CAIE A Level 9709

Mathematics 2023 · Oct/Nov

17 Questions Q&A Available
AI Paper Analysis & Study Guide
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This CAIE A Level Mathematics paper mainly tests pure mathematics topics, especially trigonometric identities and equations, functions, coordinate geometry, and calculus. Students can expect structured questions that build in parts, such as verifying identities before using them to solve equations, finding domains and ranges, solving equations from function compositions, and working with graphs and intersections of curves.…

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Questions & Model Answers 17 Qs

Q7(a)
Short Answer 1 mark
Verify the identity
Q7(b)
Short Answer 1 mark
Prove the identitytan1+1tan
Q7(c)
Short Answer 1 mark
Using the results of
Q7(c)(b)
Short Answer 1 mark
, solve the equationtan1+1tan =4 cos1, for 0 x=x+a where ais a positive constant.
Q7(a)
Short Answer 3 marks
Find an expression for f x.
Q7(b)
Short Answer 1 mark
(i)State the domain of the function f
Q7(ii)
Short Answer 1 mark
State the range of the function f
Q7(c)
Short Answer 1 mark
Given that , solve the equation gf x=0. [3] y= 3x 2+ 12 y= 2x 2+ 13x The diagram shows curves with equations y=2x 2+13x 2andy=3x 2+12. The curves intersect at points AandB.
Q7(a)
Short Answer 1 mark
Find the coordinates of AandB. [4] 10The equation of a curve is
Q7(a)
Structured 6 marks
Find the x-coordinates of the stationary points of the curve and determine their nature.
Q7(b)
Short Answer 1 mark
State the set of values for which the function f is increasing. [1] 11The coordinates of points A,BandCare6, 4,p, 7and14, 18respectively, wherepis a constant. The line ABis perpendicular to the lineBC.
Q7(a)
Short Answer 1 mark
Given that A circle passes through the points A,BandC.
Q7(b)
Short Answer 3 marks
Find the equation of the circle.
Q7(c)
Short Answer 1 mark
Find the equation of the tangent to the circle at C, giving the answer in the formdx+ey+f=0, where d,eandfare integers. [3] Additional Page If you use the following lined page to complete the answer
Q7(c)(s)
Short Answer 1 mark
to any question
Q7(c)(s)
Short Answer 1 mark
, the question number
Q7(c)(s)
Short Answer 1 mark
must be clearly shown. 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.
Paper Details
Board CAIE
Level A Level
Subject Mathematics
Code 9709
Year 2023
Session Oct/Nov
Q&A 17 questions
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