June 09-paper 3-GCSE Maths

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H
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 *
INSTRUCTIONS TO CANDIDATES
· Write your name clearly in capital letters, your Centre Number and Candidate Number in the boxes above.
· Use 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, however additional paper may be used if
necessary.
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.
· This document consists of 20 pages. Any blank pages are indicated.
No calculator can
be used for this
paper
© OCR 2009 [100/5935/0] OCR is an exempt Charity
SP (KN) T66416/5 Turn over

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Page 2

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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
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…read more

Page 3

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Mr Smith did a survey of how students travelled to school.
He displayed his results in a table.
Complete the table.
..........................................................................................................................................................
..........................................................................................................................................................
..........................................................................................................................................................
Bus Walk Car Total
Boys 21 13 57
Girls 8
Total 40 100
[3]
2 A jacket can be bought in a shop or online.
Online price
Shop price
Jacket £50
Jacket, usually £75
1 plus 15% postage and
Sale, ­
5 off packing
Which method of buying the jacket is cheaper, and by how much?
Show all your working clearly.…read more

Page 4

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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 3
(i) Draw a grouped frequency diagram to show this information.
Show your scales and label your axes clearly.…read more

Page 5

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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?
...........................................................................................................................................
...........................................................................................................................................
(iii) ____________________________ [2]
(b) At the supermarket, Jack is doing a survey about eating sweets.
This is his questionnaire.
`How many chocolate bars do you eat?'
A few A lot
(Please tick one box.)
Write down two things that are wrong with Jack's questionnaire.…read more

Page 6

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Show that x = 2 is the solution of this equation.
9x ­ 1 = 4x + 9
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
______________________________________________________________________ [2]
(b) Solve.
x
­­3=5
2
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
(b) ____________________________ [2]
5 (a) In a carton of Squashy, orange juice and water are mixed in the ratio 3 : 7.
How many litres of orange juice are needed to make 60 litres of Squashy?
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................…read more

Page 7

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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.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
(a) _________________________ cm2 [2]
(b) Reflect triangle A in the line x = 3.
Label the image P. [2]
(c) Rotate triangle A 90° clockwise about (0,0).
Label the image Q.…read more

Page 8

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List the integer values, n, which satisfy
3 < n 7.
...................................................................................................................................................
...................................................................................................................................................
(a) ____________________________ [2]
(b) (i) Solve this inequality.
3x ­ 2 > 4
...........................................................................................................................................
...........................................................................................................................................
(b)(i) ____________________________ [2]
(ii) Show your solution to part (i) on the number line below.…read more

Page 9

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Here are the first four terms of a sequence.
25 20 15 10
Find an expression for the nth term of this sequence.
...................................................................................................................................................
...................................................................................................................................................
(a) ____________________________ [2]
(b) Here are the first four terms of another sequence.
1 4 9 16
The nth term of this sequence is n 2.
Write down an expression for the nth term of the following sequence.
3 6 11 18 ..........
...................................................................................................................................................…read more

Page 10

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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?
...................................................................................................................................................
...................................................................................................................................................
(a) ____________________________ [2]
(b) Do the results suggest that the spinner is fair?
Give a reason for your answer.…read more

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