June 09-paper 3-GCSE Maths

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GENERAL CERTIFICATE OF SECONDARY EDUCATION
MATHEMATICS SYLLABUS A J512/03
Paper 3
(Higher Tier)

Monday 18 May 2009
*OCE/T66416*

Candidates answer on the question paper

OCR Supplied Materials:
Afternoon
None
Duration: 2 hours
Other Materials Required:
· Geometrical instruments
· Tracing paper (optional)

* J 5 1 2 0 3…

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Formulae Sheet: Higher Tier

a

Area of trapezium = 1 (a + b)h h
2

b

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…

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1 Mr Smith did a survey of how students travelled to school.
He displayed his results in a table.

Complete the table.

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Bus Walk Car Total

Boys 21 13 57

Girls 8

Total 40 100
[3]

2 A jacket can be bought in a shop or…

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3 (a) The table shows the distribution of waiting times (in minutes) that customers spent at the
checkout of a supermarket.

Waiting time (minutes) Frequency

0 up to 2 8

2 up to 4 19

4 up to 6 11

6 up to 8 6

8 up to 10…

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(ii) Write down the modal class for these waiting times.

(a)(ii) _____________________ minutes [1]

(iii) One of these customers is chosen at random.

What is the probability that this customer waited 6 minutes or more?

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(iii) ____________________________ [2]

(b) At the supermarket, Jack is doing a survey…

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4 (a) Show that x = 2 is the solution of this equation.

9x ­ 1 = 4x + 9

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______________________________________________________________________ [2]

(b) Solve.
x
­­3=5
2
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(b) ____________________________ [2]

5 (a) In a carton of Squashy, orange juice and…

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6
y

6

5

4

3
A
2

1

­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 x
­1

­2

­3

­4

­5

­6

(a) Triangle A is drawn on a 1 cm square grid.

Work out the area of triangle A.

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7 (a) List the integer values, n, which satisfy

3 < n 7.

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(a) ____________________________ [2]

(b) (i) Solve this inequality.

3x ­ 2 > 4

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(b)(i) ____________________________ [2]

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

­5 ­4 ­3 ­2…

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8 (a) Here are the first four terms of a sequence.

25 20 15 10

Find an expression for the nth term of this sequence.

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(a) ____________________________ [2]

(b) Here are the first four terms of another sequence.

1 4 9 16

The nth term of this…

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10 Jo wanted to know if this spinner was fair.
She spun it a number of times. 1

2
4
3
The table shows her results.

Number 1 2 3 4

Frequency 115 129 132 124

(a) What is the relative frequency of obtaining a 2?

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(a)…