GCSE Mathematics Higher Tier Solutions

June 2003 Paper 2

1.

2 ´ 3² ´ 7²

[3]

2.

2000 ´ (1.06)³ = £2382.03

Interest = £382.03

[4]

3.

Mean =

[4]

4.

a.

Area of trapezium CDEF = ½ (2.3 + 6.1) ´ 4.3 = 18.06

Area of rectangle ABCD = 6.1 ´ 4.2 = 25.62

Area of cross-section = 43.68

[3]

b.

Volume of block = 43.68 ´ 12.6 = 550.368

Density = 2000/550.368 = 3.6 g/cm³

[4]

5.

3.4     (Note: must include a calculation using a value of x at 2 d.p. to prove           this result)

[4]

6.

PQ = 3.6

SQ² = 4.3² - 3.6² = 5.53

SQ = 2.35

[3]

7.

[4]

8.

a.

(i)                 7.34 ´ 10⁷

(ii)               5.4 ´ 10^-4

[1]

[1]

b.

4.6153 ´ 10¹⁰

[2]

9.

 height = 75 ´ tan 48° = 83.3 m

[3]

b.

[3]

10.

a.

Median = 32

[1]

b.

120 - 102 = 18

[2]

11.

a.

6a⁸b³

[2]

b.

3a(a - 2c)

[2]

12.

[4]

13.

a.

[3]

b.

-86° and 94°

[2]

14.

a.

, England 6, Scotland 2, Ireland 3, France 1

[5]

b.

Give each visitor from Wales a number between 01 and 92

Select 8 numbers from the table, ignoring repeats or numbers outside of the range.

For example: 34, 45, 78, 13, 03, 65, 72, 39

[3]

15.

a.

27x¹³y⁶

[2]

b.

3/a²

[2]

16.

[4]

17.

a.

x + y

[1]

b.

y + ½ z

[1]

c.

½ z + x – y

[1]

18.

a.

[6]

19.

a.

Volume = 8(x +2)(x - 5) = 8(x² - 3x - 10) = 8x² - 24x - 80

Volume = 20.6

8x² - 24x - 80 = 20.6

Re-arranges to 8x² - 24x - 100.6 = 0

[4]

b.

[3]

c.

x = 5.35 (length cannot be negative)

Dimensions are 8 cm, 7.35 cm and 0.35 cm

[1]

20.

Time of race = 24.4 ± 0.05 s

0.1% of 200 = 0.2 m \ Length of race track = 200 ± 0.2 m

Average speed = distance ÷ time

Greatest average speed       = greatest distance ÷ least time

                                      = 200.2 ÷ 24.35 = 8.22 ms^-1

Least average speed                    = least distance ÷ greatest time

                                      = 199.8 ÷ 24.45 = 8.17 ms^-1

[5]

21.

[7]