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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…

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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…

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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).…

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7 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…

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9 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…

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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…

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13 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…

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Copyright Information
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whose work is used in this paper. To avoid the issue of disclosure of answer-related information to candidates, all…

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