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Learn/ A Level Mathematics/ Past Papers/ 2020/ May/June 2020 /Paper 3 (Variant 2)

Pure Mathematics 3 — Variant 2

A Level Mathematics · 9709/32 · May/June 2020

Question Paper

PDF · 128 KB · 20 pages

Mark Scheme

PDF · 417 KB · 13 pages

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Questions

3 of 10 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]
Find the quotient and remainder when 6x4+x3−x2+5x−66x^{4} + x^{3} - x^{2} + 5x - 6 is divided by 2x2−x+12x^{2} - x + 1.
3 [5]
Find the exact value of ∫14x32ln⁡x dx\int_{1}^{4} x^{\frac{3}{2}} \ln x \, \mathrm{d}x.
5
5(a) [3]
Express 2cos⁡x−5sin⁡x\sqrt{2}\cos x - \sqrt{5}\sin x in the form Rcos⁡(x+α)R\cos(x + \alpha), where R>0R > 0 and 0∘<α<90∘0^\circ < \alpha < 90^\circ. Give the exact value of RR and the value of α\alpha correct to 3 decimal places.
5(b) [4]
Hence solve the equation 2cos⁡2θ−5sin⁡2θ=1\sqrt{2}\cos 2\theta - \sqrt{5}\sin 2\theta = 1, for 0∘<θ<180∘0^\circ < \theta < 180^\circ.

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