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Learn/ A Level Mathematics/ Past Papers/ 2024/ May/June 2024 /Paper 2 (Variant 1)

Pure Mathematics 2 — Variant 1

A Level Mathematics · 9709/21 · May/June 2024

Question Paper

PDF · 2.6 MB · 16 pages

Mark Scheme

PDF · 245 KB · 13 pages

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Questions

4 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 [3]
A curve has equation y=2tan⁡x−5sin⁡xy = 2\tan x - 5\sin x for 0⩽x<12π0 \leqslant x < \frac{1}{2}\pi. Find the xx-coordinate of the stationary point of the curve. Give your answer correct to 3 significant figures.
2 [5]
A curve has equation x2ln⁡y+y2+4x=9x^{2}\ln y + y^{2} + 4x = 9. Find the gradient of the curve at the point (2,1)(2, 1).
3
3(a) [2]
Sketch on the same diagram the graphs of y=∣3x−8∣y = |3x - 8| and y=5−xy = 5 - x.
3(b) [4]
Solve the inequality ∣3x−8∣<5−x|3x - 8| < 5 - x.
3(c) [2]
Hence determine the largest integer NN satisfying the inequality ∣3e0.1N−8∣<5−e0.1N|3\mathrm{e}^{0.1N} - 8| < 5 - \mathrm{e}^{0.1N}.
4
4(a) [4]
Show that 3tan⁡2θ+tan⁡(θ+45∘)≡tan⁡2θ+8tan⁡θ+11−tan⁡2θ3\tan 2\theta + \tan(\theta + 45^{\circ}) \equiv \frac{\tan^{2}\theta + 8\tan\theta + 1}{1 - \tan^{2}\theta}.
4(b) [3]
Hence solve the equation 3tan⁡2θ+tan⁡(θ+45∘)=43\tan 2\theta + \tan(\theta + 45^{\circ}) = 4 for 0∘<θ<180∘0^{\circ} < \theta < 180^{\circ}.

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