# June 08-paper 4-GCSE Maths

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GENERAL CERTIFICATE OF SECONDARY EDUCATION J512/04
MATHEMATICS SYLLABUS A
Paper 4 (Higher Tier)
MONDAY 2 JUNE 2008 Afternoon
Time: 2 hours

Candidates answer on the question paper
*CUP/T47404*

Electronic calculator
Geometrical instruments
Tracing paper (optional)

INSTRUCTIONS TO CANDIDATES

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Formulae Sheet: Higher Tier

Volume of prism = (area of cross-section) x length cross-
section
h
lengt

In any triangle ABC
C
a b c
Sine rule = =
sin A sin B sin C b a

Cosine rule a 2 = b 2 +c 2 ­ 2bc cos…

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1 (a) Calculate.

(i) 7.6
­­­­­­­­
12.5 ­ 6.8
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(a)(i) _____________________[1]

­­­
0.4
5 2
(ii)

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(ii) _____________________[2]

(b) (i) Calculate.

25.3 ­ 2.73

Write down all the figures on your calculator display.

(b)(i) _____________________[1]

(ii) Give your answer to part (b)(i) correct to 2 significant figures.…

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3 An electrician uses this graph to work out how much to charge for each job.

160

140

120

100
Charge (£)
80

60

40

20

0
0 1 2 3 4 5
Hours

The charge for a job is made up of a fixed fee plus an amount…

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4 Clare is reading a poetry book.

(a) The shortest poem in the book has one verse and the longest poem has six verses.
The poems in the book are from ten to fifteen lines in length.

Design a two-way table for Clare to record the number of verses…

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5 Calculate the area of this trapezium.

3.3 cm

NOT TO SCALE
10.4 cm

8.7 cm

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______________________ cm² [2]

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6 (a) A quadrilateral has angles as shown.

5w
NOT TO SCALE

w

29°

106°

Work out the value of w.

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(b) (i) Here is a regular hexagon.

120°

Explain why each interior angle is 120°.

_____________________________________________________________________

_____________________________________________________________________

___________________________________________________________________[2]

(ii) This shape is made from six congruent isosceles triangles and a regular hexagon.

28°
x
NOT TO SCALE

Find the size of angle x.

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7 The diagram shows the garden of a house.
There is a security light, S, in the garden and two security lights, A and B, on the house wall.
The lights are at ground level.

House wall
A B

Scale: 1 cm represents 2 m

S

The security light…

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8 Use trial and improvement to solve this equation.

x3 + x = 8

Show all your trials and their outcomes.

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__________________________[4]

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9 Calculate the value of x.

NOT TO SCALE
x…

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10 (a) (i) Solve.

4x ­ 5 < 9

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(a)(i) _____________________[2]

(ii) Represent your solution to part (a)(i) on the number line below.

­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5
[1]

(b) Expand and simplify.

(i) 2(4x + 5) ­ 3(x ­ 2)…