June 08-paper 3-GCSE Maths

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H
GENERAL CERTIFICATE OF SECONDARY EDUCATION J512/03
MATHEMATICS SYLLABUS A
Paper 3 (Higher Tier)
MONDAY 19 MAY 2008 Morning
Time: 2 hours
Candidates answer on the question paper
*CUP/T47403*
Additional materials (enclosed): None
Additional materials (required):
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.
WARNING
You are not allowed to use a
calculator in this paper. FOR EXAMINER'S USE
This document consists of 20 printed pages.
SPA (KN) T47403/3 © 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
1
Area of triangle = ab sin C
2
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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A 100 g box of breakfast cereal contains 20 g of fruit and 80 g of oats.
Write the ratio of fruit to oats in its simplest form.
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(a) ___________ : ___________[1]
(b) What weight of fruit is in a 250 g box of the same cereal?
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(b) _____________________ g [2]
(c) As a special offer, the 250 g of cereal is increased by 20%.
What weight of cereal is in the special offer box?
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Page 4

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The probability that Rovers will win their next match is 0.6.
The probability that Rovers will lose their next match is 0.15.
Work out the probability that Rovers will draw their next match.
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(a) _______________________[2]
(b) A weather man says `There is a 40% chance of rain today.'
Tracy says `That means there is a 60% chance of it being sunny today.'
Explain why Tracy is not correct.…read more

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ABCDEFGH is a cuboid. H
z
With the x, y and z axes shown, G
A is the point (3,0,0), y
E
F
B is the point (8,0,0),
D is the point (3,6,0),
M D
E is the point (3,0,4).…read more

Page 6

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In triangle ABC, C
· AB is x cm long
· BC is twice the length of AB
· AC is 10 cm longer than AB.
The perimeter of the triangle is 42 cm.
A x B
Write down an equation in x and solve it.
NOT TO SCALE
Use your answer to find the lengths of the sides of the triangle.…read more

Page 7

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A
1
­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 x
­1
­2
­3
B
­4
­5
(a) Describe the translation that moves triangle A onto triangle B.
_________________________________________________________________________
_______________________________________________________________________[1]
(b) Reflect triangle A in the line x = 3.
Label the image P. [1]
(c) Rotate triangle A 90° anticlockwise about the origin.
Label the image Q.…read more

Page 8

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Draw the graph of y = 3x ­ 1.
You may use the table below to help you.
x
y
y
5
4
3
2
1
­1 0 1 2 x
­1
­2
­3
­4
[3]
(ii) Use your graph to solve the equation 3x ­ 1 = 0.
(a)(ii) _____________________[1]
(b) Rearrange y = 3x ­ 1 to make x the subject.
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Page 9

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Multiply out.
3(2x ­ 5)
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(a) _______________________[1]
(b) Factorise completely.
4a + 2ac
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Page 10

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Write 200 as a product of its prime factors, using powers.
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(a) _______________________[3]
(b) Simplify each of the following.
(i) y5 × y3
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(b)(i) _____________________[1]
y5
(ii) ­­
y3
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(ii) _____________________[1]
(iii) (2y 5)3
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...........................................................................................................................................…read more

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