June 08-paper 4-GCSE Maths

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H
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*
Additional materials (enclosed): None
Additional materials (required):
Electronic calculator
Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS TO CANDIDATES
· Write your name in capital letters, your Centre Number and Candidate Number in the boxes above.
· Use blue or black ink. Pencil may be used for graphs and diagrams only.
· Read each question carefully and make sure that you know what you have to do before starting your
answer.
· Show your working. Marks may be given for a correct method even if the answer is incorrect.
· Answer all the questions.
· Do not write in the bar codes.
· Write your answer to each question in the space provided.
INFORMATION FOR CANDIDATES
· The number of marks is given in brackets [ ] at the end of each question or part question.
· The total number of marks for this paper is 100.
· You are expected to use an electronic calculator for this paper.
· Use the button on your calculator or take to be 3.142 unless the question says otherwise.
FOR EXAMINER'S USE
This document consists of 20 printed pages.
SPA (KN) T47404/4 © OCR 2008 [100/1118/3] OCR is an exempt Charity [Turn over

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Page 2

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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 A
A B
c
Area of triangle = 1
2
ab sin C
r
Volume of sphere = 4 r3
3
Surface area of sphere = 4 r 2
Volume of cone = 1 r 2h…read more

Page 3

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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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(ii) _____________________[1]
_________________________________________________________________________________
2 A formula for changing degrees Fahrenheit (F) into degrees Celsius (C) is
5
C = (F ­ 32) × ­ .…read more

Page 4

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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 for the time that the job lasts.
(a) How much is the fixed fee?
(a) £ ______________________[1]
(b) How much would the electrician charge for a job that lasts 5 hours?
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Page 5

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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 and the number of
lines for the poems in the book. [3]
(b) Clare counted the number of letters in each word of one poem.
There were 28 words in the poem.…read more

Page 6

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Calculate the area of this trapezium.
3.3 cm
NOT TO SCALE
10.4 cm
8.7 cm
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______________________ cm² [2]
_________________________________________________________________________________
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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Page 7

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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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Page 8

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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 in the garden comes on when it detects movement within 7 m.
Each security light on the house wall comes on when it detects movement within 4 m.
A fox is in the garden.…read more

Page 9

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Use trial and improvement to solve this equation.
x3 + x = 8
Give your answer to one decimal place.
Show all your trials and their outcomes.
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__________________________[4]
_________________________________________________________________________________
9 Calculate the value of x.
NOT TO SCALE
x
3.2 cm
6.5 cm
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Page 10

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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)
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(b)(i) _____________________[3]
(ii) (x + 7)(x ­ 3)
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...........................................................................................................................................…read more

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