CAIE A Level 9709

Mathematics 2025 · May/June

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26 Questions Q&A Available

Questions & Model Answers 26 Qs

Structured 4 marks

Find the coordinates of the points of intersection of the curve and the line with equations xyy25 24 += and xy24 0++=.

Structured 4 marks

The coefficient of x in the expansion of px +eo is 1280. Find the value of the constant p.

Short Answer 1 mark

A point P is moving along the curve with equation yaxx12 2=- in such a way that the x-coordinate of P is increasing at a constant rate of 5 units per second.

Q4(a)

Short Answer 3 marks

Find the rate at which the y-coordinate of P is changing when x9=. Give your answer in terms of the constant a.

Q4(b)

Short Answer 2 marks

Given that the curve has a minimum point when x =, find the value of a.

Short Answer 1 mark

The equation of a curve is cosyx42 3=+ for x02GG r.

Q5(a)

Short Answer 2 marks

State the greatest and least possible values of y.

Q5(b)

Short Answer 1 mark

Sketch the curve. [2] r 2r rr r

Q5(c)

Structured 6 marks

Hence determine the number of solutions of the equation cosxx42 32 1+= - for x02GG r. [1] The diagram shows the curve with equationx54 and the line yx63=- . The line and the curve intersect at the point P which has y-coordinate 3. Find the area of the shaded region.

Q7(a)

Short Answer 1 mark

Prove the identitytan tans incos cosc os ii i

Q7(b)

Short Answer 1 mark

Hence solve the equationcos sincos cos ii i tani A B The diagram shows the circle with equation xy xy1483 60 +- ++ = and the line y2=-. The line intersects the circle at the points A and B. The centre of the circle is C.

Q7(a)

Short Answer 3 marks

Find the coordinates of A, B and C .

Q7(b)

Short Answer 2 marks

Find the angle ACB in radians. Give your answer correct to 3 significant figures.

Q7(c)

Structured 4 marks

The chord AB divides the circle into two segments. Find the area of the larger segment.

Short Answer 1 mark

The equation of a curve is such that =-. It is given that the curve has a stationary point at (,)219- .

Q9(a)

Short Answer 1 mark

Find an expression for

Q9(b)

Short Answer 2 marks

Find the x-coordinate of the other stationary point of the curve, and determine the nature of this stationary point.

Q9(c)

Short Answer 3 marks

Find the equation of the curve.

Q9(d)

Structured 4 marks

Find the equation of the normal to the curve at the point where =- and x is positive. Express your answer in the form pxqyr0++ =, where p, q and r are integers.

Q10(a)

Short Answer 1 mark

The first, second and third terms of an arithmetic progression are 4k, k and 8k respectively, where k is a non-zero constant.

Q10(i)

Short Answer 2 marks

Find the value of k.

Q10(ii)

Short Answer 3 marks

Find the sum of the first 20 terms of the progression.

Q10(b)

Structured 5 marks

The fourth and sixth terms of a geometric progression are 36 and 6 respectively. The common ratio of the progression is positive. Find the sum to infinity of the progression. Give your answer in the form , where a, b and c are integers.

Q11(a)

Short Answer 1 mark

Express xx42 ++ in the form ()xa b ++ , where a and b are integers. [2] The functions f and g are defined as follows. ()xx x42f =+ + for x2G- ()xx 4g=-- for x2H-

Q11(b)

Short Answer 1 mark

(i) Find an expression for ()xf

Q11(ii)

Short Answer 1 mark

Find an expression for ()()xgf Additional page If you use the following page to complete the answer to any question, the question number must be clearly shown. BLANK PAGE * 0000800000019 * Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable ef fort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. BLANK PAGE * 0000800000020 *

Paper Details

Board	CAIE
Level	A Level
Subject	Mathematics
Code	`9709`
Year	2025
Session	May/June
Q&A	26 questions

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