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Learn/ A Level Mathematics/ Past Papers/ 2024/ May/June 2024 /Paper 2 (Variant 2)

Pure Mathematics 2 — Variant 2

A Level Mathematics · 9709/22 · May/June 2024

Question Paper

PDF · 2.7 MB · 16 pages

Mark Scheme

PDF · 239 KB · 12 pages

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Questions

5 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.

1 [4]
Solve the inequality ∣5x+7∣>∣2x−3∣|5x + 7| > |2x - 3|.
2 [4]
Use logarithms to solve the equation 62x−1=5e3x+26^{2x-1} = 5e^{3x+2}. Give your answer correct to 4 significant figures.
4 [7]
A curve is defined by the parametric equations x=4cos⁡2t,y=3sin⁡2t,x = 4\cos^{2}t, \quad y = \sqrt{3}\sin 2t, for values of tt such that 0<t<12π0 < t < \frac{1}{2}\pi. Find the equation of the normal to the curve at the point for which t=16πt = \frac{1}{6}\pi. Give your answer in the form ax+by+c=0ax + by + c = 0 where aa, bb and cc are integers.
5
The polynomial p(x)\mathrm{p}(x) is defined by p(x)=9x3+18x2+5x+4\mathrm{p}(x) = 9x^{3} + 18x^{2} + 5x + 4.
5(a) [3]
Find the quotient when p(x)\mathrm{p}(x) is divided by (3x+2)(3x + 2), and show that the remainder is 66.
5(b) [5]
Find the value of ∫02p(x)3x+2 dx\int_{0}^{2} \frac{\mathrm{p}(x)}{3x+2} \, \mathrm{d}x, giving your answer in the form a+ln⁡ba + \ln b where aa and bb are integers.
7
7(a) [2]
Prove that 2sin⁡θcosec⁡2θ≡sec⁡θ2\sin\theta \operatorname{cosec} 2\theta \equiv \sec\theta.
7(b) [5]
Solve the equation tan⁡2θ+7sin⁡θcosec⁡2θ=8\tan^{2}\theta + 7\sin\theta \operatorname{cosec} 2\theta = 8 for −π<θ<π-\pi < \theta < \pi.
7(c) [3]
Find ∫8sin⁡212xcosec⁡2x dx\int 8\sin^{2}\frac{1}{2}x \operatorname{cosec}^{2}x \, \mathrm{d}x.

Published by Cambridge Assessment International Education. Reproduced for study use.