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

97

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.