June 09-paper 4-GCSE Maths

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H
GENERAL CERTIFICATE OF SECONDARY EDUCATION
MATHEMATICS SYLLABUS A J512/04
Paper 4
(Higher Tier)
Monday 1 June 2009
*OCE/T66408*
Candidates answer on the question paper
OCR Supplied Materials:
Morning
None
Duration: 2 hours
Other Materials Required:
· Electronic calculator
· Geometrical instruments
· Tracing paper (optional)
* J 5 1 2 0 4 *
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.
· 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.
· The total number of marks for this paper is 100.
· This document consists of 20 pages. Any blank pages are indicated.
© OCR 2009 [100/5935/0] OCR is an exempt Charity
SP (KN) T66408/5 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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Joan has a recipe for making chocolate buns.
The recipe uses 150 g of flour and 25 g of cocoa powder to make 12 buns.
(a) How much flour should Joan use to make 18 buns?
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(a) ___________________________ g [2]
(b) What is 25 g out of 175 g expressed as a percentage?
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(b) __________________________ % [2]
2 Calculate.
22.4
(a) ­­­­­­­
3.6 + 2.8
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(a) ____________________________ [1]
(b) 36 + (4.5)2
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...................................................................................................................................................…read more

Page 4

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Rachael decides to bath her dog, Oscar. She runs water into the bath, puts Oscar in the bath,
baths Oscar, takes him out and then empties the bath.
The graph shows the depth of water in the bath.
30
25
20
Water depth
(cm) 15
10
5
0
0 5 10 15 20 25 30 35 40
Time (minutes)
(a) Which is quicker, running water into the bath or emptying it?
Explain how you can tell.…read more

Page 5

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Calculate the average speed for a journey of 420 miles that takes 3 hours 30 minutes.
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_________________________ mph [3]
5 Enlarge the triangle by scale factor 2 from centre A.…read more

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Sally conducted an experiment on reaction times.
One day ten students were woken at 4 am and their reaction times were measured.
Another day their reaction times were measured mid-morning after a full night's sleep.
The reaction times, in seconds, are shown in the table.
Student A B C D E F G H I J
4 am
4.3 6.8 6.9 7.4 6.0 4.8 5.6 4.0 8.5 3.6
reaction time
Mid-morning
3.4 5.9 6.2 6.7 5.4 4.2 4.4 3.0 7.5 2.…read more

Page 7

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Another student, John, has a mid-morning reaction time of 5.0 seconds.
Use your line of best fit to estimate John's reaction time if he was woken at 4 am.
(d) __________________________ s [1]
(e) Explain why it may not be appropriate to use your line of best fit to estimate the mid-morning
reaction time of a student whose 4 am reaction time is 2.0 seconds.
_________________________________________________________________________
______________________________________________________________________ [1]
7 (a) Calculate the area of a circle of radius 6 cm.
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...................................................................................................................................................…read more

Page 8

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Z
46° 67° NOT TO
SCALE
a
X
Y
(a) Find the size of angle a.
Give a reason for your answer.
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a = _______________° because _______________________________________________
______________________________________________________________________ [2]
(b) Find the sizes of the other angles in triangle XYZ.
What type of triangle is XYZ?
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Angles are _______________° and _______________°.…read more

Page 9

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Eight identical squares have a total area of 2312 mm2.
The length of the side of each square is x mm.
Write an equation in x and work out the value of x.
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_____________________________ [3]
10 The capacity of a tank is 8 gallons.
The empty tank was filled with petrol.
The petrol cost 123.9 pence per litre.
1 litre is approximately equal to 0.22 gallons.
Calculate how much it cost to fill the tank with petrol.…read more

Page 10

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Use trial and improvement to solve this equation.
x 3 ­ x = 10
Give your answer to one decimal place.
Show all your trials and their outcomes.
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_____________________________ [4]
12 A fair spinner is numbered from 1 to 5.
The spinner is spun twice.
By listing the possible outcomes, or otherwise, work out the probability that the number obtained
on the second spin is less than the number obtained on the first spin.…read more

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