JUNE 09 OCR ADDITIONAL MATHS FSMQ PAST PAPER

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FREE-STANDING MATHEMATICS QUALIFICATION
ADVANCED LEVEL
ADDITIONAL MATHEMATICS 6993
Candidates answer on the Answer Booklet Friday 5 June 2009
OCR Supplied Materials: Afternoon
· 16 page Answer Booklet
· Graph paper Duration: 2 hours
Other Materials Required:
None
*6993*
* 6 9 9 3 *
INSTRUCTIONS TO CANDIDATES
· Write your name clearly in capital letters, your Centre Number and Candidate Number in the spaces provided
on the Answer Booklet.
· 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.
· Answer all the questions.
· Do not write in the bar codes.
· You are permitted to use a scientific or graphical calculator in this paper.
· Final answers should be given correct to three significant figures where appropriate.
INFORMATION FOR CANDIDATES
· The number of marks is given in brackets [ ] at the end of each question or part question.
· You are advised that an answer may receive no marks unless you show sufficient detail of the working to
indicate that a correct method is being used.
· The total number of marks for this paper is 100.
· This document consists of 8 pages. Any blank pages are indicated.
© OCR 2009 [100/2548/0] OCR is an exempt Charity
3R­8K18 Turn over

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Formulae Sheet: 6993 Additional Mathematics
C
In any triangle ABC
b a
Cosine rule a2 = b2 + c2 - 2bc cos A
A c B
Binomial expansion
When n is a positive integer
n n-1 n n-2 2 n n-r r
(a + b)n = an + a b+ a b + ... + a b + . . .…read more

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Section A
1 The angle is greater than 90 and less than 360 and cos = 2
3
. Find the exact value of tan . [3]
2 Find the equation of the normal to the curve y = x3 + 5x - 7 at the point (1, -1). [5]
3 A is the point (1, 5) and C is the point (3, p).
(i) Find the equation of the line through A which is parallel to the line 2x + 5y = 7.…read more

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The course of a cross-country race is in the shape of a triangle ABC.
AB = 8 km, BC = 3 km and angle ABC = 60 .
B
60°
Not to scale
3
8
C
A
(i) Calculate the distance AC and hence the total length of the course. [4]
(ii) The organisers extend the course so that AC = 9 km.
B
60°
Not to scale
8
A
9
C
Calculate the angle BCA.…read more

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A car accelerates from rest. At time t seconds, its acceleration is given by a = 4 - 0.2t m s-2 until
t = 20.
(i) Find the velocity after 5 seconds. [3]
(ii) What is happening to the velocity at t = 20? [1]
(iii) Find the distance travelled in the first 20 seconds. [3]
10 (i) Illustrate on one graph the following three inequalities.
yx-1
x2
2x + y 8
Draw suitable boundaries and shade areas that are excluded.…read more

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Section B
11 The shape ABCD below represents a leaf.
The curve ABC has equation y = -x2 + 8x - 9.
The curve ADC has equation y = x2 - 6x + 11.
y
B
C
A
D
x
O
(i) Find algebraically the coordinates of A and C, the points where the curves intersect. [5]
(ii) Find the area of the leaf.…read more

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In a supermarket chain there are a large number of employees, of whom 40% are male.
(a) One employee is chosen to undergo training.
What assumption is made if 0.4 is taken to be the probability that this employee is male? [1]
(b) 6 employees are chosen at random to undergo training.
(i) Show that P(all 6 chosen are female) = 0.0467, correct to 4 decimal places.…read more

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Copyright Information
OCR is committed to seeking permission to reproduce all third-party content that it uses in its assessment materials. OCR has attempted to identify and contact all copyright holders
whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced in the OCR Copyright
Acknowledgements Booklet.…read more

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