1. 2003 Paper 4

2. 1.(a) Use your calculator to work out2
( ) x 1.07
Write down all the figures on your calculator display.
Put brackets in the expression below so that its value is
x x 4.2

3. ANSWER 1798.67 2 (2.3+1.8)X x1.07= Use your calculator to work out 2

4. Put brackets in the expression below so that its value is 45.024
x x 4.2
( ) x x 4.2= =
(3.8 x 2.4) x 4.2 =
x (2.4 x 4.2) =
( x 2.4) x 4.2 =
ANSWER ( x 2.4) x 4.2

5. 2. Simon repairs computers.
He charges
£56.80 for the first hour he works on a computer and
£42.50 for each extra hour’s work.
(a) Yesterday Simon repaired a computer and charged a total of £269.30
Work out how many hours Simon worked yesterday on this computer.
Simon reduces his charge by 5% when he is paid promptly.
He was paid promptly for yesterday’s work on the computer.
(b) Work out how much he was paid.

6. ANSWER 6 hours £56.80 for the first hour he works on a computer and
£42.50 for each extra hour’s work.
(a) Yesterday Simon repaired a computer and charged a total of £269.30
Work out how many hours Simon worked yesterday on this computer.
1 hour at £5.60
£ £56.80 =
£212.50
Number of hour worked at £42.50 per hour =
£212.50÷£42.50
= 5hours
Total hours worked = 5hours + 1 hour = 6 hours
ANSWER 6 hours

7. Simon reduces his charge by 5% when he is paid promptly.
He was paid promptly for yesterday’s work on the computer.
(b) Work out how much he was paid.
5% of £ =
£13.465
5 x £ =
100
£13.47
Amount he was paid = £ £13.47
ANSWER £255.83

8. 3. o X o y
This is part of a design of a pattern found at the theatre of Diana at Alexandria
It is made up of a regular hexagon, squares and equilateral triangles. o
(a) Write down the size of the angle marked x
(b) Write down the size of the angle marked y 2
The area of each triangle is 2cm .
(c) Work out the area of the regular hexagon.
In the space below use a ruler and compass to construct an equilateral
triangle with sides of length 4 centimetres.
You must show all construction lines.

9. o X o y
This is part of a design of a pattern found at the theatre of Diana at Alexandria
It is made up of a regular hexagon, squares and equilateral triangles. o
Write down the size of the angle marked x
The triangle is an equilateral triangle.
All the sides and angles of the equilateral triangle are equal triangle. o
Angles in a triangle add up to 180 . o
Angle x = 180 ÷ 3 . O
ANSWER X = 60

10. O ANSWER Y = 120 (b) Write down the size of the angle marked y o y 4 3
Sum of angles in the hexagon = 4x180
Sum of angles in the hexagon = 720
Angle Y = 720 ÷ 6 O
ANSWER Y = 120

11. ANSWER Area hexagon = 12 cm
The area of each triangle is 2cm .
(c) Work out the area of the regular hexagon.
Area Hexagon = 6 x Area Triangle 2
Area Hexagon = 6 x 2 cm O
ANSWER Area hexagon = 12 cm

12. (d) In the space below use a ruler and compass to construct an equilateral
triangle with sides of length 4 centimetres.
You must show all construction lines.
4 cm

13. In 2002, Shorebridge Chess Club’s total income came from a council grant
and members’ fees.
Council grant £50
Members fees x £5 each
(a) (i) Work out the total income of the club for the year 2002.
(ii) Find the council grant as a fraction of the club’s total income
for the year 2002
Give your answer in the simplest form.
In 2001, the club’s total income was £1000.
The club spent 60% of its total income on a hall.
It spent a further £250 on prizes.
(b) Work out the ratio
The amount spent on the hall : the amount spent on pizzas.
Give your answer in its simplest form.

14. In 2002, Shorebridge Chess Club’s total income came from a council grant
and members’ fees.
Council grant £50
Members fees x £5 each
(a) (i) Work out the total income of the club for the year 2002.
Total income = Council grant + Member’s fees
Total income = £ x£5
Total income = £50 + £1200
ANSWER Total income = £1250

15. (ii) Find the council grant as a fraction of the club’s total income
for the year 2002
Give your answer in the simplest form.
council grant =
club’s total income
£50
£1250
ANSWER 1 25

16. ANSWER 3:1 In 2001, the club’s total income was £1000.
The club spent 60% of its total income on a hall.
It spent a further £250 on prizes.
(b) Work out the ratio
The amount spent on the hall : the amount spent on pizzas.
Give your answer in its simplest form.
amount spent on the hall = 60% of £1250
amount spent on the hall = 60 x £1250
100
amount spent on the hall = 6 x £125
amount spent on the hall = £750
The amount spent on the hall : the amount spent on prizes.
£750:£250 =
3:1
ANSWER 3:1

17. 5. 2
Flowerbed x
The diagram represents a garden in the shape of a rectangle.
All measurements are given in metres.
The garden has a flowerbed in one corner.
The flowerbed is a square of side x.
Write down an expression, in terms of x, for the shortest side of the garden.
(b) Find an expression, in terms of x, for the perimeter of the garden.
Give your answer in its simplest form.
The perimeter of the garden is 20 metres.
(c) Find the value of x. x 5

18. ANSWER Shortest side = x + 25. 2
Flowerbed x
Write down an expression, in terms of x, for the shortest side of the garden. x 5
ANSWER Shortest side = x + 2
(b) Find an expression, in terms of x, for the perimeter of the garden.
Give your answer in its simplest form.
Perimeter = (x + 2) + (x + 5) + (x + 2) + (x + 5)
ANSWER Perimeter = 4X + 14

19. ANSWER X = 1.5 5. 5 2 x x The perimeter of the garden is 20 metres.
Flowerbed x x 5
The perimeter of the garden is 20 metres.
(c) Find the value of x.
4X + 14 = 20
4X =
4X = 6
X = 6 4
ANSWER X = 1.5

20. (a) Simplify 5p + 2q – 3p – 3q
y = 5x – 3
(b) Find the value of y when x = 4

21. ANSWER 2p – q (a) Simplify 5p + 2q – 3p – 3q 5p + 2q – 3p – 3q
5p – 3p = 2p
+ 2q – 3q =
- 1q
5p + 2q – 3p – 3q
= 2p – 1q
= 2p – q
ANSWER 2p – q

22. ANSWER y = 17 y = 5x – 3 (b) Find the value of y when x = 4

23. 7. The table shows some rows of a number pattern.1
= 1 x 2 2
Row 2
1 + 2
= 2 x 3
Row 3
= 3 x 4
Row 4
Row 8
(a) In the table, complete row 4 of the number pattern.
(b) In the table, complete row 8 of the number pattern.
(c) Work out the sum of the first 100 whole numbers.
(d) Write down an expression, in terms of n, for the sum of the n whole numbers.

24. 7. The table shows some rows of a number pattern.1
= 1 x 2 2
Row 2
1 + 2
= 2 x 3
Row 3
= 3 x 4
Row 4
Row 8
= 4x5 2
= 8x9 2
(a) In the table, complete row 4 of the number pattern.
(b) In the table, complete row 8 of the number pattern.

25. ANSWER 100x101 2 7. The table shows some rows of a number pattern.
1 + 2
= 2 x 3
Row 3
= 3 x 4
Row 4
Row 8
= 4x5 2
= 8x9 2
(c) Work out the sum of the first 100 whole numbers.
= ………………………
ANSWER 100x101 2

26. ANSWER n(n+1) 2 7. The table shows some rows of a number pattern.
= 1 x 2 2
Row 2
1 + 2
= 2 x 3
Row 3
= 3 x 4
Row 4
Row 8
= 4x5 2
= 8x9 2
(d) Write down an expression, in terms of n, for the sum of the n whole numbers.
= ………………………. + n
ANSWER n(n+1) 2

27. 8.
4.5 m
2.8 m
3.2 m
The diagram represents a large tank in the shape of a cuboid.
The tank has a base.
It does not have a top.
The width of the tank is 2.8 metres.
The length of the tank is 3.2 metres.
The height of the tank is 4.5 metres.
The outside of the tank is going to be painted. 2
1 litre of paint will cover 2.5 m
The cost of the paint is £2.99 per litre.
Calculate the cost of the paint needed to paint the outside of the tank.

28. 2 Area = 3.2x4.5 m Area = 14.4 m 4.5 m 3.2 m 2 Area = 2.8x4.5 m 2

29. ANSWER Cost of paint = £63.34 Total Area = 2 Total Area = 52.96 m
8.96 m m m m m
Total Area = 2
Total Area = m
Number of litres of paint = ÷ 2.5 litres
Number of litres of paint = litres
Cost of paint = x £2.99
ANSWER Cost of paint = £63.34

30. 2 2 ANSWER 2.5 m = 10 000 cm 2 2 9. Change 2.5 m to cm 1 m = 100 cm
9. Change 2.5 m to cm
1 m = 100 cm
1 m x 1m = 100 cm x 100 cm
1 m = cm
2.5 m = 2.5 x cm
ANSWER m = cm

31. Region Frequency Midlands 22 London 36 Southern England 8
10.Bhavana asked some people which region their favourite football team
came from.
The table shows her results.
Region
Frequency
Midlands 22
London 36
Southern England 8
Northern England 24
Complete the accurate pie chart to show these results.
Use the circle given below.
Midlands

32. Region Frequency Midlands 22 London 36 Southern England 8
Northern England 24
Angle
22 x 360 = 22 x 4 = 88 90
36 x 360 = 36 x 4 = 144 90
8 x 360 = 8 x 4 = 32 90
24 x 360 = 24 x 4 = 96 90
Total = 90

34. ANSWER x = 0.2 City Rovers Town United 0.38 0.27 0.15 X
Four teams, City, Rovers, Town and United play a competition to win a cup.
Only one team can win the cup.
The table below shows the probabilities of City or Rovers or Town winning the cup.
City
Rovers
Town
United
0.38
0.27
0.15 X =
0.8
x =
ANSWER x = 0.2

35. Here are the times, in minutes, taken to change some tyres.
In the space below, draw a stem and leaf diagram to show these times. 5 7 8 1 2
5 5 5 6
0 0 0 4 5 2 3 3 5

36. 14.
4 cm
10 cm
The diagram shows a cylinder with a height of 10 cm and radius 4 cm.
Calculate the volume of the cylinder.
Give your answer correct to 3 significant figures.
The length of a pencil is 13 cm.
The pencil cannot be broken
(b) Show that this pencil cannot fit inside the cylinder.

37. 3 ANSWER Volume = 502 cm 2 2 3 Volume = πr h = Πx4x10 cm 3
Πx4x10 cm 3
Volume = 160π cm 3
ANSWER Volume = 502 cm

38. 14. 10 cm The length of a pencil is 13 cm. The pencil cannot be broken
(b) Show that this pencil cannot fit inside the cylinder.

39. 14. 10 cm Pencil will not fit into box 12.8 cm 10 cm 8 cm
Pythagoras Theorem
c = a + b
c = 2
c = 2
c = 164
c = 164
c = 233
c = 12.8 cm

40. 13. (a) Express the following numbers as products of their prime factors.60 96
(b) Find the Highest Common Factor of 60 and 96.
(c) Find the Lowest Common Multiple of 60 and 96.

41. ANSWER 60 = 2x3x5 Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19
13. (a) Express the following numbers as products of their prime factors.
(i) 60
Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19
60 ÷ 2 = 30
60 = 2 x 30
60 = 2 x 2 x 15
30 ÷ 2 = 15
60 = 2 x 2 x 3 x 5
15 ÷ 3 = 5 2
ANSWER 60 = 2x3x5

42. ANSWER 96 = 2x3 Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19
13. (a) Express the following numbers as products of their prime factors.
(ii) 96
Prime numbers = 2, 3, 5, 7, 11, 13, 17, 19
96 ÷ 2 = 48
96 = 2 x 48
96 = 2 x 2 x 24
48 ÷ 2 = 24
96 = 2 x 2 x 2 x 12
24 ÷ 2 = 12
96 = 2 x 2 x 2 x 2 x 6
12 ÷ 2 = 6
96 = 2 x 2 x 2 x 2 x 2 x 3
6 ÷ 2 = 3 5
ANSWER 96 = 2x3

43. ANSWER Highest Common Factor = 12
(b) Find the Highest Common Factor of 60 and 96.
60 = 2 x 2 x 3 x 5
96 = 2 x 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
96 = 2 x 2 x 2 x 2 x 2 x 3
Highest Common Factor = 2 x 2 x 3
ANSWER Highest Common Factor = 12

44. ANSWER Lowest Common multiple = 480
(c) Find the Lowest Common Multiple of 60 and 96.
1x60 = 60
1x96 = 96
2x60 = 120
2x96 = 192
3x96 = 288
3x60 = 180
4x60 = 240
4x96 = 384
5x96 = 480
5x60 = 300
5x96 = 480
6x60 = 360
7x60 = 420
8x60 = 480
8x60 = 480
ANSWER Lowest Common multiple = 480

45. Cost, (£C) Frequency 0<C≤50 4 50<C≤100 8 100<C≤150 7
14. A garage keeps records of the costs of repairs to its customers’ cars.
The table gives information about the costs of all repairs which were
less than £250 in one week.
Cost, (£C)
Frequency
0<C≤50 4
50<C≤100 8
100<C≤150 7
150<C≤200 10
200<C≤250 11
(a) Find the class interval in which the median lies.
There was only one further repair that week, not included in the table.
That repair cost £1000.
Dave says “The class interval in which the median lies will change.”
(b) Is Dave correct? Explain your answer.

46. ANSWER Median class interval 150<C≤200
Cost, (£C)
Frequency
0<C≤50 4
50<C≤100 8
100<C≤150 7
150<C≤200 10
200<C≤250 11
Cumulative Frequency 4
4 + 8 =12
=19
=29
= 40
= 20.5 2
(a) Find the class interval in which the median lies.
ANSWER Median class interval
150<C≤200

47. ANSWER Median class interval same Dave is wrong
There was only one further repair that week, not included in the table.
That repair cost £1000.
Dave says “The class interval in which the median lies will change.”
(b) Is Dave correct? Explain your answer.
Cost, (£C)
Frequency
0<C≤50 4
50<C≤100 8
100<C≤150 7
150<C≤200 10
200<C≤250 11
Cumulative Frequency 4
4 + 8 =12
=19
=29
= 40
250<C 1
= 41
= 21 2
(a) Find the class interval in which the median lies.
ANSWER Median class interval same Dave is wrong

48. ANSWER Normal Price £6500 The garage also sells cars.
It offers discounts at 20% of the normal price for cash.
Dave pays £5200 cash for a car.
(c) Calculate the normal price of the car.
Normal Price x
Normal Percent = 100%
Discount Percent = 100% - 20% = 80%
Discount Price £5200
X = 100 £
X = 100 x £5200 80
ANSWER Normal Price £6500

49. 15. x x A cuboid has a square of side x cm.
The height of the cuboid is 1 cm more than the length cm. 3
The volume of the cuboid is 230 cm .
(a) Show that x + x = 230

50. Volume = length x width x height
Volume = X x X x (X+1) = 230 2
Volume = X x (X+1)
Volume = X + X

51.
The equation x + x = 230
has a solution between x = 5 and x = 6
(b) Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
X + X =
5 + 5 = =
150
X= 5
Less than 230
X + X =
216
6 + 6 = =
X= 6
More than 230

52.
The equation x + x = 230
has a solution between x = 5 and x = 6
X + X = =
X= 5.7
Less than 230
X + X = =
X= 5.8
Less than 230
X + X = =
X= 5.9
More than 230
X + X = =
X= 5.85
More than 230

53. ANSWER 5.8 3 2 X + X = 228.752 X= 5.8 Less than 230 3 2 X + X =
X + X =
X= 5.8
Less than 230
Actual value between 5.8 and 5.85
X + X =
More than 230
X= 5.85
X + X =
X= 5.9
More than 230
ANSWER 5.8

54. Answer Area circle = 177 cm 16. 15 cm
The diagrams shows a semi-circle.
The diameter of the semi-circle is 15 cm.
Calculate the area of the semi-circle.
Give your answer correct to 3 significant figures. 2
Area circle = πr
Diameter = 15 cm
radius = 15 cm ÷ 2 2
Area circle = πx7.5
radius = 7.5 cm 2
Area circle = 3.14x7.5 2
Answer Area circle = 177 cm

55. ANSWER X = 8 y = 5 y = 1 x + 1 2 5 = 1 x + 1 2 5 - 1 = 1 x 2 4 = 1 x 2
17. A straight line has equation y = 1 x + 1 2
The point P lies on the straight line.
P has a y-coordinate of 5.
(a) Find the x-coordinate of P.
y = 5
y = 1 x + 1 2
5 = 1 x + 1 2
5 - 1 = 1 x 2
= 1 x 2
1x = 2 x 4
ANSWER X = 8

56. (b) Write down the equation of a different straight line
that is parallel to
y = 1 x + 1 2
y = 1 x + 3 2
y = 1 x - 2 2
y = 1 x + 5 2

57. ANSWER x = 2y – 2 (c) Rearrange y = 1 x + 1 to make x the subject. 2
2y – 2x1 = 1 x
2y – 2 = 1 x
2y – 2 = x
ANSWER x = 2y – 2

58. ANSWER X = 4 Y = - 1 18. Solve 2x – 3y = 11 5x + 2y = 1819
x = 4
5x + 2y = 18
x = 4
5x4 + 2y = 18
20 + 2y = 18
2y =
y = – 1
2y = – 2
ANSWER X = 4 Y = - 1

59. AE = 6cm, ED = 4 cm, AB = 4.5 cm, BE = 4.8 cm
BE is parallel to CD
AE = 6cm, ED = 4 cm, AB = 4.5 cm, BE = 4.8 cm
Calculate the length of CD.
(b) Calculate the perimeter of the trapezium EBCD.

60. ANSWER CD = 8 cm CD = AD BE AE CD = 10 4.8 6 CD = 10 X 4.8 cm 6 A 6 cm
CD = 10 X 4.8 cm 6
ANSWER CD = 8 cm

61. ANSWER perimeter EBCD = 19.8 cm
(b) Calculate the perimeter of the trapezium EBCD.
perimeter EBCD = BE + ED + CD + CB
perimeter EBCD = 4.8 cm + 4 cm + 8cm + CB
AC = AD
AB AE
AC = 10
AC = 10 x 4.5 6
AC = 7.5 cm
CB = AC - AB = 7.5 cm – 4.5 cm
CB = 3 cm
perimeter EBCD = 4.8 cm + 4 cm + 8cm + 3 cm
ANSWER perimeter EBCD = 19.8 cm

62. ANSWER y = 1.62x10 20. 2 y = ab a+b 6 a = 3 x 10 7 b = 2 x 10 Find y.
y = ab
a+b 6
a = 3 x 10 7
b = 2 x 10
Find y.
Give your answer in standard form correct to 3 significant figures
y = 3x10x 2x10
3x10+2x10 2
y = ab
a+b
y = x10
y = x10
y = x10
y = x10 7
2.3x10
y = x10 6
y = √2.6x10
½ x 6
y = x10 3
ANSWER y = x10

63. The diagram shows triangle ABC. BC = 9.5 cm O Angle ABC = 90
21. O 38
The diagram shows triangle ABC.
BC = 9.5 cm O
Angle ABC = 90
Angle ABC = 38
Work out length AB
Give your answer to 3 significant figures. B C
8.5 cm

64. ANSWER AB = 5.8 cm 21. Work out length AB opp = adj tanθ o38 B C
8.5 cm
Work out length AB
adj
opp = adj tanθ o
AB = 6.5x tan38
ANSWER AB = 5.8 cm

65. The probability tree diagram has been started in the space below.
Julie does a statistical experiment. She throws a dice 600 times.
She scores six 200 times.
Is the dice fare? Explain your answer.
Julie then throws a fair red dice once and a fair blue dice.
Complete the probability tree diagram to show the outcomes.
Label clearly the branches of the probability tree diagram.
22.
The probability tree diagram has been started in the space below.
Red Blue
Dice Dice
six
not six

66. ANSWER Dice is not fare 22. Numbers on dice 1, 2, 3, 4, 5, 6
Julie does a statistical experiment. She throws a dice 600 times.
She scores six 200 times.
Is the dice fare? Explain your answer.
Numbers on dice 1, 2, 3, 4, 5, 6
Fare dice p(six) =1/6
Expected number of sixes =1/6 x 600
Expected number of sixes =100
Julie scores six 200 times
ANSWER Dice is not fare

67. The probability tree diagram has been started in the space below.
22.
Julie then throws a fair red dice once and a fair blue dice
Complete the probability tree diagram to show the outcomes.
Label clearly the branches of the probability tree diagram.
The probability tree diagram has been started in the space below.
Red Blue
Dice Dice
1/6
six
six and six
1/6x1/6 = 1/36
1/6
six
5/6
not six
not six and six
5/6x1/6 = 5/36
not
six
1/6
six
six and not six
1/6x5/6 = 5/36
5/6
5/6
not six
not six and not six
5/6x1/6 = 25/36