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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…

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2
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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3
1 (a) 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…

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2 (a) 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%…

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3 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).
C
O
A
B
x

(a) Write down…

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6
4 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…

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5
y x=3

5

4

3

2
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.

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_______________________________________________________________________[1]

(b) Reflect triangle A in the line x =…

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6 (a) (i) 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 ­…

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9
7 (a) Multiply out.

3(2x ­ 5)

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(a) _______________________[1]

(b) Factorise completely.

4a + 2ac

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(b) _______________________[2]

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© OCR 2008 [Turn over

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10
8 (a) 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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(iii) _____________________[2]


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