Cambridge International AS & A Level: Mathematics 9709/22
Cambridge International AS & A Level: Mathematics 9709/22
Cambridge International AS & A Level: Mathematics 9709/22
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*2687987641*
MATHEMATICS 9709/22
Paper 2 Pure Mathematics 2 February/March 2020
1 hour 15 minutes
INSTRUCTIONS
³ Answer all questions.
³ Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
³ Write your name, centre number and candidate number in the boxes at the top of the page.
³ Write your answer to each question in the space provided.
³ Do not use an erasable pen or correction fluid.
³ Do not write on any bar codes.
³ If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
³ You should use a calculator where appropriate.
³ You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
³ Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
³ The total mark for this paper is 50.
³ The number of marks for each question or part question is shown in brackets [ ].
JC20 03_9709_22/FP
© UCLES 2020 [Turn over
2
1 Solve the equation 2 sin 1 + 30Å + 5 cos 1 = 2 sin 1 for 0Å < 1 < 90Å. [4]
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2 (a) Find the quotient when 4x3 + 17x2 + 9x is divided by x2 + 5x + 6, and show that the remainder
is 18. [3]
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5 (a) Sketch, on the same diagram, the graphs of y = x + 2k and y = 2x − 3k , where k is a positive
constant.
Give, in terms of k, the coordinates of the points where each graph meets the axes. [3]
(b) Find, in terms of k, the coordinates of each of the two points where the graphs intersect. [4]
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2 + 2k ≥ 2t+1 − 3k .
t
[2]
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6 A curve has equation y = x3 e0.2x where x ≥ 0. At the point P on the curve, the gradient of the curve
is 15.
_
75e−0.2x
(a) Show that the x-coordinate of P satisfies the equation x =
15 + x
. [4]
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(b) Use the equation in part (a) to show by calculation that the x-coordinate of P lies between 1.7
and 1.8. [2]
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(c) Use an iterative formula, based on the equation in part (a), to find the x-coordinate of P correct
to 4 significant figures. Give the result of each iteration to 6 significant figures. [3]
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7
y
A x
O
y = 4 sin2 x + 8 sin x + 3,
where x is measured in radians. The curve crosses the x-axis at the point A and the shaded region is
bounded by the curve and the lines x = 0 and y = 0.
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Additional Page
If you use the following lined page to complete the answer(s) to any question(s), the question number(s)
must be clearly shown.
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Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every
reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the
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