal in size to its weight.
192 km
287.5 miles
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
C21
Page 58A
Real Life Tables
London
195300
330
Nottingham100
159
Manchester
56 Liverpool
All distances are in miles.
1)
a) Write down the distance between London and Nottingham.
b) Write down the names of the two cities which are(i) The furthest apart.
(ii) The least distance apart.
c) Peter travels from London to Manchester where he collects a parcel.He then delivers the Parcel in Nottingham before returning to London.Work out the total distance travelled by Peter.
Stockport 05:26 06:16 06:55 07:15 07:55
Stoke 05:55 06:45 07:24 - -
Stafford 06:12 - 07:41 - 08:41
Euston 08:09 08:26 - 09:11 10:06
2) Here is part of a railway timetable
a) Rosie wants to travel from Stockport to Euston. She mustarrive in Euston before 09:00.
(i) What is the latest time she could depart from Stockport?
(ii) How long will her journey last?
b) James gets to Stockport station at 07:00.How long will he have to wait for the next train to Stafford?
c) Alex travels to Euston.She gets on the 07:24 train from Stoke.How long will her journey take?
195 miles
London and LiverpoolManchester and Liverpool
595 miles
06:162 hours and 10 minutes
55 minutes
2 hours and 42 minutes
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunC21
Page 58B
1)
Emma lives in Doncaster.She has to drive to Peterborough to pick up her friend, David, and then continue on toLondon to attend a graduation ceremony which begins at 11 am.The ceremony will last two hours and she will then return to Doncaster with David.
a) How far does Emma travel in order to get to London with David?
b) If Emma averages 50 mph on the return trip, at what time would she be backin Doncaster?
Stevenage48
165
Peterborough
130 Doncaster
All distances are in miles.
210 170 45 York
London
2275
195
235
Chester
Wrexham16 minutes
Gobowen35 minutes
Shrewsbury55 minutes
Welshpool76 minutes
Wellington69 minutes
Newtown90 minutes
Telford75 minutes
Wolverhampton90 minutes
2) The train route diagram show the times it takesto travel from Chester to other major stationson the line.
Use the information in the diagram to completethe following
timetables.
Wolverhampton 16:42
Wellington
Shrewsbury
Gobowen
Wrexham
Chester
Telford
Chester 04:22
Gobowen
Shrewsbury
Welshpool
Newtown
Wrexham
205 miles
4.54 pm
16:57
17:03
17:17
17:37
17:56
18:12
04:38
04:57
05:17
05:38
05:52
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
A3
Page 59A
Algebraic Expressions
1) Write down the expression you will have ifyou think of a number (let x be the number)and then:
a) add three to it
b) double it
c) multiply it by three and then subtract four
d) multiply it by itself
e) divide it by two
f) divide it by two and then add one
g) add three to it and multiply the resultby two
h) multiply it by five, add four, divide theresult by two
2) Say what the following expressionsmean in words.
a) x + 6
b) x – 7
c) 8x
d) 4x + 2
e)
f) 6(x + 7)
g) 4(3x – 1)
x5
3) If s = 2v, work out the value of swhen v = 7
4) If y = 3t + 4, work out the value of ywhen t = 5
5) If g = 2t – 1, work out the value ofg when t = 9
6) If f = 2(t + 8) and t = 3, find thevalue of f
7) If d = 3(2e – 3) and e = 5, findthe value of d
8) If c = 4 and d = 3, find thevalue of:
a) 2c
b) 2c – d
c) cd
d) 5c + 2d
e) 10cd
f) 2(c + d)
g) 5(3c – 2d)
What expression do I have ifI think of a number, double itand then add three?
Answer: 2x + 3
Say what the expression 4x + 17means in words.
Answer: Take a number, multiplyit by four and then add seventeen.
x + 3
2x
3x – 4
x2 x
2+ 1
2(x + 3)
5x + 42
Take a number and add six to it
Take a number andsubtract seven
Take a number andmultiply it by eight
Take a number, multiply it byfour and then add 2
Take a number and divide it by five
Take a number, add seven toit and multiply the result by six
Take a number, multiply it bythree, subtract 1 and thenmultiply the result by four
s = 14
y = 19
g = 17
f = 22
d = 21
8
5
12
26
120
14
30
x × x or x2
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunA3
Page 59B
The body mass index (BMI) is a measure used to show if an adult isat a healthy weight. It doesn’t apply to children, only adults.
Here is a formula for calculating BMI
A person with BMI between 18.5 and 25 is at a healthy weight.
A person with BMI less than 18.5 is underweight.
A person with BMI between 25 and 30 is overweight.
A person with BMI over 30 is obese.
BMI = (weight in kg) ÷ (height in m) ÷ (height in m)
1.82m57kg
BMI 17Underweight
1.62m74kg
BMI 28Overweight
1.74m70kg
BMI 23Healthy
1.62m55kg
BMI 21Healthy
No, she has a BMI of 16.7 and is underweight
Here are the heights and weights of the four people above.They are in no particular order.
a) Work out the BMI for each height and weight and put them in the table.Give your answers to the nearest whole number.
b) Match each height, weight and BMI with the correct person.
c) For each person, decide whether he/she is underweight, healthy,overweight or obese - write the answer next to each person.
d) A woman is 1.65 m tall and weighs 45.6 kg.She worries that she is overweight.Is she right?
Height (m) 1.74 1.82 1.62 1.62
Weight (kg) 70 57 55 74
BMI 23 17 21 28
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
A4
Page 60A
1) Write down thecoordinates of thecrosses labelledA to J.
B
E
H
AF
J
I
C
D
×
×
×
× ×
×
××
×10-1-2-3-4-5-6 2 3 4 5 6
1
-1
-2
-3
-4
-5
-6
2
3
4
5
6
x
y
×
G
2) Put crosses at the followingpoints and label them with thecorrect letters.
A (-5, 3)
B (2, -4)
C (-2, -6)
D (5.5, 3)
E (0, 0)
F (-3, 0)
G (-6, -5)
H (0, -5)
A (2, 5)
B (-4, 2)
C (-2, -5)
D (6, -4)
E (3, -2)
F (-2.5, 5)
G (-5, 0)
H (0, -3)
I (4, 1)
J (-4.5, -3.5)
10-1-2-3-4-5-6 2 3 4 5 6
1
-1
-2
-3
-4
-5
-6
2
3
4
5
6
x
y
××
× ×
×
×
×
×
G
F E
D
C
B
A
H
Coordinates in FourQuadrants
y
y
x
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunA4
Page 60B
10-1-2-3-4-5-6 2 3 4 5 6
1
-1
-2
-3
-4
-5
-6
2
3
4
5
6
x
y
×
×
×
×
×
×
y = 2x + 1
(2, 5)
(1, 3)
(0, 1)
(-1, -1)
(-2, -3)
(-3, -5)
2) Plot the following points on thegrid, draw a line through thepoints and try and work out thename of the line.
a) y = x (because y always equals x)
b) y = ½x (because the y coordinateis always half the xcoordinate)
c) y = 2x – 3 (multiply the xcoordinate by 2 andthen take away 3 andyou always get the ycoordinate)
d) x = 5 (because x always equals 5on this line)
WEARCLEAN
POTOOOOOOOO
O _ E R _ T _ O _ XMASCARA
must get heremust get heremust get here
HOROBODDR doo
(a)(b) (c) (d)
(e) (f)
(g)
Clean underwear
Potatoes(POT followed by 8 O’s) Dr Doolittle
Robin Hood(Rob in Hood)
Painless operation
P A I N
Kiss and make up
The three musketeers
y = x
y = ½x
y = 2x – 3 x = 5
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
A5
Page 61A
Horizontal & Vertical Lines
-8 -7 -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6 7 8
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
x
y
1) Draw the following lines on theaxes to the right:
a) x = 3
b) x = -4
c) y = 1
d) x = 7.5
e) y = -3
f) y = 4.5
-8 -7 -6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6 7 8
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
x
y
2) Name all the lines drawn on theaxes on the left.
Line a is: ______________
Line b is: ______________
Line c is: ______________
Line d is: ______________
Line e is: ______________
Line f is: ______________
a
bc
d
e
f
x = 3x = -4 x = 7.5
y = 1
y = -3
y = 4.5
y = -1
x = 2
x = -8
y = 5
y = 6.5
x = -2.5
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunA5
Page 61B
O 1 2 3 4 5 6 7 8 9 10 11 12
1
2
3
4
5
6
7
8
9
10
11
12
x
y
1) (i) Plot the points(0, 1)(1, 2)(2, 3)(3, 4)(4, 5)(5, 6)
(ii) Draw a line throughthese coordinates.
(iii) Name the line.
2) (i) Plot the points(0, 0)(1, 2)(2, 4)(3, 6)(4, 8)(5, 10)
(ii) Draw a line throughthese coordinates.
(iii) Name the line.
3) (i) Plot the points(0, 1)(1, 3)(2, 5)(3, 7)(4, 9)(5, 11)
(ii) Draw a line throughthese coordinates.
(iii) Name the line.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
y = x + 1 y = 2x y = 2x + 1
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
A6
Page 62A
Function Machines
1) Find the output for each of these function machines.
× 53a)
+ 57b)
× 2 – 36c)
+ 5 ÷ 313d)
÷ 2 – 710e)
– 4 × 2.57f)
2) Find the input for each of these function machines.
– 5 8a)
÷ 4 25b)
× 2 – 1 19c)
÷ 5 + 8 18d)
– 7 ÷ 2 3.5e)
× 19 – 4 -4f)
9
6
-2
7.5
15
12
13
100
10
50
14
0
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunA6
Page 62B
x
× 2– 7
× 5
– 7
– 2 10x - - - - - -
÷ 2– 5
- - -
- - -
- - -
x5 + 6
× 3
+ 1
× 2- - -
- - - - - + 3
- - -
- - -
4x + 1
- - - - - - - - - -
5x – 7- - - - - - - - - -
- - - - - - - - - -
- - - - - - - - - -
Complete the diagram below. Every time you see dashes like thisyou need to write the correct number or expression.
One of them (5x – 7) has already been done for you.
- - - - - - - - - -,
2xx – 7
x2
– 5
3x + 1
2x
– 2
× 4
+ 1
× 10
÷ 5
+ 6
+ 3
- - - - - - - - - -,
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S13
Page 63A
a) b)c) d)
e) f) g)
h)
Rotationalsymmetryorder 4
4 lines ofsymmetry
Rotationalsymmetryorder 2
2 lines ofsymmetry
Rotationalsymmetryorder 2
2 lines ofsymmetry
Rotationalsymmetryorder 2
0 lines ofsymmetry
Rotationalsymmetryorder 2
0 lines ofsymmetry
No rotationalsymmetry
1 line ofsymmetry
Rotationalsymmetryorder 3
3 lines ofsymmetry
No rotationalsymmetry
1 line ofsymmetry
1) For figures a to h, work out
i) The order of rotational symmetry.
ii) How many lines of symmetry it has.
2) Shade in six more triangles sothat this figure has rotationalsymmetry order 3
Symmetries of 2D Shapes
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunS13
Page 63B
a) Shade in one squareso that this shape hasrotational symmetry oforder 2.
1)
CHLOEBAXTER
3) Seven
b) Shade in a differentsquare so that thisshape has rotationalsymmetry of order 2.
CHLOEBAXTER
upside down in the mirror
B, X, E, C, H, O, E can all be read the same
2) Shade three more squaresso that the grid has rotationalsymmetry of order 4.
These are thetwo differentanswers
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S14
Page 64A
Measuring and Drawing Angles
a
e fg
d
c
b
1) Each of the angles below can be described as an acuteangle, an obtuse angle, a reflex angle or a right angle.
Decide which each of them are.
2) a) Draw a triangle which has three acute angles.
b) Draw a triangle which has one obtuse angleand two acute angles.
c) Draw a quadrilateral (4-sided shape) whichhas one reflex angle and three acute angles.
d) Draw a quadrilateral which has one rightangle, one acute angle and two obtuse angles.
e) Draw a quadrilateral which has two obtuseangles and two acute angles.
Obtuseangle Acute
angle
Reflex angle
Rightangle Obtuse Acute
Reflex
this isjust oneexample
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S14
Page 64B
a
b
c
d
e
65°
160°
38° 112°
39°
Use a protractor to measure theangles below.
Measuring and Drawing Angles
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S14
Page 64C
a
c
d
e
Use a protractor to measure theangles below.
b310° 245°
324°
248°
294°
Measuring and Drawing Angles
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S14
Page 64D
Draw the angle where you see the dot.Here is an example:
40° 40°
70°a) 135°b)
28°c)
171°d)
Measuring and Drawing Angles
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S14
Page 64E
340°a) 305°b)
245°c)
193°d)
Draw the angle where you see the dot.
Measuring and Drawing Angles
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunS14
Page 64F
a) Measure, very carefully, angles A, B and C.
b) Add the angles together.
c) What do they add up to?
d) Tear or cut along the wavy lines.
e) Fit the angles together to form a straight line.
1)
a) Draw some more triangles.Don’t forget ones like these
b) For each triangle, label the angles A, B and C.It doesn’t matter which is which.
Fill in the table below.
2)
Triangle 1
Angle A Angle B Angle CAll three anglesadded together
Triangle 2
Triangle 3
Triangle 4
123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234123456789012345678901234567890121234
123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345123456789012345678901234567890121234567890123456789012345
1234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901123456789012345678901234567890112345678901234567890123456789011234567890123456789012345678901
Tear or cut here
A
B C
75°72° 33°
180°
180°
180°
180°
180°
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S15
Page 65A
Angle Facts
50°35°
a
42° b
c
65°
70°
70°80°
85°
d
55°
e
120°
58°f
g
h
95°138°
45°
125°
65°
58°
122°122°
1) Work out the size of angles a to h.
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunS15
Page 65B
C
68°
a 34°
b
123°c
68°
68 + 68 = 136180 – 136 = 44
= 44°
180 – 34 = 146146 ÷ 2 = 73
73°= 73°180 – 123 = 57
57°
57°
= 66°180 – 57 – 57 = 66
110°
xA
D
E70°
70°
40°
40°
= 30°
This becomes easier if you turn the rhombus so thatyou can see the diamond shape easily.Put dashes on all the equal sides.
1)
2)
Angle x
B
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
S16
Page 66A
Areas of Rectangles
1) Find the areas of the following four rectangles.
9 cm
4 cm
5 m
3 m
9.6 cm
2.8 cm
12 m
3.5 m
a) b)
c)
d)
2) Find the lengths of the missing sides.
Area = 24 cm26 cm
?
Area = 96 cm2
12 cm
?Area =
253.44 cm2
13.2 cm
?
Area = 36 cm2
Area = 15 m2
Area = 26.88 cm2
Area = 42 m2
4 cm
8 cm 19.2 cm
b)a) c)
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunS16
Page 66B
123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890123456789012345678901234567890121234567890123456789012345678901212345678901234567890
10 cm
14 cm
8 cm
6 cm
1) Find the area of the shaded section.
2) Find the area of the shape below.
15 cm
6 cm
10 cm
7 cm
Area of largerectangle = 140 cm2
Area of smallrectangle = 48 cm2
Area of shadedsection = 92 cm2
3 cmArea of thisrectangle = 45 cm2
Area of thisrectangle =
42 cm2
Area of theshape = 87 cm2
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
D6
Page 67A
1) Estimate a probability (decimal) to go with these:
a) You will be on time for school on the nextschool day.
b) It will snow sometime this week.
c) Your teacher will smile at least once tomorrow.
d) You will have a disagreement with one of your friends.
e) England will win the World Cup in 2018.
f) England or France will win the World Cup in 2018.
2) Work out an exact probability (as a fraction)for these events:
a) If you flip a coin you will get a ‘head’.
b) If you flip two coins you will get two ‘heads’.
c) If you roll a dice you will get a 6.
d) If you roll two dice you will get two 6’s.
e) If you flip a coin and roll a dice you will geta ‘head’ and a 6.
f) If you flip three coins you will get three ‘heads’.
g) If you flip three coins you will get two ‘heads’and a tail in any order.
h) If you flip three coins you will get at leastone ‘head’.
i) If you roll two dice and add the scorestogether you will get a total of 4.
Your teacher will need tocheck this answer.
This depends on what monthit is and where you live.
It might be better not to showyour teacher this answer.
Only you and yourfriends can check this.
This is your opinion.
To be correct, this answermust be bigger than theanswer to question e).
12
14
16
112
18
38
78
336
136
Probability
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunD6
Page 67B
1 2 3 4 5 6 7 8 9 10 11 12
1 2 3 4 5 6 7 8 9 10 11 12
R I V E R
The key to winning this game is to realise that not all totalscores are equally likely.
A total of 1 will never happen, of course.
The probabilities for each total are as follows:
1 0
2 136
3 236
4 336
5 436
6 536
7 636
8 536
9 436
10 336
11 236
12 136
Score
ProbabilityScore
Probability
This would be a very good line-upfor the horses.There are other similar ones whichare just as good.
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
D7
Page 68A
The Mean Average
1) a) Move blocks around so thatthe heights of the five towersare the same.
b) What is the mean averagenumber of blocks in eachtower?
2) a) Move blocks around so thatthe heights of the five towersare the same (you may haveto cut some blocks).
b) What is the mean averagenumber of blocks in eachtower?
3) In a spelling test, the results for the class (out of 10) are:
3, 6, 8, 8, 4, 1, 7, 6, 2, 9, 3, 8, 4, 1, 1, 3, 5 and 2
a) Work out the mean average score for the class.
b) How many children had a score below the mean average?
4) Two Year 6 classes had a ‘times table test’ which wasmarked out of 20.
The marks in David’s class were:
14, 12, 19, 20, 20, 15, 14, 12, 13, 3, 18, 19, 16, 14, 12, 6
Harry was in the other class and the marks were:
9, 12, 17, 17, 16, 14, 18, 20, 8, 13, 16, 14, 18, 8
Use the mean average to work out which class didbetter in the test.
43.5
Mean average for David’s class: 14.1875Mean average for Harry’s class: 14.28571Harry’s class did best.
4.5
10
© Mathswatch Ltd
Level 5
Answers
N13 N14 N15 N16 N17 N18 C14 C15 C16 C17 C18 C19 C20 C21A3 A4 A5 A6 S13 S14 S15 S16 D6 D7
Just For FunD7
Page 68B
878
52
1) If the mean average number on thesefive cards is 6, what is the number on thebottom card?
2) If the mean average number on theseeight cards is 4.25, what is the numberon the bottom card?
845
26
4
7 3
3) John rolled a dice thirty times andput the results into this table.
Work out his mean average score.
Score Frequency
1 4
2 3
3 5
4 6
5 4
6 8
4) What is the mean averagenumber of arms per personin Britain?
5) Can you find out the meannumber of children perfamily in the UK?
8
3
3.9
1.999....Very close to 2 butdefinitely not quite 2
Widely reportedas 1.8
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
N19
Page 69
Fraction Decimal Percentage
50%
40%
0.25
0.7
11013
Fraction Decimal Percentage
35%
5%
0.6
0.6
68100
1350
1) Complete the tables.
a) b)
2) Put these fractions, decimals and percentagesin order, smallest to largest.
a) , 49%, , 0.55
b) 27%, 0.2, ,
c) , 95%, 0.99,
d) , 0.6, , 30%
e) 0.125, 10%, , 0.09
12
3514
310
910
97100
13
23
11100
3) Chris says that is halfway between 0.5 and 100%.
Is Chris correct? You must explain your answer.
34
4) Emily says that 0.2 is halfway between 10% and .
Is Emily correct? You must explain your answer.
35
0.5
0.1
0.3
0.4
25%
10%
33.3%
70%
1214
71025
60%
66.6%
68%
26%
0.05
0.26
0.68
0.35
23120
72035
49%12 0.55
35
0.214 27%
310
0.9997
10095%9
10
30% 0.623
13
0.0911
10010% 0.125
Yes. 0.5 is and 100% is and is halfway between them.24
44
34
No. 10% is 0.1 and is 0.6 and 0.2 is not halfway between them.35
Fractions, Decimalsand Percentages
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 70
N20Improper Fractions and
Mixed Numbers
54
127
165
83
209
4712
307
253
758
1009
2) Convert the following mixed numbers to improper fractions.
a) f)
b) g)
c) h)
d) i)
e) j)
35
23
27
14
35
311
58
19
45
34
1
2
5
3
11
10
7
9
6
12
3) Put these numbers in order, lowest to highest.
a) 3.5, 3 ,
b) 7 , 7.14,
c) 1 , 98%, , 1
15
113
14
345
54
110
141
232
571
292
153
138
274
389
11123
1911
85
94
173
185
797
919
618
495
6911
514
3 3.515
113
345
7.14 7 14
98% 1 1 110
54
1) Convert the following improper fractions to mixed numbers.
a) f)
b) g)
c) h)
d) i)
e) j)
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 71
N21Prime Numbers,HCF and LCM
1) Split up the following numbers into the product of their prime factors.
a) 12 d) 120
b) 45 e) 550
c) 72 f) 1296
2) Find the Highest Common Factor (HCF) of the following numbers.
a) 4 and 6 d) 300 and 525
b) 8 and 16 e) 374 and 918
c) 36 and 48 f) 45, 90 and 105
3) Find the Lowest Common Multiple (LCM) of the following numbers.
a) 8 and 12 d) 4, 6 and 8
b) 30 and 45 e) 24 and 84
c) 15 and 18 f) 72 and 96
4) The bells at Kings School ring every 6 minutes.
At Queens School the bells ring every 5 minutes.
At Princess School the bells ring every 9 minutes.
All three bells ring together at 8.30 am.
When is the next time the bells of the three schools will ring together?
2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
2 × 5 × 5 × 11
2 × 2 × 2 × 3 × 5
2 × 2 × 2 × 3 × 3
3 × 3 × 5
2 × 2 × 3
2
8
12
75
34
15
24
90
90
24
168
288
10 am
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 72
C22Percentage
of an Amount
1) Work out the following:
a) 50% of 80
b) 50% of 48
c) 50% of 15
d) 25% of 120
e) 25% of 90
2) Work out the following:
a) 10% of 150
b) 10% of 26
c) 50% of 12
d) 25% of 12
e) 75% of 12
3) Work out the following:
a) 10% of £40
b) 5% of £40
c) 15% of £40
d) 5% of £70
e) 15% of £380
4) Work out the following:
a) 20% of £50
b) 45% of £9
c) 80% of £11
d) 35% of £6
e) 65% of £824
5) Jamie received £26 pocket money last week.
He spent it as follows: 10% on sweets,
25% on magazines
15% on games
How much did Jamie have left?Show your working.
6) Tony had £40 saved up and gave 35% of it to his younger sister, Ella.
Ella gave 20% of what she was given to her younger brother, Ben.
Ben gave 30% of what he was given to his younger brother, Tim.
Tim spent 75% of what he was given on buying a toy for his hamster, Hammy.
How much was the toy for Hammy?
= 40
= 24
= 7.5
= 30
= 22.5
= 15
= 2.6
= 6
= 3
= 9
= £4
= £2
= £6
= £3.50
= £57
= £10
= £4.05
= £8.80
= £2.10
= £535.60
10% + 25% + 15% = 50%Therefore he had 50%left which is £13
£0.63
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 73
C23
3) Increase the following numbers by 10%
a) 40 e) 75
b) 140 f) 505
c) 810 g) 12
d) 320 h) 123
4) Decrease the following numbers by 10%
a) 20 e) 25
b) 160 f) 445
c) 80 g) 13
d) 190 h) 7
5) Work out the following:
a) Increase £400 by 5% e) Increase 250 m by 50%
b) Decrease £120 by 15% f) Decrease £820 by 75%
c) Decrease 500 km by 20% g) Increase 60 kg by 60%
d) Increase 96 kg by 10% h) Decrease £26 by 35%
6) A shop is having a sale and all prices are reduced by 25%.
a) Work out the sale price of an item normally priced at £18.40
b) Work out the sale price of an item normally priced at £99
Find 10% of the number and add it on.
Find 10% of the number and take it away.
44 82.5
154 555.5
891 13.2
352 135.3
18 22.5
144 400.5
72 11.7
171 6.3
£420 375 m
£102 £205
400 km 96 kg
105.6 kg £16.9
£13.80
£74.25
2) Describe how you would decrease a number by 10%.
Percentage Increaseand Decrease
1) Describe how you would increase a number by 10%.
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 74
C24Addition and Subtraction
of Fractions
1) Work out the following, simplifying youranswers where possible.
a) e)
b) f)
c) g)
d) h)
27
37+ =
38
18+ =
79
29 =
16
23+ =
16
23+ =
45
12 =
1415
35 =
7
9
18 18+ =
6 6+ =
15 15 =
2) Work out the following, simplifying youranswers where possible.
a) f)
b) g)
c) h)
d) i)
e) j)
38
48+ =
12
13+ =
12
25+ =
510
110 =
911
511 =
57
35 = 3
812+ =
512
16+ =
56
14 =
45
110 =
89
56 =
2) Write the missing numbers in each of these fraction sums.
a)
b)
c)
d)
13 6+ =
85 15 =
37
12 =
15 14 =
+
1
1
1
1
5
5
12
25
56
56
310
13
3 12
14 9
1 4
78
411
56
435
910
712
712
710
78
118
4
21
9
12
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 75
C25Multiplication and Division of
Integers by Fractions
1) Work out the following, giving your answers in their simplest forms
a) 3 × e) 4 ×
b) 7 × f) 10 ×
c) 2 × g) × 6
d) 9 × h) × 3
14
17
45
13
49
38
89
215
2) Work out the following, giving your answers in their simplest forms
a) of £40 e) of 30 cm
b) of 20 km f) of £16
c) of 120 kg g) of 7000 g
d) of £99 h) of £500
12
3) Work out the following, giving your answers in their simplest forms
a) 3 ÷ e) 10 ÷
b) 7 ÷ f) 8 ÷
c) 12 ÷ g) 3 ÷
d) 9 ÷ h) 15 ÷
14
12
13
15
23
45
57
23
15
14
19
25
78
47
34
4) An industrial machine takes of an hour to produce a very special tool.
How long would it take the machine to produce 12 of the tools?
34
5) A road is 20 km long. Road signs are to be installed every ofa kilometre. How many signs will be needed?
23
34
1
85
3
169
154
163
25
£20
4 km
30 kg
£11
12 cm
£14
4000 g
£375
12
14
36
45
15
10
215
452
9 hours
30 signs, assuming that there isn’t asign at the beginning of the road.
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 76
A7 Substitution
1) Using a = 3, work out
a) a + 5 d) 2a + 1
b) 7 – a e) 13 –
c) 6a f) a2 + 2a – 20
a3
2) Using x = 5 and y = 2, work out
a) x – y d) 5y – 5x
b) y – x e) x2 + 3y
c) 3x + 2y f) – xy4xy
3) Using a = 3, b = 1 and c = -2, work out
a) a + b + c d) ab – c
b) 2b + c e) ac + 5b
c) c – a + b f) c2 – 2ab
4) Using x = 3, work out
a) x2 – 2x
b) 2x2 + x + 1
c) x3 – 2x2 – 5
5) If = 3.142 and r = 9, work out
a) 2 r
b) r 2
8
4
18
7
12
-5
3
-3
19
-15
31
0
2
0
-4
5
-1
-2
3
22
4
56.556
254.502
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 77
A8 Trial and Improvement
1) Using a trial and improvement method,solve the equation x2 – x = 56
You must show ALL your working.
2) Using a trial and improvement method,solve the equation x3 + 2x = 72
You must show ALL your working.
x = 6 36 – 6 = 30 Lowx = 7 49 – 7 = 42 Lowx = 8 64 – 8 = 56Therefore, x = 8
x = 2 8 + 4 = 12 Lowx = 5 125 + 10 = 135 Highx = 4 64 + 8 = 72Therefore, x = 4
3) The equation x2 + 3x = 37has a solution between 4 and 5.
Use a trial and improvement method to find this solution.Give your answer to one decimal place.
You must show ALL your working.
4) The equation x3 – 2x = 9has a solution between 2 and 3.
Use a trial and improvement method to find this solution.Give your answer to one decimal place.
You must show ALL your working.
x = 4 42 + 3 × 4 = 28 Lowx = 5 52 + 3 × 5 = 40 Highx = 4.9 4.92 + 3 × 4.9 = 38.71 High
x = 4.8 4.82 + 3 × 4.8 = 37.44 High
x = 4.7 4.72 + 3 × 4.7 = 36.19 Lowx = 4.75 4.752 + 3 × 4.75 = 36.8125 LowTherefore, x = 4.8 to one decimal place.
x = 2 23 – 2 × 2 = 4 Lowx = 3 33 – 2 × 3 = 21 Highx = 2.1 2.13 – 2 × 2.1 = 5.061 Low
x = 2.2 2.23 – 2 × 2.2 = 6.248 Low
x = 2.3 2.33 – 2 × 2.3 = 7.567 Low
x = 2.35 2.353 – 2 × 2.35 = 8.277875 LowTherefore, x = 2.4 to one decimal place.
x = 2.4 2.43 – 2 × 2.4 = 9.024 High
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 78
A9Algebraic Simplification
1) Simplify these expressions
a) 3a + 4a = f) 3r – 2r + 4r =
b) b + 4b = g) 5t – 3t + t + 2t =
c) 5x – x = h) 7p – p + 2p – 5p =
d) 6d + 3d – 2d = i) -4y + 2y – y + 4y =
e) 2k + k + k – 3k = j) -2c + c – 3c – c =
2) Simplify these expressions
a) a + b + a + b = f) 6x – 4y + 7y – 2x =
b) 3a + 2a + 4b + b = g) 2k – 3l – k + 10l =
c) 7x + 2y + x + 3y = h) 3m + 5n + 7m – 7n =
d) 5r + 6p – 2r – 3p = i) v – 4w – 5v – 2w =
e) 4c + 8d – 3c + d = j) -3x – y – 3y – x =
3) Simplify these expressions
a) 7xy – 2xy = f) 6m + 2pr – m + 3rp =
b) 5cd + 3dc = g) 10a2d + 2y – 3da2 + y2 =
c) x2 + 4x2 + 2x2 = h) bz2 + 4t3 – 3t3 – 5zb2 =
d) 9y3 + y – 2y3 = i) 2r2b + 5r2 – r + 6br2 =
e) 3ab + 7ab – 2a = j) 8x3y + 2w – 5w – 3yx3 =
7a
5b
4x
7d
k
5r
5t
3p
y
-5c
2a + 2b
5xy
5a + 5b
8x + 5y
3r + 3p
c + 9d
4x + 3y
k + 7l
10m – 2n
-5v – 6w
-4x – 4y
8cd
7x2
7y3 + y
10ab – 2a
5m – 5pr
7a2d + 2y + y2
bz2 + t3 – 5zb2
8br2 + 5r2 – r
5x3y – 3w
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 79
A10Linear Equations
1) Solve
a) x + 5 = 8 f) 2x = 14
b) x + 7 = 9 g) 3x = 30
c) x – 3 = 12 h) = 8
d) x – 6 = 10 i) = 7
e) 2 + x = 5 j) = 8
x = 3
x = 2
x = 15
x = 16
x = 3
x = 7
x = 10
x = 16
x = 35
x = 6
2) Solve
a) 5x + 2 = 17 f) + 3 = 7
b) 3x – 1 = 17 g) – 2 = 4
c) 2x + 10 = 20 h) – 1 = 9
d) 4x – 7 = 29 i) + 5 = 11
e) 4 + 2x = 14 j) + 6 = 8
x2x5
2x53x2
4x5
x = 3
x = 6
x = 5
x = 9
x = 8
x = 30
x = 25
x = 4
x = 2.5x = 5
3) Using the statement: “I think of a number, double it,and subtract 1. I get 7.”
a) Form an equation.
b) Solve the equation to find the number that was thought of.
4) Using the statement: “I think of a number, multiply it by 7,and add 3. I get 80.”
a) Form an equation.
b) Solve the equation to find the number that was thought of.
5) Using the statement: “I think of a number, multiply it by 2,divide the result by 3 and then subtract 5.I get 5.”
a) Form an equation.
b) Solve the equation to find the number that was thought of.
2x – 1 = 7
x = 4
7x + 3 = 80
x = 11
x = 15
– 5 = 52x3
x2x5
4x3
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 80
A11Generate a Number
Sequence
1) Write the first five terms of each sequence
a) Start at 1 and add 5 d) Start at 8 and subtract 4
b) Start at 30 and subtract 4 e) Start at -10 and add 6
c) Start at 11 and add 9 f) Start at 4 and subtract 3
2) For each sequence, describe the rule and find the next two terms
a) 5, 7, 9, 11, ___, ___ d) -1, 2, 5, 8, ___, ___
b) 11, 16, 21, 26, ___, ___ e) 6, 2, -2, -6, ___, ___
c) 22, 19, 16, 13, ___, ___ f) -42, -35, -28, -21, ___, ___
3) Here is a pattern made up of sticks
a) Write the pattern as a number sequence.
b) Describe the rule.
c) Find the next five terms of the sequence.
4) For each sequence, find the first 5 terms and the 10th term.
a) 3n – 1
b) n + 2
c) 5n + 2
d) 4n – 7
e) 10n + 9
1, 6, 11, 16, 21
30, 26, 22, 18, 14
11, 20, 29, 38, 47
8, 4, 0, -4, -8
-10, -4, 2, 8, 14
4, 1, -2, -5, -8
13 15
31 36
10 7
11 14
-10 -14
-14 -7
Add 2
Add 5
Subtract 3
Add 3
Subtract 4
Add 7
5, 9, 13
Add 4
17, 21, 25, 29, 33
2, 5, 8, 11, 14, . . . . . . . , 29
3, 4, 5, 6, 7, . . . . . . . , 12
7, 12, 17, 22, 27, . . . . . . . , 52
-3, 1, 5, 9, 13, . . . . . . . , 33
19, 29, 39, 49, 59, . . . . . . . , 109
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 81
A12
Pattern 1 Pattern 2 Pattern 3
1)
a) Draw pattern 4
b) How many lines would be in Pattern 6?
c) How many lines would be in Pattern n?
2) Work out the nth term of the following number patterns.
a) 2, 4, 6, 8, . . . .
b) 3, 5, 7, 9, . . . .
c) 5, 8, 11, 14, . . . .
d) 1, 5, 9, 13, . . . .
e) 12, 22, 32, 42, . . . .
f) 2, 8, 14, 20, . . . .
g) 3, 4.5, 6, 7.5, . . . .
3) Write down the first four terms and the 10th term of the followingnumber patterns.
a)
b)
c)
d)
e)
f)
g)
n 3n
n 3n + 2
n n – 3
n 2n + 5
n 3n – 7
n 5n + 3
n 4n – 1
5n + 1n
31
2nn
2n + 1n
3n + 2n
4n – 1n
10n + 2n
6n – 4n
1.5n + 1.5n
3, 6, 9, 12, . . . . . 30
5, 8, 11, 14, . . . . . 32
-2, -1, 0, 1, . . . . . 7
7, 9, 11, 13, . . . . . 25
-4, -1, 2, 5, . . . . . 23
8, 13, 18, 23, . . . . . 53
3, 7, 11, 15, . . . . . 39
Finding the nth Term
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 82
A13Straight Line Graphs
-5 -4 -3 -2 -1 O 1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
11
12
13
x
y
x -2 -1 0 1 2 3 4 5y
1) a) Complete the table of values for y = 3x – 2
b) Plot the graph of y = 3x – 2
c) Use your graph to estimate the value of xwhen y = 2
d) Use the graph to estimate the value of xwhen y = -4
-3 -2 -1 O 1 2 3 4
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
y
x
2) a) Plot the graphof y = 2x – 4
b) Plot the graphof x + y = 1
1310741-2-5-8
Approximately 1.3
Approximately -0.7
y = 2x – 4x + y = 1
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 83
A14
The graph, above, shows Jade’s journey by scooter from herhouse to university with some stops along the way.
a) How long did the journey take?
b) How many breaks did Jade take throughout her journey?
c) At what time did Jade take her first break?
d) How long did the first break last?
e) What was Jade’s average speed between 3 pm and 4 pm?
f) What was Jade’s average speed between 4.30 pm and 5 pm?
g) What was Jade’s average speed between 5.30 pm and 7 pm?
4 hours
2
4 pm
30 minutes
20 mph
40 mph
20 mph
Distancein miles
3 4 5 6 7 80
10
20
30
40
50
60
70
80
pm pm pm pm pm pmTime
Distance - Time Graphs
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
2) The graph below shows three different mobile phone tariffs.
Tariff 1Pay as you go50p per minute.
Tariff 2£15 per month and30p per minute
Tariff 3£40 per month,100 free minutes then10p per minute
a) Match each tariffwith its graph, A, B or C
b) Every month, Jamesneeds about 90 minstalk time.Work out which tariff wouldbe best for him. Explain your answer.
c) Tariff 4 is announced. This is £10 per month, 40 free minutes then 30p per minute.Draw a line on the graph to show this tariff.
Page 84
A15 Real Life Graphs
1) Use the conversion graph below to convert :
a) 80 km to miles
b) 35 miles to km
c) 40 km to miles
d) 60 miles to km
e) 100 miles to km
f) 140 km to miles
0 10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
0Kilometres
Miles
0 20 40 60 80 100 120 140 1600
10
20
30
40
50
60
Costin £
Monthly used minutes
A
BC
50
56
25
96
160
86
T1 is C T2 is B T3 is A
T3 is best because it costs £40.
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 85
S17
a) b) c)
d) e) f) g)
1) Write down the names of the quadrilaterals a) to g)
8 cm
14 cm
9 cm
A
12 cm
8 cm
9 cm
B
16 cm
10 cm
C
Number of linesof symmetry
Order of rotationalsymmetry AreaShape
A
B
C
2) Fill in the table for quadrilaterals A, B and C.
Rhombus Trapezium Irregularquadrilateral
SquareKite
Rectangle Parallelogram
None
None
2
2
None
2
112 cm2
90 cm2
80 cm2
Properties of Quadrilaterals
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 86A
S18 Nets of 3D Shapes
a) Draw a net of this cube. b) Draw a net of this cuboid.
3 squares
3 squares
3 squares
2 squares1 square
4 squares
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 86B
S18 Nets of 3D Shapes
Draw a net of this triangular prism.
12 squares
5 squares13 squares
4 squares
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 87
S19
7 cm
40° 65°A B
C
AC = 6.6 cm
6 cm
25°120°
A B
C
AC = 9.1 cm
110°
80°
A B
C
D
4 cm
3.5 cm
CD = 5 cm
3 cm
3 cm3 cm
3 cm
3 cm
A B
C
DE
F
CD = 3 cm
BA
C
6 cm
7 cm4.5 cm
r = 58°s = 37°
8 cm
5 cm 5 cm
A B
C
3 cm
7.5 cm
5 cmt = 138°
A B
C
D
E
7 cm
80° 70°
4 cm
5 cmu = 81°
1)
2)
a)
b)
c)
d)
a)
b)
c)
d)
Constructions
A B
C
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 88
S20 Geometric Problems
In every question below, calculate the missing angles indicated by theletters. None of the diagrams are drawn accurately.
46° 78°
a
29°
35°
b
41°
c 57°
d
50°
e
235°
f50°
g
74°85°
40°
h
24°
64° e
f 35° g
h
40°
ji 55°
l
k
44°a 115°
b53°
c
38°
d
72°
115°e
125° 72°f 143° 45°
g
20°
32°
h36°
148°
65°
a
145°
73°
b 68° 54°
c32°
d
1)
2)
3)
56°
116° 49°
33°
52°
64°110°
35°
70° 70° 62.5°
62.5°
136°
65° 70°
310°
125°
146° 211°
37°
80° 141°
126°
106°
60° 109°
83°
80°
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 89
S21
a
bc
e
fg
d58°
28°b
d
105°f
153°
79°
h
i
jk
l
mn
o64° 70°
p q
r s
t
a
61°
72°
64°
71°
a
bc
d
e
80°
24°
37°
a
In every question below, calculate the missing angles indicated by theletters. None of the diagrams are drawn accurately.
1)
124°c
2)
e
137°
3)
4)
45°
40°
b
c
de
37°28°
124°
105°
137° 153°
58°58°
122°
122°58°
122°
122°
101° 79°79°
79°
79°
101°
101°
101°64° 70°
46°
64° 70°
47°
40° 45°95°
45°
45°
64°
24°
71°
100°
Corresponding andAlternate Angles
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 90A
S22 Enlargement
12345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678
123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901123456789012345678901
123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345
123456789012341234567890123412345678901234123456789012341234567890123412345678901234123456789012341234567890123412345678901234123456789012341234567890123412345678901234123456789012341234567890123412345678901234123456789012341234567890123412345678901234123456789012341234567890123412345678901234
1234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678
1234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567
Enlarge the following shapes with scale factor 2, using the dot as the centre of enlargement.
a) b)
c) d)
e) f)
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 90B
Enlargement
12345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789123456789012345678901234567890121234567891234567890123456789012345678901212345678912345678901234567890123456789012123456789
1234567890123456789012345678901234567890123456789012345678901234567890
123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678123456789012345678901234567890121234567812345678901234567890123456789012123456781234567890123456789012345678901212345678
12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678
1234567890123123456789012312345678901231234567890123123456789012312345678901231234567890123
1234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678
12345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567
Scale factor 3 Scale factor 3
Scale factor 4 Scale factor 0.5
a) b)
c) d)
A
B
C
D
2) Use dots to mark on the grids the positions of the centres of enlargement.
a) b)
1) Enlarge the following shapes using the dots as the centres of enlargement.
S22
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 91
S23Similar Shapes
1) In each of the following questions, the two shapes aremathematically similar.
Work out the lengths of the missing sides.
a) b)
c) d)
12 cm
?
4 cm
7 cm
4 cm
?
8 cm
10 cm
8.2 cm
7 cm
?
9.8 cm
4.2 cm
?10 cm
2 cm16.6 cm
?
2) a) Work out the length of CD.
b) Work out the length of AE.
A
B
CD
E
5 cm
3 cm
10 cm
4 .5 cm
21 cm
5 cm
83 cm 11.48 cm
3 cm
7.2 cm
6.25 cm
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 92A
S24Area of a Triangle
1) Find the areas of the following triangles
a) b) c) d)
8 cm 5 cm
6 cm 7 cm 1 cm
0.6 cm
13 cm 15 cm
2) Find the areas of the following triangles
a) b)
c)
12 cm
5 cm
13cm
2.8 cm
1.3 cm2.5 cm
30 cm
40 cm
50 cm
3) Find the areas of the following triangles
a) b)
13 cm
8 cm 8.6 cm6.4 cm
26.4 cm
18.2 cm
c)
d)
14 cm
20 cm
e) 36 cm
28 cm
24 cm2
17.5 cm2
0.3 cm2
97.5 cm2
30 cm21.625 cm2
600 cm2
52 cm2
27.52 cm2
240.24 cm2
140 cm2
504 cm2
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 92B
S24Area of a Triangle
16 cm
20 c
m
5 cm
3 cm
7 cm
6 cm
14 cm
22 c
m
20 cm
26 c
m
4 cm
5 cm
9 cm 6 cm
5 cm 8 cm
7 cm
7 cm
2) Find the areas of the following shaded parts of rectangles
a) b) c)
6 cm
wArea = 12 cm2
8 cm
x
Area =18 cm2
Area =12.5 cm2
y
4 cm
1) Find the lengths w, x, y and z
Area = 40.5 cm2
z z
3) The two squares are drawn on 1 cm square grids.Find the areas of the squares.
a) b)
a) b)
c)
d)
1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
1234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789
1234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789123456789012345678901234567891234567890123456789012345678912345678901234567890123456789
12345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678123456789012345678901234567812345678901234567890123456781234567890123456789012345678
w = 4 cmx = 4.5 cm
y = 6.25 cm
z = 9 cm
154 cm2
163.5 cm2
384.5 cm2
17 cm2 13 cm2
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 93
S25
1234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901
123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456
12345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901123456789012345678901234567890121234567890112345678901234567890123456789012123456789011234567890123456789012345678901212345678901
123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678123456789012345678901234567890121234567890123456789012345678
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
1) Find the areas of the five parallelograms on this cm square grid.
a) b)
c)
d)
e)
2) Find the areas of these four parallelograms
8.4 cm
3.6 cm
19 cm
19.8 cm
13 cm
12.3 cm 20 cm
18 cm
22 cm
40 cm2 9 cm2 4 cm2
15 cm2 1 cm2
360 cm2
30.24 cm2 376.2 cm2
159.9 cm2
a) b)
c)
d)
Area of aParallelogram
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 94
S26
20 cm10 cm
15 cm
19 cm
7 cm
11 cm
30 cm
22 cm
14 cm
15 cm6 cm8 cm
4.2 cm1.6 cm
2.1 cm
19 cm8 cm
?
20 cm
7 cm
9 cm
6 cm
3 cm1) Find the volume of the following:
a) b)
c) d)
2) Find the height of this cuboid
Volume = 1140 cm3
3) The cuboid below is made out ofsteel and has a rectangular hole allthe way through it.
If 1 cm3 of steel has a mass of 8 g,what is the mass of the cuboid?
Vol = 3000 cm3 Vol = 1463 cm3
Vol = 9960 cm3
Vol = 14.112 cm3
Ht = 7.5 cm
mass = 8784 g
Volume of a Cuboid
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 95
S27
20 cm10 cm
15 cm
19 cm
7 cm
11 cm
4.2 cm1.6 cm
2.1 cm
23 cm8 cm
9.5 cm
1) Find the surface area of the following:
a) b)
c) d)
Surface area = 1300 cm2 Surface area = 838 cm2
Surface area = 957 cm2 Surface area = 37.8 cm2
30 cm
22 cm
14 cm
15 cm6 cm8 cm
20 cm
7 cm
9 cm
6 cm
3 cm
3) The shape below consists of acuboid glued onto another cuboid.
If the whole shape - including thebase - is painted, work out thearea which will be painted.
2) The cuboid below is made out ofsteel and has a rectangular hole allthe way through it.
All the surfaces are paintedincluding the base and the sides ofthe rectangular hole.Work out the area which will bepainted.
Surface area = 892 cm2
Surface area = 3112 cm2
Surface Area of a Cuboid
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 96
S28
8 cm6.5 cm
9.4 cm
14 cm 9.6 cm16.7 cm
1) Find the circumference of the following circles
a) b) c)
d) e) f)
60°
The circumference of the earth isapproximately 40000 km.
If you had a piece of string which was 6.3 mlonger than 40000 km and put it around theearth, how far away from the earth, all the wayround, would the extra 6.3 m allow it to be?
a) 0.1 mm b) 1 mm c) 1 cm d) 1 m
2) Find the perimeter of the following
10 cm
11 cm
12 cm18 cma) b) c)
d) 3)
C = 50.272 cmC = 40.846 cm
C = 59.0696 cm
C = 43.988 cmC = 52.4714 cm
C = 30.1632 cm
P = 46.278 cmP = 39.281 cm
P = 80.556
P = 30.473 cm.
In all questions, take to be 3.142π
Circumference of a Circle
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 97A
S29 Area of a Circle
In all questions, take to be 3.142π
8 cm6.5 cm
9.4 cm
14 cm 9.6 cm16.7 cm
1) Find the areas of the following circles
a) b) c)
d) e) f)
60°
2) Find the areas of the following
10 cm
11 cm
12 cm18 cma) b) c)
d)
130°
e)
A = 201.088 cm2
A = 132.7495 cm2
A = 277.62712 cm2
A = 153.958 cm2
A = 218.068095 cm2
A = 72.39168 cm2
A = 127.251 cm2 A = 95.0455 cm2
A = 339.336 cm2
A = 52.36 cm2
A = 50.18472 cm2
.
5 cm
.
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 97B
S29 Area of a Circle
32 cm16 cm
= 2 cm
24 cm
A square touching acircle at four points
14 cm
14 cm
18 cm
In each question, find the area of the shaded section.
a) b)
c) d)
e)f)
A = 54.912 cm2 A = 164.736 cm2
A =42.042 cm2
A = 763.506 cm2
A =351.904 cm2
A = 657.792 cm2
In all questions, take to be 3.142π
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
12345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678
1234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678123456781234567812345678
123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789123456789
Page 98
D8Bar Charts and
Frequency Diagrams
1) A group of pupils were askedfor their favourite colour.Here are the results.
Draw a suitable chart toshow this information.
Colour Frequency
Red 8
Blue 10
Purple 9
Green 4
Yellow 7
Time in mins Frequency
5
6
12
11
10
0 < t < 10
10 < t < 20
20 < t < 30
30 < t < 40
40 < t < 50
2) A group of people were given a puzzle to solve.The time taken by each individual to complete the puzzlewas recorded in the table below.
Draw a suitable chart to showthis information.
1
2
3
4
5
6
7
8
9
10
11
0Red Blue Purple Green Yellow
Fre
quen
cy
Favourite colour
0 10 20 30 40 500
1
2
3
4
5
6
7
8
9
10
11
12
13
Time in minutes
Favourite Colours
Time to Solve a Puzzle
Fre
quen
cy
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 99
D91) The heights and weights of some children are shown in the table, below.
a) Plot the informationfrom the table.
b) Describe the correlationbetween height and weight.
c) Draw a line of best fit.
d) Estimate the weight of achild of similar age to thegroup above with a heightof 155 cm.
Height(cm)
Weight(kg)
132
34
145
40
150
43
140
35
175
60
168
54
177
62
162
51 57
162
51
165
58
149
40
150
41
135
33
159
44
160
50
170
2) The scatter graph below relates car engine sizes to their fuel consumption in mpg.
a) Describe the correlationshown by the data.
b) A car has an mpg of 25.Estimate the engine size.
0 1 2 3 40
10
20
30
40
50
60mpg
Engine size (litres)
130 140 150 160 170 18030
40
50
60
70
Height (cm)
Positive correlation
46 kg
Negative correlation
2 litres
Your answer will depend onyour line of best fit which youmust have drawn.
Scatter Graphs
Your answer will dependon your line of best fit.
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 100
D10Pie Charts
1) The table on the right shows how far 90 visitorsto a museum have travelled.
Draw a pie chart to show this information.
Distance
Within the city
Within 30 milesof the city
Over 30 milesfrom the city
Overseas
Frequency
13
9
20
48
.
2) The table shows the land usage of a farm.
Draw a pie chart to show this information.
Land usage Area(hectares)
Arable
Pasture
Woodland
Waste
80
70
50
40.
90
360° ÷ 90 = 4°
× 4 = 52°
× 4 = 36°
× 4 = 80°
× 4 = 192°
240
360° ÷ 240 = 1.5°
× 1.5 = 120°
× 1.5 = 105°
× 1.5 = 75°
× 1.5 = 60°
Within thecity
Within 30miles of the
city
Over 30miles from
the city
Overseas
Arable
Pasture
Woodland
Waste
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
2) A survey was done by a school to find out how people travel to the school.
Altogether, 100 people were asked and the results can be seen below.
a) Complete the two-way table.
b) How many people cycle to school?
c) How many female pupils go to school by taxi?
Page 101
D11 Two-Way Tables
1) 160 pupils in a school are asked to choose a new colour for theschool tie. They can only choose from Blue, Green or Red.
Some of the results are shown in this two-way table.
Complete the two-way table.
Blue Green Red Total
30 27 28 85
35 26 14 75
65 53 42 160
Male
Female
Total
Walk Car Cycle Taxi Bus Total
12 3 6 1 3 25
2 1 5 6 6 20
7 12 6 6 1 32
4 8 2 7 2 23
25 24 19 20 12 100
Male pupils
Female pupils
Male teachers
Female teachers
Total
19
6
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 102
D12Surveys
2) Beth wants to find out two things:the types of books people prefer to readhow much time, on average, they spend reading books
a) Design two suitable questions for Beth to use in her questionnaire.
b) She decides to ask her questions to the first ten people going into thepublic library on a Saturday morning.
Give one reason why this might not be a good way to carry out the survey.
Italian Food
French Food
Indian Food
Chinese Food
Tally Frequency
Which is your favourite type of book?
Romance Thriller Comedy Other
How much time do you spend reading books per week?
Less than 3 hours Between 3 and 5 hours More than 5 hours
This would be a biased sample because people who go to thelibrary might read more, in general, than others.
Types of Food
1) Lesley wants to find out the types of food people like best.She is going to ask people to choose between Italian Food,French Food, Indian Food and Chinese Food.
Design a suitable table for a data collection sheet she coulduse to collect this information.
Please specify
© Mathswatch Ltd
Level 6
Answers
N19 N20 N21 C22 C23 C24 C25 A7 A8 A9 A10 A11 A12 A13S19 S20 S21 S22 S23 S24 S25 S26 S27 S28
A14 A15S29 D8 D9 D10 D11 D12 D13
S17 S18
Page 103
D131) A counter is taken at random from set 1 followed by another counter
at random from set 2.
a) Write down all the possible pairs of counters that may be chosen.
b) What is the probability that 3B will be picked?
c) What is the probability that any pair of counters will be chosenexcept 3B?
d) What is the probability that the pair of counters chosen willinclude an odd number?
Further Probability
1 2
3
A
B
C
D
Set 1 Set 2
2) The two spinners on the right are spun and theirscores added together to give a total.
a) Draw a possibility space to show all the totals.
b) What is the probability of scoring a total whichis bigger than 5?
1
2 34 3
4 5
6
3) Every Tuesday the main school dinner is eitherSausages, Chicken, Pizza or Tuna.
Use the table below to work out the probability thatthe main dinner will be Pizza next Tuesday.
School dinner Sausages Chicken Pizza Tuna
Probability 0.24 0.18 ? 0.47
1A 1B 1C 1D2A 2B 2C 2D3A 3B 3C 3D1
12
812
1 2 3 4
3
4
5
6
4
5
6
7
5
6
7
8
6
7
8
9
7
8
9
10
1316
0.240.180.470.89
1 0.89 = 0.11
0.11
1112
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
N22Rounding to
1 Significant Figure
1) Round the following to 1 significant figure.
a) 478 cm
b) 450 cm
c) 449 cm
d) 12761 m
e) 28481 km
2) Round the following to 1 significant figure.
a) 673.8 cm
b) 4017.9 kg
c) 246.83 m
d) £45.38
e) 20482.1 kg
3) Round the following to 1 significant figure.
a) 0.26 ml
b) 0.043 g
c) 0.0671 m
d) 0.000256 km
e) 0.3822 m
4) Round the following to 1 significant figure.
a) 962 m
b) 0.923 cm
c) 0.971 cm
d) 0.096 km
e) 0.00985 km
5) Round the following to 1 significant figure.
a) £631428
b) 0.00573 g
c) £3614.68
d) 0.493 ml
e) £968
500 cm
500 cm
400 cm
10000 m
30000 km
700 cm
4000 kg
200 m
£50
20000 kg
0.3 ml
0.04 g
0.07 m
0.0003 km
0.4 m
1000 m
0.9 cm
1 cm
0.1 km
0.01 km
£600000
0.006 g
£4000
0.5 ml
£1000
Page 104
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
C26
Page 105
Percentage Increaseand Decrease
1) a) Increase £400 by 16%
b) Increase £750 by 24%
c) Increase £2000 by 38%
d) Increase £14500 by 19%
e) Increase £16.50 by 30%
2) a) Decrease £700 by 32%
b) Decrease £36 by 14%
c) Decrease £1970 by 40%
d) Decrease £3000 by 12.5%
e) Decrease £3124 by 16.25%
3) A sports shop reduces the price of all its trainersby 15% in the Spring sale.Before the sale, one pair of trainers cost £74.How much are they after the reduction?
4) Tim took up weightlifting.In his first session he could bench-press 45 kg.Four weeks later he could bench-press 22% more.How much could he now lift to the nearest kg?
5) If a manager of a shop reduces the price of a£1500 piano by 15% and then, four weeks later,increases the reduced price by 15%, how muchdoes it now cost?
£464
£930
£2760
£17255
£21.45
£476
£30.96
£1182
£2625
£2616.35
£62.90
55 kg
£1466.25
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
C27Addition and Subtraction
of Fractions
1) Work out
a)
b)
c)
d)
e)
13
+ 12
35
+ 14
27
+ 35
12
+ 29
310
+ 37
2) Work out
a)
b)
c)
d)
e)
23
+ 16
35
+ 310
12
+ 45
56
+ 35
712
+ 34
3) Work out
a)
b)
c)
d)
e)
23
+ 34
12
+ 57
25
+ 12
710
+ 15
34
+ 56
4) Work out
a)
b)
c)
d)
e)
12
+ 15
34
+ 23
16
+ 13
29
+ 23
12
+ 310
1
2
3
1
2
2
1
3
2
4
1
1
1
1
2
5) Work out
a)
b)
c)
d)
e)
23
12
34
23
45
34
56
23
34
38
6) Work out
a)
b)
c)
d)
e)
34
45
16
23
29
56
12
78
7) Work out
a)
b)
c)
d)
e)
12
12
25
110
23
1115
34
58
23
49
8) Work out
a)
b)
c)
d)
e)
4
1
1
2
5
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1
2
3
2
6
2
1
1
1
3
cm
34
2 cm
9) Find the perimeter of the rectangle below.Give your answer as a mixed number.
cm
cm
10) Find the perimeter of the triangle below. Give your answer as a mixed number.
11) If a length of copper tubing is 20 cm long and Jim
cuts off a piece that is 17 cm long, what is the length
of the copper tubing left over?
14
3 13
2 512
3 314
3 712
56
1720
3135
1318
5170
16
112
120
16
310
11415
1 18
4 29
3 710
3 89
6 45
56
910
310
1330
13
14
120
2 12
1 718
310
718
4
38
67
12 16
cm 3 34
cm
1
1
1
910
3
910
1
3 512
4 12
38
12
34
1
2
5 58
2
45
12
29
56
38
56
5
17
3
4
1
2
5
+
–
+
–
–
1
1
2
2
5
3
524
8
2
12
1
58
cm58
1
35
2 1320
cm
Page 106
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
C28Multiplication and Division
of Fractions
1) Work out
a)
b)
c)
d)
e)
12
× 34
23
× 45
1011
× 23
49
× 25
47
× 19
2) Work out
a)
b)
c)
d)
e)
23
× 35
37
× 56
89
× 610
12
× 89
710
× 521
3) Work out
a)
b)
c)
d)
e)
12
× 89
23
× 67
611
× 18
25
× 1011
34
× 89
4) Work out
a)
b)
c)
d)
e)
12
× 15
34
× 23
16
× 25
29
× 15
47
× 1315
1
2
1
4
3
2
3
4
2
3
2
2
2
1
1
5) Work out
a)
b)
c)
d)
e)
23
12
34
23
25
34
37
611
34
38
6) Work out
a)
b)
c)
d)
e)
34
15
47
79
14
67
35
910
12
38
7) Work out
a)
b)
c)
d)
e)
12
12
25
110
13
1115
34
58
23
49
8) Work out
a)
b)
c)
d)
e)
23
34
25
12
2
3
1
2
5
1
4
5
3
2
14
4
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
÷
1
1
2
2
1
3
1
1
1
4
cm
34
2 cm
9) Find the area of the rectangle below.Give your answer as a mixed number.
12
1 cm
12
2 cm
10) Find the area of the triangle below. Give your answer as a mixed number.
11) Jim has a length of copper tubing which is 85 cm long.
He wants to cut it into pieces which are 4 cm long.
If there is no wastage, how many pieces will Jim get?
34
14
3 13
1 13
2 27
2744
4
3 13
38
815
2033
845
463
1 13
1 18
815
1114
2
57
3 111
2 12
1 913
31213
5 12
10
10
2 23
6 23
25
514
815
49
16
58
928
2 58
2 89
4
13
18
10
6 23
78
9 16
cm2 1 78
cm2
20
Page 107
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 108
C29Numbers Between 0 and 1(Multiplication and Division)
1) Work out the answers to the following:
a) 24 × 0.2
b) 13 × 0.4
c) 60 × 0.7
d) 243 × 0.2
e) 0.6 × 700
2) Work out the answers to the following:
a) 314 × 0.02
b) 836 × 0.001
c) 800 × 0.006
d) 418 × 0.003
e) 411 × 0.09
3) Work out the answers to the following:
a) 0.2 × 0.4
b) 0.1 × 0.03
c) 0.02 × 0.06
d) 0.08 × 0.003
e) 0.05 × 0.08
4) Work out the answers to the following:
a) 62 × 0.14
b) 2.7 × 2.5
c) 613 × 0.042
d) 42.3 × 1.8
e) 228 × 0.063
5) Work out the answers to the following:
a) 6 ÷ 0.2
b) 8 ÷ 0.1
c) 9 ÷ 0.3
d) 4 ÷ 0.02
e) 7 ÷ 0.002
6) Work out the answers to the following:
a) 62 ÷ 0.2
b) 51 ÷ 0.3
c) 4.56 ÷ 0.04
d) 22.5 ÷ 0.05
e) 14.7 ÷ 0.007
7) Work out the answers to the following:
a) 7.24 ÷ 0.2
b) 8.13 ÷ 0.3
c) 1.512 ÷ 0.07
d) 0.16 ÷ 0.008
e) 0.0732 ÷ 0.04
8) Work out the answers to the following:
a) 0.718 ÷ 0.2
b) 0.0141 ÷ 0.003
c) 0.24 ÷ 0.012
d) 1.625 ÷ 0.0013
e) 47.1 ÷ 0.15
4.8
5.2
42
48.6
420
6.28
0.836
4.8
1.254
36.99
0.08
0.003
0.0012
0.00024
0.004
8.68
6.75
25.746
76.14
14.364
30
80
30
200
3500
310
170
114
450
2100
36.2
27.1
21.6
20
1.83
3.59
4.7
20
1250
314
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 109
C30EstimatingAnswers
1) Estimate the value of:
a) 21 × 34
b) 42 × 56
c) 17 × 62
d) 29 × 78
e) 66 × 96
2) Estimate the value of:
a) 510 × 724
b) 86 × 2146
c) 753 × 184
d) 48 × 6315
e) 3642 × 1356
3) Estimate the value of:
a)
b)
c)
d)
e)
6119
7643
36278
73896
416781
4) Estimate the value of:
a)
b)
c)
d)
e)
35712 × 23
92434 × 13
172 × 411430
625 × 4316 × 38
972 × 36817 × 23 × 18
5) Estimate the value of:
a) 8 ÷ 0.12
b) 6 ÷ 0.24
c) 5 ÷ 0.49
d) 7 ÷ 0.012
e) 23 ÷ 0.18
6) Estimate the value of:
a)
b)
c)
d)
e)
215 × 380.183
18.3 × 31.20.017
405 × 2740.488
46 × 6.20.135
24 × 5100.53
600
2400
1200
2400
7000
350000
180000
160000
300000
4000000
3
2
5
7
0.5
2
3
200
30
50
80
30
10
700
115
20000
3000
40000
30000
240000
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 110
C31Using a Calculator
1) Using a calculator, work out the value of:
a) 24 + 16 ÷ 4
b) 3 + 8 ÷ 2 × 3
c) 60 × 2 – 20 ÷ 4
d) (2 + 7 × 8) × 4
e) (3 + 7) × (8 – 2)
2) Using a calculator, work out the value of:
a) 63 – (24 + 35)
b) (37 – 26) ÷ 104
c) 28 ÷ 23 × 52
d) 53 × 35
e) 220 – 38
3) Using a calculator, work out the value of:
a) 256 × 24 – 169
b) 365 × 365
c) 550 – 21
d) 28 + 34 – 13
e) 46 × 28 ÷ (32 – 1)
4) Using a calculator, work out the value of:
a)
b)
c)
7 + 4 × 818 – 5
63 – 23
(32 + 7) ÷ 2
d)
e)
62 × 24 + 23
43 + 32 + 33
284 – 29 – 112(3 + 17) × 100
729 + 2164
28
15
115
232
60
-43
0.2123
800
30375
1042015
243
365
23
18
128
3 100
26 1.32
6
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 111
A16Further Algebraic
Simplification
1) Simplify the following
a) 6 × x
b) 2 × x × y
c) 6 × x × 3 × y
d) s × t × u
e) 7 × s × 2 × t × u
2) Simplify the following
a) x × x × x × x
b) t × t × t × t × t × t × t
c) g × g
d) x × x × x × y × y × y × y
e) x × y × x × y × y
3) Simplify the following
a) x × x2
b) y3 × y4
c) x2 × x3 × x
d) g × g × g2 × g4
e) x2 × x3 × x4 × x5
4) Simplify the following
a) 3x2 × 2x3
b) 5x × 4x2
c) 6y3 × 2y4
d) 9x2 × x3
e) 4x3 × 2x × 3x2
5) Simplify the following
a) 3x2y3 × 2x3y4
b) 2xy4 × 3x2y
c) 5x3y4 × 2x2y2
d) 2x2y × x4y2
e) 3x3y × 2xy2 × 3x2y2
6) Simplify the following
a) x8 ÷ x2
b) 9y6 ÷ 3y2
c) 14y3 ÷ 2y2
d) 20x5 ÷ 4x
e) 16x8 ÷ 8x2
7) Simplify the following
a)
b)
c)
d)
e)
12x6
3x2
20x3
2x
5x4
x2
6x5
3x3
300x9
10x2
8) Simplify the following
a)
b)
c)
d)
e)
12x3y4x
15x4y3
3xy
20x3y5
4x2y3
14x2y2
7xy
30x2y3z6
3xy2z4
9) Find the value of
a) 40
b) 60
c) 120
d) z0
e) x0
6x
2xy
18xy
stu
14stu
x4
t7
g2
x3y4
x2y3
x3
y7
x6
g8
x14
6x5
20x3
12y7
9x5
24x6
6x5y7
6x3y5
10x5y6
2x6y3
18x6y5
x6
3y4
7y
5x4
2x6
4x4
10x2
5x2
2x2
30x7
3x2y
5x3y2
5xy2
2xy
10xyz2
1
1
1
1
1
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 112
A17Expanding and
Simplifying Brackets
1) Expand
a) 2(x + 3)
b) 2(x – 4)
c) 5(2x + 1)
d) 7(3x – 1)
e) 4(2a + 7)
2) Expand
a) 2x(3x + 1)
b) 3x(4x – 2)
c) 2x(x + 1)
d) 3x(2x – y)
e) 5x(3x + 2y)
3) Expand and simplify
a) 2(x + 3) + 4(x + 1)
b) 3(2x + 1) + 2(5x + 2)
c) 4(x + 1) + 3(3x + 4)
d) 6(2x + 3) + 5(x + 2)
e) 4(3x + 2) + 5(2x + 1)
4) Expand and simplify
a) 2(5x + 3) + 3(x – 1)
b) 3(4x + 5) + 2(3x – 4)
c) 5(2x – 1) + 3(2x + 5)
d) 2(3x – 4) + 3(x + 2)
e) 3(2x – 1) + 4(3x – 2)
5) Expand and simplify
a) 3(x + 2) – 2(x + 3)
b) 4(2x + 3) – 3(2x + 1)
c) 5(3x – 2) – 2(x – 2)
d) 2(5x – 1) – 4(2x – 3)
e) 3(2x + 7) – 2(3x + 2)
6) Expand and simplify
a) (x + 2)(x + 2)
b) (x + 3)(x + 5)
c) (x + 7)(x + 1)
d) (x + 4)(x + 3)
e) (x + 7)(x + 2)
7) Expand and simplify
a) (2x + 1)(3x + 2)
b) (4x + 3)(2x + 1)
c) (3x + 4)(3x + 2)
d) (5x + 2)(5x + 7)
e) (2x + 10)(2x + 4)
8) Expand and simplify
a) (x + 5)(x – 3)
b) (x – 2)(x + 4)
c) (x – 6)(x – 2)
d) (x + 7)(x + 3)
e) (x – 8)(x – 2)
9) Expand and simplify
a) (2x – 1)(3x + 4)
b) (5x – 2)(3x – 1)
c) (3x + 4)(2x – 3)
d) (5x – 1)(5x – 2)
e) (4x + 2)(3x – 5)
Expand and simplify
a) (x + 5)2
b) (x – 2)2
c) (2x + 3)2
d) (3x – 1)2
e) (4x + 3)2
10)
2x + 6
2x – 8
10x + 5
21x – 7
8a + 28
6x2 + 2x
12x2 – 6x
2x2 + 2x
6x2 – 3xy
15x2 + 10xy
6x + 10
16x + 7
13x + 16
17x + 28
22x + 13
13x + 3
18x + 7
16x + 10
9x – 2
18x – 11
x
2x + 9
13x – 6
2x + 10
17
x2 + 4x + 4
x2 + 8x + 15
x2 + 8x + 7
x2 + 7x + 12
x2 + 9x + 14
6x2 + 7x + 2
8x2 + 10x + 3
9x2 + 18x + 8
25x2 + 45x + 14
4x2 + 28x + 40
x2 + 2x – 15
x2 + 2x – 8
x2 – 8x + 12
x2 + 10x + 21
x2 – 10x + 16
6x2 + 5x – 4
15x2 – 11x + 2
6x2 – x – 12
25x2 – 15x + 2
12x2 – 14x – 10
x2 + 10x + 25
x2 – 4x + 4
4x2 + 12x + 9
9x2 – 6x + 1
16x2 + 24x + 9
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 113
A18Factorisation
1) Factorise the following
a) 6x – 2
b) 8x + 14
c) 6x + 9
d) 10x – 5
e) 12x + 18
2) Factorise the following
a) x2 + x
b) t2 – t
c) x3 + x
d) x5 – x2
e) a7 + a4
3) Factorise the following
a) 3x2 + 6x
b) 8x3 – 2x
c) 12a2 + 4a3
d) 20x4 – 6x2
e) 7x3 + 8x
4) Factorise the following
a) 6x2y4 + 4xy3
b) 4x3y4 + 2x2y2
c) 10x4y3z – 5xy5z
d) 16a2b3c4 + 3ab2c3
e) 9x2y4z – 6xy2z
5) Factorise the following
a) 10x + 4
b) x4 – x2
c) 9x5 – 12x2
d) 12x2y3 + 4xy2
e) 24x3yz4 – 10xz2
2(3x – 1)
2(4x + 7)
3(2x + 3)
5(2x – 1)
6(2x + 3)
x(x + 1)
t(t – 1)
x(x2 + 1)
x2(x3 – 1)
a4(a3 + 1)
3x(x + 2)
2x(4x2 – 1)
4a2(3 + a)
2x2(10x2 – 3)
x(7x2 + 8)
2xy3(3xy + 2)
2x2y2(2xy2 + 1)
5xy3z(2x3 – y2)
ab2c3(16abc + 3)
3xy2z(3xy2 – 2)
2(5x + 2)
x2(x2 – 1)
3x2(3x3 – 4)
4xy2(3xy + 1)
2xz2(12x2yz2 – 5)
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 114
A19Solving Difficult Equations
1) Solve the following
a) 2x + 3 = 19
b) 3x – 2 = 13
c) 5x – 1 = 9
d) 3 + 2x = 23
e) 12 – 3x = 9
2) Solve the following
a) 2(3x – 1) = 22
b) 3(x + 7) = 18
c) 4(5x – 2) = 12
d) 66 = 6(2x + 3)
e) 20 = 5(x – 6)
3) Solve the following
a)
b)
c)
d)
e)
x – 62 = 3
x + 83 = 5
2x – 13 = 5
6x + 12 = 8
7x – 35 = 5
4) Solve the following
a) 2x + 7 = x + 12
b) 4x – 5 = 2x + 3
c) 7x + 2 = 3x + 26
d) 6x – 7 = 4x – 5
e) 3x + 4 = x – 7
5) Solve the following
a) x – 6 = 2x – 13
b) 3x + 4 = 5x – 8
c) 4x + 17 = x – 4
d) 5 – 2x = x – 7
e) 2x – 1 = 14 – 3x
6) Solve the following
a) 2(3x – 1) = 4x + 7
b) 3(x + 4) = 2(x – 5)
c) 5(2x – 3) = 3(3x + 4)
d) 2(2x – 1) = 5(2x – 4)
e) 2(2x + 3) = 5(x + 3)
7) Solve the following
a)
b)
c)
d)
e)
2(x + 1)3
= 6
4(2x – 3)5
= 4
2(4x – 5)3
= x + 10
3(5x + 4)2
= 7x – 8
2(x + 7)34 – x =
x = 8
x = 5
x = 2
x = 10
x = 1
x = 4
x = -1
x = 1
x = 4
x = 10
x = 12
x = 7
x = 8
x = 2.5
x = 4
x = 5
x = 4
x = 6
x = 1
x = -5.5
x = 7
x = 6
x = -7
x = 4
x = 3
x = 4.5
x = -22
x = 27
x = 3
x = -9
x = 8
x = 4
x = 8
x = -28
x = 25
-
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 115
A20Rearranging a Formula
1) Rearrange to make x the subjectof the formula
a) y = x – 2
b) y = x + 7
c) y = x + t
d) y = 5x + 3
e) y = 2x – 4
2) Rearrange to make x the subjectof the formula
a) 3x + 2 = y
b) 4x – 1 = y
c) ax – 3 = y
d) ax + m = t
e) x + y = t
3) Rearrange to make x the subjectof the formula
a) y = x + t – v
b) ax – c = y
c) y = ax – tv + c
d) y + x = ct
e) c + ax + t = y + m
4) Rearrange to make x the subjectof the formula
a)
b)
c)
d)
e)
5x – 24 = y
ax + cm = y
x – 45
y =
t + mxyk =
5) Rearrange to make x the subjectof the formula
a)
b)
c)
d)
e)
y = 3x42x5y = – 8
cxty = + m
y = abx + c
mxt + c = y
6) Rearrange to make x the subjectof the formula
a) y = 4(x + t)
b) y = a(x – m)
c) at(c + x) = y
d) y + m = a(c + x)
e) t – v = m(x – y)
7) Rearrange to make x the subjectof the formula
a)
b)
c)
d)
e)x + 2
3 = y
x – u4 = y
x + ab = c
3(x + 2)c = y
a(x + b)c = d
t(x + c)d = e + f
x = y + 2
x = y – 7
x = y – t
x = y – 35
x = y + 42
x = y – 23
x = y + 14
x = y + 3a
x = t – ma
x = t – y
x = y – t + v
x = y + ca
x = y + tv – ca
x = ct – y
x = y + m – c – ta
x = 3y – 2
x = 5y + 4
4y + 25
my – ca
x =
x =
yk – tmx =
4y3x =
5(y + 8)2x =
t(y – m)cx =
y – cx =
t(y – c)mx =
ab
x =y4
– t
x =ya
+ m
x =yat
– cy + m
a – cx =t – vm + yx =
x = 4y + u
x = bc – a
cy3
– 2x =
cda
– bx =
d(e + f)t
– cx =
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 116A
A21Trial and Improvement
1) The equation x2 + 3x = 37has a solution between 4 and 5.
Use a trial and improvement method to find this solution.Give your answer to one decimal place.
You must show ALL your working.
2) The equation x2 – 4x = 6has a solution between 5 and 6.
Use a trial and improvement method to find this solution.Give your answer to one decimal place.
You must show ALL your working.
x = 4 42 + 3 × 4 = 28 Lowx = 5 52 + 3 × 5 = 40 Highx = 4.9 4.92 + 3 × 4.9 = 38.71 High
x = 4.8 4.82 + 3 × 4.8 = 37.44 High
x = 4.7 4.72 + 3 × 4.7 = 36.19 Lowx = 4.75 4.752 + 3 × 4.75 = 36.8125 Low
Therefore, x = 4.8 to one decimal place.
x = 5 52 – 4 × 5 = 5 Lowx = 6 62 – 4 × 6 = 12 Highx = 5.1 5.12 – 4 × 5.1 = 5.61 Low
x = 5.2 5.22 – 4 × 5.2 = 6.24 High
x = 5.15 5.152 – 4 × 5.15 = 5.9225 Low
Therefore, x = 5.2 to one decimal place.
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 116B
A21Trial and Improvement
2) The equation x3 – 2x = 9has a solution between 2 and 3.
Use a trial and improvement method to find this solution.Give your answer to one decimal place.
You must show ALL your working.
x = 2 23 – 2 × 2 = 4 Lowx = 3 33 – 2 × 3 = 21 Highx = 2.1 2.13 – 2 × 2.1 = 5.061 Low
x = 2.2 2.23 – 2 × 2.2 = 6.248 Low
x = 2.3 2.33 – 2 × 2.3 = 7.567 Low
x = 2.35 2.353 – 2 × 2.35 = 8.277875 Low
Therefore, x = 2.4 to one decimal place.
x = 2.4 2.43 – 2 × 2.4 = 9.024 High
1) The equation x3 + 3x = 114has a solution between 4 and 5.
Use a trial and improvement method to find this solution.Give your answer to one decimal place.
You must show ALL your working.
x = 4 43 + 3 × 4 = 76 Lowx = 5 53 + 3 × 5 = 140 Highx = 4.6 4.63 + 3 × 4.6 = 111.136 Low
x = 4.7 4.73 + 3 × 4.7 = 117.923 High
x = 4.65 4.653 + 3 × 4.65 = 114.494625 High
Therefore, x = 4.6 to one decimal place.
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 117
A22Inequalities
-5 -4 -3 -2 -1 0 1 2 3 4 5
1) Represent the inequalities on the number lines.
a) x < 3
b) -1 < x < 4
c) -3 < x < 3
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
2) Write down the inequalities shown below
a)
b)
c)
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
3) If x is an integer, what are thepossible values of x?
a) -4 < x < 2
b) -3 < x < 1
c) 1 < x < 5
d) -3 < x < 4
e) -7 < x < -4
<
-5 < x < 2
-1 < x < 3
-3 < x < 5
-4, -3, -2, -1, 0, 1, 2
-3, -2, -1, 0
2, 3, 4, 5
-2, -1, 0, 1, 2, 3, 4
-7, -6, -5, -4
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 118
A23Solving Inequalities
1) Solve
a) 2x – 1 > 7
b) 3x + 4 < 19
c) 5x – 7 < 18
d) 2x + 9 > 5
e) 4x + 11 < 14
2) Solve
a)
b)
c)
d) 12 > 2x – 1
e) 20 < 5 + 5x
x3 < 7
x5 – 1 > 3
2x3 + 4 < 9
3) Solve
a) 2(5x – 1) < 18
b) 3(4x + 2) > 60
c) 42 > 2(6x + 15)
d) 4(1 + x) < 12
e) 8(2x – 1) >12
4) Solve
a) 2x + 7 < x + 9
b) x – 6 > 3x – 18
c) 4x + 3 < 2x – 9
d) 2x – 4 > 7x – 34
e) 2(x + 3) < x – 1
x > 4
x < 5
x < 5
x > -2
x < 0.75
x < 21
x > 20
x < 7.5
x < 6.5
x > 3
x < 2
x > 4.5
x < 1
x < 2
x > 1.25
x < 2
x < 6
x < -6
x < 6
x < -7
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 119
A24Understanding
Straight Line Graphs
O 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
1) Find the gradients ofthe lines A to F.
A
BC
D
E
F
O 1 2 3 4 5
2
4
6
8
10
12
14
16
18
20
x
y
2) Find the gradients ofthe lines G to K.
G
HI
J
K
-4 -3 -2 -1 O 1 2 3 4 5 6
-4
-3
-2
-1
1
2
3
4
5
6
x
y
3) Find the equations oflines A and B.
-4 -3 -2 -1 O 1 2 3 4 5 6
-4
-3
-2
-1
1
2
3
4
5
6
x
y
4) Find the equations oflines C, D and E.
A
B
C
D
E
0
5
3
-0.25
-1
-4
-88
-10
41
y = 3x + 2
y = x – 3
y = -2x + 4
y = 0.5x
y = 0.25x – 2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345
123456789012312345678901231234567890123123456789012312345678901231234567890123
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567123456712345671234567
123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012123456789012
A25Regions
Page 120
1) a) Shade the region represented by x < -1
b) Shade the region represented by x > 3
-5 -4 -3 -2 -1 O 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
2) a) Shade the region represented by y < -1
b) Shade the region represented by y > 2
-5 -4 -3 -2 -1 O 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
3) Shade the region represented by -3 < x < 2
-5 -4 -3 -2 -1 O 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
4) Shade the region represented by 1 < y < 4
-5 -4 -3 -2 -1 O 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
5) Shade the region where -1 < x < 3and -4 < y < -2
-5 -4 -3 -2 -1 O 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
6) Shade the region where -3 < x < 2and -1 < y < 4
-5 -4 -3 -2 -1 O 1 2 3 4 5
-5
-4
-3
-2
-1
1
2
3
4
5
x
y
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
A26Simultaneous Equations
Graphically
Page 121
1) a) Complete the table of values for y = x + 2
b) Draw the graph of y = x + 2
c) Complete the table of values for x + y = 7
d) Draw the graph of x + y = 7
e) Use your graph to solve the simultaneousequations y = x + 2 and x + y = 7
O 1 2 3 4 5 6 7 8
1
2
3
4
5
6
7
8
x 0 1 2 3 4
y
y
x
-6 -5 -4 -3 -2 -1 O 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
62) Using a graphical method, solve the
simultaneous equations
y = 2x – 3 and y = 6 – x
y
x
3) Solve the simultaneous equations y = x + 6 and y = 3 – x
4) Solve the simultaneous equations y = x – 14 and y = 2 – 3x
7 6 5 4 3
x = 2.5, y = 4.5
x = 3, y = 3
x = -1.5, y =4.5
x = 4, y = -10
x 0 1 2 3 4
y 2 3 4 5 6
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
A27Simultaneous Equations
Algebraically
Page 122
1) Solve 3x + y = 11
4x – y = 3
2) Solve 2x – 5y = 3
4x + 5y = 21
3) Solve x – 2y = 3
3x + 2y = 5
4) Solve x + 3y = 10
x + y = 6
5) Solve 3x + 2y = 3
2x + 2y = 5
6) Solve 5x – 3y = 23
2x – 3y = 11
7) Solve 3x – 2y = 6
x + y = 7
8) Solve 6x + y = 10
2x – 3y = 10
9) Solve 2x + 7y = 11
3x – 2y = 4
10) Solve 4x + 3y = 9
5x + 2y = 13
11) Solve 2x + 3y = -7
7x – 2y = -12
12) Solve 3x – 2y = 5
9x + 5y = -7
13) In the first week of opening, a zoo sold200 adult tickets and 300 child tickets. Thetakings for that week were £2600.
In the second week, 500 adult tickets weresold and 400 child tickets were sold. Thetakings for the second week were £5100.
Form two equations and solve them tofind the price of an adult ticket and theprice of a child ticket.
14) If you multiply Sid’s age by four and Tony’sage by five and add the answers togetherit comes to 259 years.
However, if you multiply Sid’s age byseven and then take away two timesTony’s age the answer is 120 years.
Form two equations and solve them to findthe ages of Sid and Tony.
15) If nine rats and seven ferrets cost £116.75and four rats and six ferrets cost £88, howmuch would five rats and four ferrets cost?
16) If a mouse and a goldfish cost £1.10 andthe mouse costs £1 more than the goldfish,how much does the goldfish cost?
x = 2, y = 5
x = 4, y = 1
x = 2, y = -0.5
x = 4, y = 2
x = -2, y = 4.5
x = 4, y = -1
x = 4, y = 3
x = 2, y = -2
x = 2, y = 1
x = 3, y = -1
x = -2, y = -1
x = , y = -213
Adult ticket is £7
Child ticket is £4
Sid is 26
Tony is 31
£66.25
5p
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
A28nth Term of Quadratic
Sequences
Page 123
1) Find the nth term of
a) 1, 4, 9, 16, 25, . . . .
b) 2, 5, 10, 17, 26, . . . .
c) 0, 3, 8, 15, 24, . . . .
2) Find the nth term of
a) 1, 4, 9, 16, 25, . . . .
b) 2, 8, 18, 32, 50, . . . .
c) 0.5, 2, 4.5, 8, 12.5, . . . .
3) Find the nth term of
a) 3, 9, 19, 33, 51, . . . .
b) 1, 7, 17, 31, 49, . . . .
c) 11, 41, 91, 161, 251, . . . .
4) For the following nth terms,find the first three terms and the tenth term
a) n2 + 4
b) n2 – 3
c) n2 + 10
d) n2 + 2n
e) n2 – n
5) For the following nth terms,find the first three terms and the tenth term
a) 4n2
b) 2n2 + 3n
c) 3n2 – 2n
d) n2 + n + 1
e) 2n2 + 4n – 3
n2
n2 + 1
n2 – 1
n2
2n2
0.5n2
2n2 + 1
2n2 – 1
10n2 + 1
5, 8, 13, . . . . . 104
-2, 1, 6, . . . . . 97
11, 14, 19, . . . . . 110
3, 8, 15, . . . . . 120
0, 2, 6, . . . . . 90
4, 16, 36, . . . . . 400
5, 14, 27, . . . . . 230
1, 8, 21, . . . . . 280
3, 7, 13, . . . . . 111
3, 13, 27, . . . . . 237
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
A29Graphs of Quadratic and
Cubic Functions
Page 124A
x -2 -1 0 1 2
y 2 -1 -2 -1 2
3
7
1) a) Complete the table of values for y = x2 – 2
b) Draw the graph of y = x2 – 2
-2 -1 O 1 2 3
-3
-2
-1
1
2
3
4
5
6
7
c) Use the graph to estimate thevalues of x when y = 1
2) a) Complete the table of values for y = 4x2
b) Draw the graph of y = 4x2
c) Use the graph to estimate thevalue of y when x = 1.5
-2 -1 O 1 2-2
2
4
6
8
10
12
14
16
y
x
x
y
x -2 -1 0 1 2
y 16 4 0 4 16
×
×
×
×
×
×
×
×
×
×
×
x = -1.7, 1.7
y = 9
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
A29Graphs of Quadratic and
Cubic Functions
Page 124B
x -2 -1 0 1 2
y 0 -1 0 3 8
3
15
1) a) Complete the table of values for y = x2 + 2x
b) Draw the graph of y = x2 + 2x
c) Use the graph to estimate thevalues of x when y = -0.5
2) a) Complete the table of values for y = x2 – 2x + 1
b) Draw the graph of y = x2 – 2x + 1
c) Use the graph to estimate thevalue of y when x = 2.5
y
x
x
y
x -2 -1 0 1 2
y 9 4 1 0 1
-2 -1 O 1 2 3-1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
3
4
-2 -1 O 1 2 3
1
2
3
4
5
6
7
8
9
10
11
12
13
×
×
××
×
×
×
× ×
×
×
×
x = -0.4, -1.7
y = 2.2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
A29Graphs of Quadratic and
Cubic Functions
Page 124C
x -2 -1 0 1 2
y 1 -3 -3 1 9
1) a) Complete the table of values for y = 2x2 + 2x – 3
b) Draw the graph of y = 2x2 + 2x – 3
c) Use the graph to estimate thevalues of x when y = -2
2) a) Complete the table of values for y = x3 + x
b) Draw the graph of y = x3 + x
y
x
x
y
x -2 -1 0 1 2
y -10 -2 0 2 10
-2 -1 O 1 2
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-2 -1 O 1 2
-10
-8
-6
-4
-2
2
4
6
8
10
×
×
××
×
×
×
×
×
×
x = 0.4, -1.3
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
S30Pythagoras’ Theorem
Page 125A
123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789123456789012345678912345678901234567891234567890123456789
12345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345678901234512345
12345123451234512345
1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123123456789012345678901231234567890123456789012312345678901234567890123
123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345123456789012345
1) Use Pythagoras’ theorem to work out the areas of squares A and B.
AB
2) Use Pythagoras’ theorem to work out the areas of squares C and D.
Area25 cm2
Area100 cm2
CArea
841 cm2
Area441 cm2
D
10squares
13squares
125 cm2
400 cm2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
S30Pythagoras’ Theorem
Page 125B
1) Find the lengths of the sides of these three squares.
a) b) c)
Area529 cm2 Area
210.25 cm2
Area152.7696 cm2
2) Find the lengths of the sides labelled a to d.
8 cm
15 cm
a
12 cm
35 cmb
29 cm
21 cm
c25 cm
24 cm
d
23 cm 14.5 cm 12.36 cm
17 cm 37 cm
20 cm
7 cm
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Pythagoras’ Theorem
Page 125C
1) Calculate the lengths of the sides a to f, giving each answer to 1 decimal place.
12 cm
7 cm 18 cm 13 cm
6.4 cm
12 cm
a
b
c
13.8 cm3.7 cm
9.6 cm
4.5 cm
15.8 cm
18.3 cm
d
ef
2) Calculate the lengths of the sides a and b, giving each answer to 1 decimal place.
17 cm
10 cm13 cm
15 cm
a
b
3) Find the height of this isosceles triangle.Give your answer to 1 decimal place.
13 cm
16 cm
4) Find the area of this isosceles triangle.
25 cm
14 cm
13.9 cm
12.4 cm
10.2 cm
13.3 cm
10.6 cm
9.2 cm
13.7 cm
19.8 cm
8 cm
13 cm
10.2 cm
7 cm
24 cm
168 cm2
S30
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 126A
S31Areas of
Compound Shapes
1) Find the areas of the following shapes:
7 cm
4 cm
12 cm
6 cm
8 cm
9 cm
a) b) c)
d) e)
16 cm10 cm
2) Find the areas of the following shapes:
14 cm
13 cm
5 cm
9 cm
20 cm17 cm
18 cm
6 cm
12 cm
7 cm 7 cm
5 cm 3 cm4 cm
a) b)
c)
Take to be 3.142
28 cm2
36 cm2 36 cm2
314.2 cm2201.088 cm2
142 cm2
174 cm2
100 cm2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
12345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123123456789012345678901234567890121234567890123456789012312345678901234567890123456789012123456789012345678901231234567890123456789012345678901212345678901234567890123
Page 126B
S31Areas of
Compound Shapes
1) Find the areas of the following shapes:
7 cm
9 cm
4 cm
5 cm
12 cm
5 cm9 cm
13 cm
11 cm
9 cm6 cm
6 cm
2) Find the areas of the shaded parts of the following:
a) b) c)
123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456
1234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012123456789012345678901234567890121234567890121234567890123456789012345678901212345678901212345678901234567890123456789012123456789012
123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789123456789012345678901234567890121234567890123456789
14 cm
8 cm
11 cm
5 cm15 cm
11 cm
7 cm
8 cm
15 cm
6 cm
24 cm
Take to be 3.142 when needed.a) b)
c)d)
40.5 cm2
109 cm2
57 cm2
137 cm2
111.888 cm2
123.552 cm2
84 cm2
15 cm
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 126C
S31Areas of
Compound Shapes
Find the areas of the shapes below:
Take to be 3.142
16 cm
22 cm12 cm
20 cm
20 cm
23 cm
a)
b)
c)
452.544 cm2
224.556 cm2
67.0695 cm2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 127
S32Volumesof Prisms
Find the volumes of the prisms, below.Take to be 3.142 for questions c and d.
5 cm
6 cm
8 cm
3 cm
8 cm
10 cm
4 cm
5 cm19 cm
23 cm
12 cm
13 cm
2 cm
9 cm
10 cm
6.4 cm
25.7 cm
30 cm
a) b)
c) d)
e) f)
Volume = 240 cm3
Volume = 120 cm3
Volume = 251.36 cm3
Volume = 6522.0065 cm3
Volume = 1380 cm3
Volume = 2448 cm3
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 128
S33Surface Area
of Triangular Prisms
1) Find the total surface area of this triangular prism.
10 cm
12 cm 13 cm
20 cm
2) Find the total surface area of this triangular prism.
7.2 cm
6.5 cm9.7 cm
3) Find the total surface area of this triangular prism.You will need to use Pythagoras’ theorem at somestage to get the answer.
10.2 cm
14 cm
24 cm
840 cm2
23 cm
585 cm2
1102.8 cm2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 129
S34Loci
1) Draw the locus of all the points that are 1.2 cm away from the line AB.
A B
2) Draw the locus of all the points that are 1.5 cm away from the rectangle ABCD.
3) Radio signals can be heard within a 4.5 km radius of transmitter A and a 5.5 km radiusof transmitter B. Show, by shading, the area where radio signals can be heard from bothtransmitters at the same time. Use a scale of 1 cm represents 1 km.
A B
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 130
S35Enlargement by a
Negative Scale Factor
O 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
1) Enlarge line AB with scale factor -2 andpoint (7, 6) as the centre of enlargement.
A
B
O 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
2) Enlarge line AB with scale factor -3 andpoint (3, 4) as the centre of enlargement.
A
B
O 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
3) Enlarge triangle ABC with scale factor -2and point (7, 6) as the centre of enlargement.
A
B
O 1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
x
y
A
B
4) Enlarge triangle ABC with scale factor -1.5and point (4, 5) as the centre of enlargement.
C
C
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 131
S36Bounds
1) The length of a bracelet is 24 cm measured tothe nearest centimetre.
a) Work out the lower bound of the length ofthe bracelet.
b) Work out the upper bound of the length ofthe bracelet.
2) The length of a snake is 80 cm measured tothe nearest 10 centimetres.
a) Work out the lower bound of the length ofthe snake.
b) Work out the upper bound of the length ofthe snake.
3) The weight of a necklace is 145 g measured tothe nearest 5 grams.
a) Work out the lower bound of the weight ofthe necklace.
b) Work out the upper bound of the weight ofthe necklace.
4) The length of a line is given as 17.2 cmmeasured to the nearest tenth of a centimetre.
a) Work out the lower bound of the length ofthe line.
b) Work out the upper bound of the length ofthe line.
5) A rectangle has a length of 80 cm and a width of60 cm, both measured to the nearest 10 cm.
a) Work out the lower bound of the area ofthe rectangle.
b) Work out the upper bound of the perimeterof the rectangle.
6) A right-angled triangle has lengths as shown, allmeasured to the nearest centimetre.
a) Work out the lower bound of the area ofthe triangle.
b) Work out the upper bound of the area ofthe triangle.
80 cm
60 cm
12 cm
5 cm
23.5 cm
24.5 cm
75 cm
85 cm
142.5 g
147.5 g
17.15 cm
17.25 cm
4125 cm2
300 cm
25.875 cm2
34.375 cm2
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 132
S37Compound Measures
1) A car travels at 60 mph for 3 hours.How far does the car travel?
2) A cyclist cycles for 4 hours and covers a distance of 48 miles.What was her average speed in miles per hour?
3) How long would it take a train which travels at an average speedof 80 mph to cover a distance of 400 miles?
4) A runner runs at a speed of 12 km/h for 3 hours and 15 minutes.How far does he run?
5) An aeroplane flies at an average speed of 510 mph.How long would it take to fly a distance of 2720 miles?
6) If a worm travels a distance of 8.25 m in 2 hours and 45 minutes, work outhis average speed in metres per hour.
7) 12.5 cm3 of mercury has a mass of 170 g.Work out the density of mercury.
8) Platinum has a density of 21.4 g/cm3.What is the mass of 35 cm3 of platinum?
9) A quantity of ice had a mass of 62.56 g.Knowing that ice has a density of 0.92 g/cm3, work out how muchice there was, in cm3.
15000 cm3 of nitrogen has a mass of 18.765 g.Work out the density of nitrogen in g/cm3.
15000 cm3 of gold has a mass of 289.5 kg.Work out the density of gold in g/cm3.
10)
11)
180 miles
12 mph
5 hours
39 km
5 hours and 20 minutes
3 metres per hour
13.6 g/cm3
749 g
68 cm3
0.001251 g/cm3
19.3 g/cm3
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 133A
D14Averages from Tables
1) Sally conducted a survey to see how many sandwiches each pupilbrought to school in her class per day.The results can be seen in the table.
a) What is the modal number of sandwiches brought to school?
b) What is the median number of sandwiches brought to school?
c) Work out the mean number of sandwiches brought to school.Give your answer to 1 decimal place.
24
2) 50 hippos were captured over the course of a year and weighed.The results can be seen in the table, below.
Work out an estimate for the mean weight of a hippo.Give your answer to 1 decimal place.
22.9 w < 3.2<
Weight of hippoin tonnes
Frequency
5
9
15
12
7
1.4 w < 1.7<
1.7 w < 2.0<
2.0 w < 2.3<
2.3 w < 2.6<
2.6 w < 2.9<
3 sandwiches
3 sandwiches
2.3 sandwiches
2.2 tonnes
No. ofsandwiches
Frequency
1
5
6
12
0
1
2
3
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 133B
D14Averages from Tables
Jenny had a theory that if asked to guess the length of a line, childrenunder the age of 10 would overestimate the length but adults wouldunderestimate the length.
To help her decide if she was correct she asked 100 under-10s and100 adults to guess the length of a 34 cm line.
The results can be seen in the two tables, below.
Use the results in the tables to see if Jenny was correct.Show all your workings.
Estimate oflength in cm
Frequency
4
11
24
39
22
20 l < 24<
24 l < 28<
28 l < 32<
32 l < 36<
36 l < 40<
Children under the ageof 10 estimates
Estimate oflength in cm
Frequency
2
6
16
62
14
20 l < 24<
24 l < 28<
28 l < 32<
32 l < 36<
36 l < 40<
Adult estimates
Estimate for the meanlength is 32.56 cm
Estimate for the meanlength is 33.2 cm
The estimate for the mean for under-10s showthat, on average, they underestimated the lengthby 1.44 cm.On average, the adults underestimated by 0.8 cm.Therefore, Jenny is not correct because bothgroups underestimated the length of the line.
© Mathswatch Ltd
Level 7
Answers
C27 C28 C29 C30 C31 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25C26N22S30 S31 S32 S33 S34 S35 S36 S37 D14 D15A27 A28 A29A26
Page 134
D15Relative Frequency
1) Peter bought an unfair dice from a Joke Shop.He didn’t know how the dice was biased and so he rolled it100 times and noted down which numbers came up.
He found that the number 6 occurred 8 times.
a) What is the relative frequency of getting a six?
b) If Peter rolls the dice 400 times, estimate how many6s he will roll.
2) Mary had a bag containing four different colour marbles.She chose a marble, noted its colour and then replaced it,80 times.
The results can be seen in this table.
a) Estimate the probability that a blue marble will bechosen on the next pick.
b) If a marble is chosen and replaced 280 times,estimate how many times you would expect tochoose a red marble.
ColourNo. of times
chosen
12
24
18
26
Red
Blue
Green
Yellow
3) Benford’s law says that if you look at real-life sources ofdata (heights of mountains, populations of countries, etc)the number 1 will be the first digit with relative frequency 0.3
If you go through any newspaper and write down the first 20numbers you come across, about how many of the numberswould you expect to begin with a ‘1’.
0.08 or 8100
32
or 0.32480
42 times
6
© Mathswatch Ltd
1) Total weight Weights to use
1 1
2 2
3 3
4 1 + 3
5 2 + 3
6 1 + 2 + 3
7 7
8 1 + 7
9 2 + 7
10 3 + 7
11 1 + 3 + 7
12 2 + 3 + 7
13 1 + 2 + 3 + 7
Answers to question 1which takes a pupil toLevel 3 and allows U3to be shaded.
All the weights from 1 kg to 13 kgcan be made
Using and Applying Maths
Weights QuestionsLevel 3
Page 135A
© Mathswatch Ltd
2)
Total weight Weights to use
1 1
2 2
3 1 + 2
4 4
5 1 + 4
6 2 + 4
7 1 + 2 + 4
8 8
9 1 + 8
10 2 + 8
11 1 + 2 + 8
12 4 + 8
13 1 + 4 + 8
14 2 + 4 + 8
15 1 + 2 + 4 + 8
1kg 2kg 4kg8kg
Using and Applying Maths
Weights QuestionsLevel 4
Answers to question 2.
Page 135B
© Mathswatch Ltd
3)
Total weight Weights to use
1 12 23 1 + 24 45 1 + 46 2 + 47 1 + 2 + 48 89 1 + 810 2 + 811 1 + 2 + 812 4 + 813 1 + 4 + 814 2 + 4 + 815 1 + 2 + 4 + 816 1617 1 + 1618 2 + 1619 1 + 2 + 1620 4 + 1621 1 + 4 + 1622 2 + 4 + 1623 1 + 2 + 4 + 1624 8 + 1625 1 + 8 + 1626 2 + 8 + 1627 1 + 2 + 8 + 1628 4 + 8 + 1629 1 + 4 + 8 + 1630 2 + 4 + 8 + 1631 1 + 2 + 4 + 8 + 16
1kg 2kg4kg
8kg
16kg
a)b) If you had six
weights, the bestones to have wouldbe:
1kg
2kg
4kg
8kg
16kg
32kg
With seven weightsit would be best tohave:
1kg
2kg
4kg
8kg
16kg
32kg
64kg
You can see thatevery extra weightshould be doublethe highest weightso far.
For n weights, you shouldhave
1, 2, 4, 8, . . . 2n-1
Definitely not necessaryfor level 4
Using and Applying Maths
Weights QuestionsLevel 4
Answers to question 3which, along with ques-tion 2, takes a pupil toLevel 4 and allows U4to be shaded.
Page 135C
© Mathswatch Ltd
4)
Total weight Weights to use
1 12 3 - 13 34 3 + 15 9 - 3 - 16 9 - 37 9 + 1 - 38 9 - 19 910 9 + 111 9 + 3 - 112 9 + 313 9 + 3 + 114 27 - 9 - 3 - 115 27 - 9 - 316 27 + 1 - 9 - 317 27 - 9 - 118 27 - 919 27 + 1 - 920 27 + 3 - 9 - 121 27 + 3 - 922 27 + 3 + 1 - 923 27 - 3 - 124 27 - 325 27 - 3 + 126 27 - 127 2728 27 + 129 27 + 3 - 130 27 + 331 27 + 3 + 132 27 + 9 - 3 - 133 27 + 9 - 334 27 + 9 + 1 - 335 27 + 9 - 136 27 + 937 27 + 9 + 138 27 + 9 + 3 - 139 27 + 9 + 340 27 + 9 + 3 + 1
1kg 3kg 9kg27kg
Weights needed to give allweights from 1 kg to 40kgwith no gaps.
For two weights we need theweights 1 and 3.
For three weights we need1, 3 and 9
For four weights we need1, 3, 9 and 27
To get the next weight in aset we multiply the highestweight in the previous setby 3.
For n weights, you should have
1, 3, 9, 27, . . . 3n-1
Definitely not necessaryfor level 5
Using and Applying Maths
Weights QuestionsLevel 5
Answers to question 4which takes a pupil toLevel 5 and allows U5to be shaded.
Page 135D
© Mathswatch Ltd
LEVEL 3 leading to U3 being shaded
Try different approaches to overcomedifficulties.
Organise work and check results.
Understand a general statement byfinding particular examples.
Review work and reasoning.
EVIDENCE
Question 1 is answered with all 13 weightseventually being found. Some help by theteacher can be given.
Work is organised, possibly in table form.It may not be ordered (ie the weights from 1to 13 will be seen but may not be in order).
Reasoning is clearly seen with the ways ofgetting the weights being shown.ie to get a weight of 7 we use 1 + 2 + 4
A general statement might be made such as“All the weights from 1 kg to 13 kg can befound”. This statement might be implied byseeing the ways of making these weights.The teacher may have to prompt the pupil tomake the statement.
LEVEL 4 leading to U4 being shaded
Develop own strategies for solvingproblems.
Use own strategies in a practicalcontext.
Present information in a clear andorganised way.
Search for a solution by trying out ideasof their own.
EVIDENCE
Questions 2 and 3 are answered.
Work is organised in ordered tables.
Pupils can answer the question “what do younotice?” by explaining that if you add aweight to the set it should be double the lastbiggest weight. Or, they may say the weightsare 1, 2, 4, 8, 16, etc where you get the nextweight by doubling the previous one.
LEVEL 5 leading to U5 being shaded
Check results considering whether theyare reasonable.
Solve word problems.
Show understanding of situations bydescribing them mathematically usingsymbols, words and diagrams.
Draw simple conclusions of their ownand give an explanation of theirreasoning.
EVIDENCE
Question 4 is answered.
Clear evidence can be seen of the pupilbreaking down the problem, probablyconsidering the case of having just twoweights. He/she will try having weights of 1, 2and 1, 3, and 1, 4. 1, 3 will be seen to givethe most possibilities.
Three weights will then be looked at and1, 3, 9 will finally be found.
Conjectures will probably be made and aprediction for the next weight will be seen.This will then be tested.
A general rule will be given (each extraweight should be three times the largestweight of the previous set).
Using and Applying MathsTeacher Markscheme
Page 135E
These worksheets should be usedtogether with the Balances video clip.
Extras
Balances 1 Answers
1) 2)
3) 4)
5) 6)
510
5
14
7
7
77
7
6 6
2020
Page 136A
These worksheets should be usedtogether with the Balances video clip.
Extras
Balances 2 Answers
1) 2)
3) 4)
6)5)
10
4 1 5
9 91818
10
40
5 5
6
1026 26
6 6
17 17
Page 136B
These worksheets should be usedtogether with the Balances video clip.
Extras
Balances 3 Answers
1) 2)
3) 4)
3
7
2
8
5
10
5
3
6
6
22
12
2121
17
6
4824
12
5
Page 136C
These worksheets should be usedtogether with the Balances video clip.
Extras
Balances 4 Answers
1) 2)
6)
1 1
13
6
1
101
12
5
20
32
11
262
3
1 2
1
24
4)
1
42 2
4
2
1
163)
4 4
3
2
1
11
16
5)
2
48
2
814
1
32
The 1, 1 and 2 canbe in any of thesethree circles.
2
Page 136D
These worksheets should be usedtogether with the Balances video clip.
Extras
Balances 5 Answers
1)
2)
Smallest possible
Highest possible
2
33
1
41
2
99
52
1
6
5
16
37
Page 136E
© Mathswatch Ltd
These worksheets should be usedtogether with the Congruent Halvesvideo clip.
1234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
1234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
1234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456
1234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
1234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345
12345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456
1)2)
3) 4)
5)
Extras
Congruent Halves Answers
6)
Page 137A
© Mathswatch Ltd
These worksheets should be usedtogether with the Congruent Halvesvideo clip.
123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567
123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
12345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567
7) 8)
9)
10)
Extras
Congruent Halves Answers
Page 137B
© Mathswatch Ltd
These worksheets should be usedtogether with the Congruent Halvesvideo clip.
123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567
123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567
123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567
11)
12)13)
Extras
Congruent Halves Answers
Page 137C
© Mathswatch Ltd
These worksheets should be usedtogether with the Congruent Halvesvideo clip.
12345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345123456789012345678901234567890121234512345678901234567890123456789012123451234567890123456789012345678901212345
123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567123456789012345678901234567890121234567
123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345123456789012345678901234512345678901234567890123451234567890123456789012345
123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456123456789012345678901234561234567890123456789012345612345678901234567890123456
14) 15)
16)
17)
Extras
Congruent Halves Answers
Page 137D
© Mathswatch Ltd
These worksheets should be usedtogether with the Congruent Halvesvideo clip.
12345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456
1234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456
123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456123456789012345678901234567890121234561234567890123456789012345678901212345612345678901234567890123456789012123456
18)
19)20)
Extras
Congruent Halves Answers
Page 137E
© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.
Extras
Circles Answers
13cm 9cm
15.6cm
1) 2)
3)
C = 40.846 cm C = 28.278 cm
C = 49.0152 cm
Find the circumference ofthe circles below
(138A)
Page 2
© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.
Extras
Circles Answers
2cm
5cm
1.8cm
7.5c
m
1)
2)
3)
4)
C = 12.568 cm
C = 31.42 cm
C = 11.3112 cm
C = 47.13 cm
Find the circumference ofthe circles below
(138B)
Page 3
© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.
Extras
Circles Answers
4cm
11cm
1.3cm
9.6c
m
1)
2)
3)
4)
A = 50.272 cm2
A = 380.182 cm2
A = 5.30998 cm2
A = 289.56672 cm2
Find the area of the circlesbelow
(138C)
Page 6
© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.
Extras
Circles Answers
24cm 17cm
16.9cm
1) 2)
3)
A = 452.448 cm2
A = 227.0095 cm2
A = 224.346655 cm2
Find the area of the circlesbelow
(138D)
Page 7
© Mathswatch LtdThese worksheets should be usedtogether with the Circles video clip.
Extras
Circles Answers
13cm
30cm
30cm 11cm
12cm 15.6cm 19.2cm
53cm
23cm
1)
2)
3)
A = 369.002 cm2
11cm
A = 25.9545 cm2
A = 625.162 cm2
Find the area of the shadedsections
(138E)
Page 8