MATHS REVISIONMATHS REVISIONBY CAITLIN GREGORYBY CAITLIN GREGORY

Square numbers• A square number is when you times a number

by its self Eg 4 squared is 4 x 4 which equals 16.

• Use the table below which shows you all the square numbers

Multiples• Multiples are really just times tables.• EG: The multiples of 2 are all the numbers in the 2

times table:2, 4, 6, 8, 10 and so on.

• The multiples of 5 are all the numbers in the 5 times table:5, 10, 15, 20, 25 and so on. Questions: list 5 of these

times tables1. Four Times Tables2. Six Times Tables3. Seven Times Tables4. Eight Times Tables 5. Twelve Times Tables

4, 8, 12, 16, 206, 12, 18, 24, 307, 14, 21, 28, 358, 16, 24, 32, 4012, 24, 36, 48, 60

Common Big and Small Numbers Name NumberTrillion 1,000,000,000,000 Billion 1,000,000,000 Million 1,000,000Thousand 1,000 Hundred 100ten 10Unit 1 1Tenth 0.1Hundredth 0.01Thousandth 0.001Millionth 0.000 001Billionth 0.000 000 001Trillionth 0.000 000 000 001

Factors• Factors are numbers that divide

exactly into another number.• EG: The factors of 12, are 1, 2, 3, 4, 6

and 12Questions:1. The factors of 1 are 2. The factors of 2 are 3. The factors of 3 are 4. The factors of 4 are 5. The factors of 5 are

8. The factors of 8 are 9. The factors of 9 are 10. The factors of 10 are

6. The factors of 6 are 7. The factors of 7 are

Answers:1. One2. One and two3. One and three4. One, two and four5. One and five6. One, two, three and six7. One and seven8. One, two, four and eight9. One, three and nine10. One, two, five and ten

Prime NumbersA Prime Number is a number that can be divided

evenly only by 1, or itself. And it must be a whole number greater than 1.

Example: 5 can only be divided evenly by 1 or 5, so it is a prime number.but 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number

Questions: 1. Is the number 18 prime? no 5. Is the number 97 prime? yes 2. Is the number 45 prime? no 3. Is the number 79 prime? yes4. Is the number 90 prime? no

Algebra - Substitution"Substitute" means to put in the place of another.

• Substitution• In Algebra "Substitution" means putting

numbers where the letters are:• If you had x5+12= and you knew that x=2

and if a number and letter together means you’ve got to times them then you know all you have to do is 5x2+12= and then you can work out the answer in this case the answer is 22

Nth term• Nth term is when you replace

some letters for numbers

• Use this page to help you:

Finding the nth term•8,11,14

• The common difference is 3, so it must be related to the 3 times table (3n)

• The 3 times table is 3, 6, 9, ...The sequence is 8, 11, 14, ....

• Every term in the sequence is 5 more than the corresponding term in the 3 times table, so the nth term is 3n + 5.

Finding the nth term for a quadratic sequence

Finding nth term of a sequence

Eg. 2,5,10,17,262. Not a constant difference so we have to fine out the second difference.

3.This second difference is constant at 2.This means the nth term will start with n².4. But if you do replace 1 for n it will be 1² which is 1 but the first number

is 2 the difference between 2 and 1 is 1.If you replace 2 for n it will be 2² which is 4 but the second number is 5 the difference between 5 and 4 is 1.We can see here that it the terms in the sequence are 1 number high each time so we write the answer as…..

n²+1

1. Find the first difference.

Nth term2nd differences:• 2 = n²• 4 = 2n²• 6 = 3n²

Mean/Average• The mean is just the average of the

numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are.

• Listen to this

Median• The Median is the "middle

number" (in a sorted list of numbers). To find the Median, place the numbers you are given in value order and find the middle number.

Mode• The mode is simply the number

which appears most often. To find the mode, or modal value, first put the numbers in order, then count how many of each number.

Range

• The range means you have to take the small number away from the bigger number to get the range.

Modal group• If you had a stem and leaf diagram like this for example • 1/1,2,6 2/4,4,4,5,7,8,9 3/1,6 4/2 5/4,7

• The mode would be the value on the "leaf" that appears most frequently so in this case it would be 24.

• However, the modal group would be the group from the "stem" that has the most values, so in this case it would focus on the 20's.

• You would write it from the number on the stem to the highest in the group, like- 20-29.

•Frequency density = frequency ÷ class width

Angles• Angles are measured in degrees. The sign for degrees is °.• One whole turn is 360°. • One quarter turn is 90° or a right angle. • One half turn is 180° or a straight line.

An angle which is small then 90

Right angle-Straight angle- Obtuse angle- Full rotation angle- Acute angle-

Is formed by cutting a circle in quarters. 90

What is:

Half a circle. 180 An angle bigger than 90 but less than 180A whole circle. 360

Angle

Draw a line to the correct images:Right angle

Straight angle

Obtuse angle

Full rotation angle

Types of angles

Circle Theorems This is when there are triangle in a circle and you have to work out missing angles in different triangles. Use this page to help you:

Question:1) 2) 3)

20

17

45 113

54

Angles 2

• Angles in a triangle 180

Angles in parallel lines• When you have a:• 1. Vertically opposite angles they are equal. Also called the

X rule.• 2. Corresponding angles they are equal. Also called F rule.• 3. Alternate angles they are equal. Also called Z rule.• 4. interior angles add up to 180°. Also called C rule.

3. 4.

2.1.

Nets of 3D shapes• There may be several

possible nets for one 3D shape.

• What nets are the following:

The net of a 3D shape is what it looks like if it is opened out flat. A net can be folded up to make a 3D shape.

1.

3.

2.

4.

5.

cube

cuboid

Square based pyramid

cylinder

cone

The Pentagram

• The Pentagram (or Pentangle) is a 5-pointed star.

• Inside a Pentagram is a Pentagon

• You can make a pentagram by first drawing a pentagon, then extending the edges.

• Or by drawing lines from corner to corner inside a pentagon

Area• Area is the size of a surface!• Eg: These shapes all have the

same area of 9:

You can also find the area by multiplying 2 numbers Eg:

Area is the size of a surface!

11cm

5cm5cm

11cm

I will multiply 5 by 11 which is 55 so the area is 55cm squared

55cm squared

Perimeter• Eg: the perimeter of this rectangle is

7+3+7+3 = 20

• The perimeter of a circle is called the circumference

Perimeter is the distance around a two-dimensional shape.

Questions on perimeter:

1.

12cm

12cm

5cm

5cm 34cm

Rotation• The distance from the centre to any point

on the shape stays the same. Every point makes a circle around the centre.

• Here a triangle is rotated around the point marked with a "+"

"Rotation" means turning around a centre

Metric system• Liquids= millilitres + litres 1 litre = 1,000

millilitres • Weight= Grams, Kilograms, Tonnes 1

kilogram = 1,000 grams 1 tonne = 1,000 kilograms

• Length= Millimetres, Centimetres, Metres, Kilometres 1 centimetre = 10 millimetres 1 metre = 100 centimetres 1 kilometre = 1000 meters

• Temperature= Celsius, Fahrenheit

Symmetry

A 2D shape is symmetrical if a line can be drawn through it so that either side of the line looks exactly the same. The line is called a line of symmetry.

Shape Lines of symmetrySquare 4Equilateral triangle 3Parallelogram 0Isosceles triangle 1Rectangle 2

Negatives• When you have+ + together it equals a + • When you have - - together it equals a +• When you have + - together it equals a -• When you have - + together it equals a –• Eg: 2 + -5 would be 2 – 5 because a +-

together = - so the answer is -3

Questions:

2.

1.

Money• You have 10p

How much change will you get? 7p

3p change

Answer 4p

6p change

Answer

How much change will you get?

1.

2.

What is a product?

• The product is the answer you get when you multiply numbers. For example: If you multiply two times eight, the product (also know as the answer) is sixteen.

Multiplying decimals 1• You have to make both the decimal numbers

into whole numbers multiply it by 10, 100, 1000 etc then do the sum with whole numbers then divided the answer by the number you multiplied it by. Don’t forget to do divide twice if you have two numbers.

Multiplying Decimals 2

• 1 x 1 = 1• 0.75 x 0.75 = 0.5625• O.5 x 0.5 = 0.25• 0.25 x 0.25 = 0.0625

Multiplying Indices

Dividing Indices

Bracket Indices

Multiplying indices with different numbers

Indices

• Say we had this question 2( x 3 ) I would have to do 2 times which will be 2 then we will put that to the side. Then we will do 2 times 3 which will be 6 . Then we put the answers together to get the answer 2 +6 .

Adding like fractions

Multiplying mixed number fractions 2

1. Write out the sum

2. Write the mixed number as an improper fraction3. Cancel by dividing the top and bottom number by the number that equally goes into each number

4.

Adding fractions

6 2 8 4

Subtracting fractions 1 3 4 6

Multiplying fractions 2 5 3 6

Dividing fractions2 13 5

simplifying• Anything times by 0 is 0• Anything times by 1 is itself• Multiplying a number by itself is

called squaring

Volume of cuboid

22

Volume of a triangular prism

2

Volume of a cylinder

2

Questions

Pi equals

3.14

Perimeter of a circle

D

D stands for diameter.

Diameter

Area of a circle

R²

R stands for radiusRadius

Circumference of a circle

DOR2R

Properties of a circle

Radius

Chord

Sector

Arc length• Θ• 360º X D

ORX

2R

• Θ• 360º

Congruent

• The word 'Congruent' in maths means that two or more things are exact same size and shape. They should slot together when you place the shapes together.

Y=mx+cc

C

c

Gradient/Slope

• The method to calculate the Gradient is:

• Divide the change in height by the change in horizontal distance

• Gradient = Change in Y• Change in X

Please go to the next slide for some examples of this

The Gradient (also called Slope) of a straight line shows how steep a straight line is.

Examples1. The Gradient of this line

= 3/3= 1. So the Gradient is equal to 1

2. The Gradient of this line = 4/2 =2. (The line is steeper, and so the Gradient is larger)

3. The Gradient of this line = 3/5= 0.6. (The line is less steep, and so the Gradient is smaller) Click here

for some questions

Y Intercept

• In the above diagram the line crosses the Y axis at 1.

• So the Y intercept is equal to 1.

The Y intercept of a straight line is simply where the line crosses the Y axis.

Click here for some questions

• B-rackets• I-ndices• D-ivision• M-ultiplication• A-ddition• S-ubtraction

Mixed numbers to improper fractions

http://www.youtube.com/watch?v=shpf9krdXQQ

Percentage to decimal• Percent means "per 100", so 50% means 50 per 100, or

simply 50/100. If you divide 50 by 100 you get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the "%" sign. The Easy Way: The easy way to divide by 100 is to move the decimal point 2 places to the left, so From Percent To Decimal move the decimal point 2 places to the left, and remove the "%" sign.

Cubic function

Click here to see a video explaining this.

Reciprocal function

Click here to see a video explaining this.

Pythagoras Theorem

• A² + B² = C²• √c²

A

B

C?

OR

Pythagoras Theorem 2

• C² - B² = A²• √A²

A?

B

C

Angles in a triangle• To figure out the angle inside any

shape your have to do 180º(n-2)• N stands for the number of sides a

shape has.• Example:

This shape has 6 sides so 6-2=4. Then you have to do 180ºx4=720º.The interior angles add up to 720. To find each individual angle do 720º / 6 = 120º

OR

• See how many triangles can be formed in the shape. Then times it by 180º.

• Example:As you can see we can create 6 triangles from this octagon. We then do 180ºx6=1080º.We can do the same for each individual angle.1080º/8=135º

Cumulative frequency• N always stands for how many

numbers there are in the sequence.

• Lower quartile - ⅛• Median - ⅛• Upper quartile - ⅛

4

2

4

n

N

3n

Mode – Most oftenRange – largest – smallestMedian – middle when in orderMean – Total of added numbers / number of numbers

3D shapes• Vertices – corners

• Edges – sides/edges

• Faces - faces

Volume• H x w x l

• H=height• W=width• L=length

Probability• I have 2 dice• 1 has the numbers 2,4,6,8 on• The other dice has the numbers 2,3,4,5 on• If I roll both dice and add both number

together. What would the probability be that I get an even total?

• Green=even+ 2 4 6 82 4 6 8 103 5 7 9 114 6 8 10 125 7 9 11 13

P(Even number)= 8 = 1 16 2

• Expand the brackets

• (y+9)(y+2)

Answer:

Y² +11y

18

•Simplify

•6y² + 12y•You have to think of a number and/or letter

that goes into both 6 and 12. In this case it will be 6. Then complete the simplifying.

• Answer : 6y(y+2)

Cumulative frecuency-finding the median and interquartile range for grouped data

• Watch this video

Sine rule – no right angle, a matching pair

(angle)

65

10 7.1

θ

Sin 65 Sin θ10 7.1

=

=10Sin θ 7.1Sin 65

Sin θ = 7.1xSin 6510

θ =Sin ( )

7.1xSin 6510

-1

θ = 40.1

Sine rule – no right angle, a matching pair

(side)

Cosine rule – no right angle, no matching pair• a²= b²+ c² - 2bc Cos A

9km

12km

x

20A B

C

ab

c

a²=9²+12²-2 x 9 x 12 x Cos 20a²= 81 + 144 -2 x 9 x 12 x Cos 20a²= 225 – 202.974a²= 22.026a²=√22.026a=4.7km

Interior angles

•n-2 x 180

Exterior angles

•Always add up to 360˚