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TRANSCRIPT
1
2
3
4
Decimals, Fractions and Percentages
(with a calculator)
5
6
Bodmas
Whole Number
7
Ratio and Proportion Simplifying
Expressing and simplifying
8
Direct Proportion
Splitting a ratio up
9
Mixed questions
10
11
Calculations in Social Context Wages
12
13
14
15
Algebra Simplifying
16
Simplifying – Extension
17
Evaluating
18
19
20
21
Removing brackets
22
23
Factorising
24
Solving Equations
Answers
25
26
27
Extension Equations
Problem Solving Equations
28
29
Symmetry Line Symmetry
30
31
32
33
34
35
36
Rotational Symmetry
37
38
39
Probability
40
41
42
43
Changing the subject of the formula
44
Straight Line
45
46
Distance, Speed and Time
1. In each of the following, find the average speed in an appropriate unit.
a b c d e
Distance 150km 440km 980km 54cm 500m
Time 4 h 55sec 14 h 4·5sec 40 min
2. In each of the following, find the distance travelled.
a b c d e
Average speed 48km/h 600km/h 2½ km/h 45cm/s 300m/s
Time 4 h 6h 40 min 4½ h 2½ sec 2 min
3. In each of the following, find the time taken.
a b c d e
Distance 4200 km 27 cm 440 m 1·7 m 3 km
Average Speed 600v km/h 54 cm/s 55 m/s 85 cm/s 7·5 m/min
4. What average speed must I keep up to travel to Salzburg from Rotterdam, a
distance of 1035 km, in 9 hours ?
5. The Royal Scot train leaves Glasgow at 1000 and reaches London at 1645. If
the distance is 624 km, what is the average speed, correct to the nearest km/h ?
6. A spacecraft travelling at an average speed of 17600 km/h takes 21 h 30 min
to reach the moon from launching time. Estimate the distance from the earth
to the moon correct to the nearest 1000 km.
7. An artificial satellite orbits the earth once every 2 h 10 min. If its average
speed is 23200 km/h, what is the length of its orbit correct to the nearest 100
km ?
8. A jet air airliner leaves New York and flies at an average speed of 825 km/h.
How long will it take to reach London which is 6600 km away ?
47
9. If a man walks at an average speed of 6 km/h, how far will he walk
in 25 minutes ?
10. If a motor car covers 30 km in 40 minutes, find its average speed in km/h.
How long will a journey of 112½ km take if the driver keeps up the same
average speed but stops for half an hour for coffee on the way ?
11. A boy can walk to school in 15 minutes. If he can cycle three times as fast as
he can walk, how long does it take him to cycle to school ?
The distance from his house to the school is 1200 m. Calculate his average
walking speed and his average cycling speed in km/h.
12. The times of some trains between Aberdeen and Edinburgh are as follows :
Aberdeen dep 0730 1205 1745 1915
Dundee arr 0902 1342 1922 2055
dep 0905 1352 1929 2100
Kirkcaldy dep – 1500 2025 2158
Edinburgh arr 1030 1540 2105 2239
a If the trains which stop at Kirkcaldy halt there for 2 minutes, find the actual
travelling time of each train between Aberdeen and Edinburgh.
b The distance between Aberdeen and Edinburgh is 190 km. find the average
speed of each train for the whole journey, to the nearest km/h.
13. The world record for the 100 m race set in 1960 was 10 seconds.
What average speed is this in km/h ?
14. What is the speed of light ?
What is the distance between the sun and the earth ?
How long does it take light from the sun to reach the earth ?
48
Time, Distance, Speed Solutions
1.
a b c d e
Speed 37·5 km/h 8 m/s 70 km/h 12 cm/s 12·5 m/min
2.
a b c d e
Distance 192 km 4000 km 11·25 km 112·5 cm 36 km
3.
4. 1035 ÷ 9 = 115 km/h
5. 624 ÷ 6·75 = 92·444 . . . = 92 km/h (to nearest km/h)
6. 17600 × 21·5 = 378400 km = 378000 km (to 1000 km)
7. 23200 × 2·1666 . . = 50266·66 . . . = 50300 km (to 100 km)
8. 6600 ÷ 825 = 8 h
9. 6 × (25 ÷ 60) = 2·5 km
10. 45 km/h 112·5 ÷ 45 = 2·5 h 2·5 + 0·5 = 3 h
11. 5 min ; 1200 m ÷ 15 min = 1·2 km ÷ 0·25 h = 4·8 km/h ; 14·4 km/h
12. a 2 h 57 min, 3 h 23 min, 3 h 11 min, 3 h 17 min
b 63 53 57 56 km/h
13. 100 m ÷ 10 sec = 0·1 km ÷ (1/360) h = 36 km/h
a b c d e
Time 7 h ½ sec 8 sec 2 sec 6 h 40 min
49
Distance – Time Graphs.
1. The graph shows the journey of a cyclist who travelled between
two towns 40 miles apart.
Using the graph, find the
following :
a The time the cyclist began
the journey
b The time at which he
stopped
c For how long he stopped
d Between which times he
was cycling the fastest.
e His average speed for the
whole journey.
2. The graph shows a car journey of 80 miles,
which Tricia and Mike took when they were in Yorkshire on
holiday. They stopped twice to visit places of interest.
a At what times did they stop ?
b How long did they spend on the second visit ?
c How long in total did they spend travelling ?
d What was their average speed for the 80 mile journey ?
50
4. The graph shows Hazel‘s
motorway journey. At one point
she was held up by road works.
a At what time did Hazel meet
the road works?
b How far did the road works
stretch?
c How long did she stop ?
d What was her average speed
for the whole journey ?
5. Dave recently travelled by car
to the Lake District.
Here is a graph of his journey.
a For how long did he stop?
b What was his fastest
average speed during the
journey ?
c What was his overall
average speed for the journey?
d At what time did he arrive
at his destination ?
3. The graph shows Sarah‘s
recent cycling trip to visit
her aunt.
a How far did Sarah
cycle?
b When was Sarah
cycling slowest ?
c What was her average
speed for the journey ?
51
6. The graph shows how three
people travelled from their
homes in the same village to
their work in the same town 10
miles away.
Paul travelled by bus, Celia
cycled
and Jim travelled by car.
The lines on the graph are
labelled a, b and c. Match
one line to each person giving
reasons.
7. Ken and Jim went on a cycling trip.
The graph shows both their journeys.
a For how long did Ken stop ?
b At what time did Jim set off ?
c At what time did they both arrive ?
d Calculate each of their average
speeds.
8. The graph shows how a cyclist and a motorist travelled between
two towns
80 kilometres apart.
a Who left first?
b Who arrived first?
c At what time
(nearest 5 min) did
the motorist pass the
cyclist ?
d Calculate each of
their average speeds.
52
9. Peter and Derek live 40 miles
apart. They each decide to cycle
to visit friends in the other town.
Their journeys are shown on the
graph.
a When did Peter leave ?
b At what time (nearest 5 min)
did they pass each other ?
c Who completed the journey
in the shorter time ?
d Calculate each of their
average speeds.
10.
The graph shows how
Mary and Gwen cycled
between their two
towns.
a At what time did they
pass each other ?
b How long did Gwen
spend resting ?
c How long did Mary
spend cycling ?
d Who had the faster
average speed ?
11. Liam is travelling to meet a client who live 60 miles away. He left
his office at 11 am and travelled the first 40 miles in 1 hour. He stopped
for 30 minutes to have lunch and then completed the journey in half an
hour.
Show his journey on a distance time graph.
53
12. Two friends live 60 kilometres apart. They arrange to meet at
some point on the road between their homes. Keith leaves at 9:45
am and cycles for 1½ hours at an average speed of 16 kph. He then
stops for 30 minutes for a rest. when he sets off again he cycles at
an average speed of 18 kph.
Brian sets out at 10 am and covers the first 14 km in 1 hour. After
a rest for half an hour, he continues at an average speed of 16 kph.
a) Show both journeys on a distance time graph.
b) At what time do they meet ?
c) Who had cycled further ?
13. Sandra sets off to complete a 20 mile sponsored walk. In training
she has averaged a speed of 4 mph. She plans to stop for 15
minutes rest every 2 hours. The walk starts at 10:30 am.
a) Show Sandra‘s walk on a distance time graph
Sandra‘s brother Graham intends to jog round the course and
reckons to average a speed of 6 mph. He sets out at 11 am.
b) Show Graham‘s run on the same distance time graph
c) At what time will Graham overtake Sandra ?
54
Distance – Time Graphs. Solutions
1. a 9 am b 11 am c 40 min d 10 am – 11 am e 10
mph
2. a 1100 1150 b 40 min c 2 h 10 min d 28·24 mph
3. a 40 miles b 0900 – 1000 c 13·33 mph
4. a 1500 b 10 miles c 30 min d 30 mph
5. a 30 min b 62·5 km/h c 45 km/h d 11 am
6. a Jim b Paul c Celia
7. a 45 min b 11 am c 1:15 pm d Ken 12·31 km/h Jim
17·78 km/h
8. a cyclist b motorist c 1:10 pm d 16 km/h 30 km/h
9. a 1030 b 1150 c Peter d Derek 13·33 mph Peter
44·55 mph
10. a 1100 b 80 min c 2 h 40 min d Mary
11.
55
12.
b 1215
c Keith
13.
a
b
c 1200
56
Significant Figures
57
Scientific Notation
58
59
60
61
Practice Unit Assessment (1) for National 4 Expressions and
Formulae 1. (a) Expand the brackets:
5(2m – 7)
(b) Expand the brackets and simplify:
2(4k + 3) + 2k.
2. Factorise 4x + 32.
3. Simplify 3m + 5n + 6m – 2n.
4. (a) When x = 2 and y = 3, find the value of 5x – 3y.
(b) Norrie is a plumber.
He calculates the cost of a job using the formula:
C = 26·5H +1·5M
where C is the cost (in pounds), H is the number of hours he works,
and M is the number of miles he travels to the job.
On one job he worked for 7 hours and travelled 32 miles.
Calculate how much Norrie charged for this particular job.
5. A skateboard ramp has been designed to have the following dimensions.
The ramp can only be used in competitions if the gradient of the slope is
greater than 0·3.
(a) Calculate the gradient of the slope.
(b) Can this ramp be used in a competition? Give a reason for your
answer.
6. Andy’s Autos have designed a new logo for their company.
Part of the design for the logo is shown on the worksheet
Complete this shape so that it has rotational symmetry of order 4, about 0.
7. An octahedral die has eight faces numbered one to eight.
When it is thrown it comes to rest on one of its faces.
What is the probability that it comes to rest on a number greater than 3?
15 m
4 m
62
Practice Unit Assessment (1) for National 4 Numeracy
1. I have just bought a new washing machine. The price was £400 + VAT.
VAT is charged at 20%.
What was the total price of the washing machine?
2. An empty container weighs 120g. When 50 lollipops were put in it the weight
was 870g.
What is the weight of one lollipop?
3. Anne is going to Malta. How many euros will she get for £150 when the
exchange rate is 1·18 euros to a pound?
4. Complete the table on the worksheet which shows departure and arrival times
for different bus journeys.
5. A car travels at a constant speed of 63 mph for 20 minutes.
How far does the car travel in this time?
6. After a lottery win of £350 000, the money was divided between the two
winners, Charlie and Fred, in the ratio 3 : 4.
Fred received £200 000.
Is this the correct amount?
Justify your answer by calculation.
7. A liquid is warmed from – 6oC to –2C.
By how many degrees has its temperature risen?
8. Some water has been added to this measuring jar.
How much more water is needed to fill the jar to 1·5 litres?
2 litre
1 litre
63
9. Two shops are selling the same holiday. They are offering these for sale with
different deals.
Which shop has the cheaper deal?
Justify your answer by calculation.
10. This triangle is right-angled.
(a) Measure the length of the longest side.
(b) Measure the size of the shaded angle.
11. Carrots are being sold in different sizes of packet in the supermarket.
Pack A contains 400g of carrots and costs £1.20
Pack B contains 200g of carrots and costs 65p
Fiona needs to buy at 1000g of carrots as cheaply as she can.
How many packs of each size should she buy?
How much will this cost?
Sun Holidays
Deposit £120
Six payments of £67·80
64
Practice Unit Assessment (1) for National 4 Relationships 1. (a) Complete the table on the worksheet for y = 2x + 1.
(b) Draw the line y = 2x + 1 on the worksheet.
2. Line CD is shown on the grid below.
Write down the equation of line CD.
3. Solve the following equation:
3y + 7 = –14
4. To find the distance of a journey we use the formula D = ST
Change the subject of the formula to T.
5. Change the subject of the formula
a = 7b + 2 to b.
x
y
0
5
10
– 5
– 10
5 10 – 5 – 10
C D
65
66
67
Circle Circumference
68
69
Area
70
71
Mixed Problems
72
73
Shapes Composite shapes
74
75
76
Nets
1 Draw the net of a cube with side length 4cm
2 Draw the net of a cuboid with dimensions 5cm x 2cm x 3cm
3 Draw the net of a square based pyramid with base
dimensions 5cm and slope height 7cm
4 Draw the net of a triangular prism with length 10cm and
cross-sectional area dimensions base 5cm and height 6cm
77
Surface Area
78
Perimeter and Area
79
80
81
82
83
84
85
86
87
Statistics
Tally Charts (frequency tables)
88
Grouped frequency tables
89
90
91
92
93
94
95
96
Practice Unit Assessment (2.1) for National 4 Numeracy
1. The diagram shows an L – shaped room which is made up from two
rectangles.
A decorative border has to be put round the room. There is 25 metres on the
roll.
Is the roll long enough for the room?
Justify your answer by calculation.
2. The number of pupils in each year group in a secondary school was recorded
and this pie chart drawn.
There are 1200 pupils in the school.
How many pupils were there in S5/6?
8m
6m
1·5m
1·5m
S3
60o
S1
S4
S2
S5/6
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3. The table below shows the amount of yearly interest a selection of banks will
pay to a customer on savings.
Bank
Less
than
£1000
£1000 to
£5000 (inc)
Between
£5000 and
£10000
£10000 or
more
A 0·5% 0·6% 0·8% 1%
B 0·6% 0·7% 0·9% 1·1%
C 0·5% 0·8% 0·8% 1%
D 0·5% 0·6% 0·7% 0·9%
For a savings amount of £6000, which bank would pay the most interest?
4. The number of people using a gym each day was recorded for a week and this
compound bar chart was drawn.
(a) How many males used the gym on Friday?
(b) Compare the use of the gym by both males and females across the
week.
5. Three mobile phone companies each have a contract available at the same
price.
Company A Company B Company C
Calls (minutes) 100 120 130
Texts 1000 750 800
Internet (Mb) 150 160 140
Amina is looking for a mobile phone contract which will give her 90 minutes
of calls, 900 texts, and 140Mb of internet use.
Which company’s plan would be best for her?
Mon
Tues
Wed
Thurs
Fri
Sat
Sun
DAY
PE
OP
LE
0
20
40
60
80
100
Female
Male
98
6. Tickets are being sold for two different prizes at a fayre.
Corinne has tickets for both.
80 tickets have been sold for prize A and 120 tickets have been sold for prize
B.
Corinne has 5 tickets for prize A and 8 tickets for prize B.
Which prize has Corinne the better chance of winning?
Justify your answer by calculation.
7. Sally scored the following marks in three of her tests.
Maths: 25 out of 40
English: 32 out of 50
Science: 38 out of 60
In which subject did she do best in?
Justify your answer by calculation.