CAIE A Level 9709

Mathematics 2023 · May/June

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18 Questions Q&A Available

Questions & Model Answers 18 Qs

Q3(a)
Short Answer 1 mark
On an Argand diagram, sketch the locus of points representing complex numbers zsatisfying
Q3(b)
Short Answer 3 marks
Find the least value of zfor points on this locus, giving your answer in an exact form.[2] 4Solve the equation 2 cos 5The complex number 2 +yi is denoted bya, whereyis a real number andy<0. It is given thata=a ain terms ofy.
Q3(b)
Short Answer 1 mark
Given that Re 6The equation cot x=3xhas one root in the interval 0<x< π, denoted by!.
Q3(a)
Short Answer 2 marks
Show by calculation that !lies between 0.5 and 1.
Q3(b)
Short Answer 2 marks
Show that, if a sequence of positive values given by the iterative formulan+1 +4 tan converges, then it converges to!.
Q3(c)
Short Answer 1 mark
Use this iterative formula to calculate !correct to 2 decimal places. Give the result of each iteration to 4 decimal places. [3] 7The equation of a curve is 3 +4xy+3y=5.
Q3(a)
Structured 5 marks
Show that 3x+2y 2x+3y y+2x=0.
Q8(a)
Structured 7 marks
The variables 4+9y 2x+1 It is given that y=0 whenx=1. yin terms ofx.
Q8(b)
Short Answer 1 mark
State what happens to the value of [1] 9Let f
Q8(a)
Structured 5 marks
Express f xin partial fractions.
Q8(b)
Short Answer 1 mark
Hence show that fxdx= The diagram shows the curve y=x+5
Q8(a)
Structured 5 marks
Find the exact coordinates of M.
Q8(b)
Short Answer 1 mark
Using the substitution the curve and the x-axis. Give your answer in the forma 13, whereais a rational number. [5] 11The points
Q8(a)
Structured 5 marks
Show that ldoes not intersect the line passing throughAandB.
Q8(b)
Short Answer 1 mark
Find the position vector of the foot of the perpendicular from Atol. [4] Additional Page If you use the following lined page to complete the answer
Q8(b)(s)
Short Answer 1 mark
to any question
Q8(b)(s)
Short Answer 1 mark
, the question number
Q8(b)(s)
Short Answer 1 mark
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Paper Details
Board CAIE
Level A Level
Subject Mathematics
Code 9709
Year 2023
Session May/June
Q&A 18 questions
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