CAIE A Level 9709

Mathematics 2024 · May/June

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26 Questions Q&A Available

Questions & Model Answers 26 Qs

Q3(a)

Short Answer 3 marks

Show that the equationcos tan7 += can be expressed as sins in12 1207 ii-- =.

Q3(b)

Short Answer 3 marks

Hence solve the equation cos tan7 += for 0 360GGicc .

Short Answer 1 mark

The function f is defined as follows: ()fxx 1=- for x12.

Q4(a)

Short Answer 1 mark

Find an expression for ()fx The diagram shows the graph of ()gyx= where ()gx for xR!.

Q4(b)

Short Answer 1 mark

State the range of g and explain whether g exists. [2] The function h is defined by ()hx for x0H.

Q4(c)

Structured 4 marks

Solve the equation ()hf fx =eo. Give your answer in the form abc+ , where a, b and c are integers.

Short Answer 1 mark

The first and second terms of an arithmetic progression are tani and sini respectively, where 11i .

Q5(a)

Short Answer 1 mark

Given that r i=, find the exact sum of the first 40 terms of the progression. [4] The first and second terms of a geometric progression are tani and sini respectively, where 11i .

Q5(b)

Short Answer 2 marks

(i) Find the sum to infinity of the progression in terms of i.

Q5(ii)

Short Answer 3 marks

Given that r i=, find the sum of the first 10 terms of the progression. Give your answer correct to 3 significant figures.

Short Answer 1 mark

The curve with equation yx x28 =- has a minimum point at A and intersects the positive x-axis at B.

Q6(a)

Structured 4 marks

Find the coordinates of A and B.

Q6(b)

Structured 5 marks

yx x2828 The diagram shows the curve with equation yx x28 =- and the line AB. It is given that the equation of AB is y Find the area of the shaded region between the curve and the line.

Short Answer 1 mark

The equation of a circle is () ()xy a61 8 -+ += . The line with equation ya x2=- is a tangent to the circle.

Q7(a)

Structured 5 marks

Find the two possible values of the constant a.

Q7(b)

Short Answer 1 mark

For the greater value of a, find the equation of the diameter which is perpendicular to the given tangent. [3] B C 2 cm rrad rrad The diagram shows a symmetrical plate ABCDEF. The line ABCD is straight and the length of BC is 2 cm. Each of the two sectors ABF and DCE is of radius r cm and each of the angles ABF and DCE is equal to r radians.

Q7(a)

Short Answer 1 mark

It is given that .cm.r04=

Q7(i)

Short Answer 2 marks

Show that the length .cm.EF24=

Q7(ii)

Structured 4 marks

Find the area of the plate. Give your answer correct to 3 significant figures.

Q7(b)

Structured 4 marks

It is given instead that the perimeter of the plate is 6 cm. Find the value of r. Give your answer correct to 3 significant figures.

Short Answer 1 mark

A function f is such that ()()fxx x6236 =- -l for xR!.

Q9(a)

Structured 4 marks

Determine the set of values of x for which ()fx is decreasing.

Q9(b)

Structured 4 marks

Given that ()f1 1=-, find ()fx.

Q10

Short Answer 1 mark

The equation of a curve is ()yx52 5 =- + for x

Q10(a)

Structured 4 marks

A point P is moving along the curve in such a way that the y-coordinate of point P is decreasing at 5 units per second. Find the rate at which the x-coordinate of point P is increasing when y32=.

Q10(b)

Short Answer 1 mark

Point A on the curve has y-coordinate 32. Point B on the curve is such that the gradient of the curve at B is 3-. Find the equation of the perpendicular bisector of AB. Give your answer in the form axbyc0++ =, where a, b and c are integers. [6] 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 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. Additional page If you use the following page to complete the answer to any question, the question number must be clearly shown.

Paper Details

Board	CAIE
Level	A Level
Subject	Mathematics
Code	`9709`
Year	2024
Session	May/June
Q&A	26 questions

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