GCSE Mathematics Higher Tier Solutions

November 2002 Paper 1

1.

4 + 5 + 9 = 18 shares; 1 share = £3600 ÷ 18 = £200

Arwyn gets 4 ´ £200 = £800
Betty gets 5 ´ £200 = £1000
Clive gets 9 ´ £200 = £1800

[3]

2.

Area of a Trapezium =

[2]

3.

a.

Scatter graph; Line of best fit through mean point.

[2]

b.

Approx. 82 kg

[1]

4.

a.

y = 10

[1]

b.

c.

x = -1.6, 2.15

[2]

[2]

d.

3x² - 2x - 6 = 5 which rearranges to 3x² - 2x - 11 = 0

[1]

5.

(i)

(ii)

Area shaded in dark (red) is the required region.

[3]

6.

a.

b)

[2]

[2]

7.

[3]

8.

[4]

9.

a.

[1]

[1]

b.

[1]

[2]

10.

a.

4, 18, 64, 116, 162, 192, 198, 200

[1]

b.

Points plotted (9.5, 4), ( 19.5, 18) etc.
Joined to form c.f. diagram

[3]

c.

36

[1]

d.

188 got less than 58, \ 12 got more than 58, \12 got a grade A

[2]

11.

Missing values are 1, 3, 1, 2

[2]

12.

a.

Ratios are not the same \the triangles are not similar

[3]

b.

Sphere

[1]

13.

[3]

14.

Ratio of lengths is 1 : 2
Ratio of areas is 1 : 2² or 1 : 4

Area of larger stamp = 4 ´ 6.4 = 25.6 cm²

[2]

15.

a.

(i)                 (3q - 10)(3q + 10)

(ii)               (3q + 10)(q - 2)

[2]

[2]

b.

[1]

16.

a.

-90° and 90°

[2]

b.

-107° and 107°

[2]

17.

a.

½ ´ 136°  :  Half the angle at the centre

[4]

b.

112° :  Cyclic quadrilateral

c.

90°  :  radius is perpendicular to the tangent

18.

a.

10, 30, 100

[1]

b.

25 + 60 = 85

c.

Frequency densities: 3, 3.5, 6.5. 2, 3
Histogram

[3]

d.

Yes, more cars are going slower

[1]

19.

(2x - 5)²  i.e. a = 2 and b = 5

[3]

20.

a.

[2]

b.

This is Rational

[3]

c.

[2]

d.

[3]

21.

a.

(i)                 XY = XO + OY = -x + y

(ii)               OQ = OX + XQ = x + ½ XY = x + ½ (-x + y) = ½ x + ½ y

(iii)              OZ = y - ³/₂ x
\OP = ½ OZ = ½ y - ³/₄ x

[3]

b.

PQ = PO + x + XQ = - ½ y + ³/₄ x + x + ½ y - ½ x = ⁵/₄ x

\PQ is parallel to OX

[2]

22.

a.

0.3 ´ 0.6 = 0.18

[2]

b.

P(Rees wins both) = 0.7 ´ 0.9 = 0.63

\P(Peter will win at least one game) = 1 - 0.63 = 0.37

[3]

23.

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