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Learn/ A Level Mathematics/ Past Papers/ 2020/ Feb/March 2020 /Paper 2 (Variant 2)

Pure Mathematics 2 — Variant 2

A Level Mathematics · 9709/22 · Feb/March 2020

Question Paper

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Mark Scheme

PDF · 232 KB · 11 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 equation 2sin⁡(θ+30∘)+5cos⁡θ=2sin⁡θ2\sin(\theta + 30^\circ) + 5\cos\theta = 2\sin\theta for 0∘<θ<90∘0^\circ < \theta < 90^\circ.
2
2(a) [3]
Find the quotient when 4x3+17x2+9x4x^{3} + 17x^{2} + 9x is divided by x2+5x+6x^{2} + 5x + 6, and show that the remainder is 1818.
2(b) [3]
Hence solve the equation 4x3+17x2+9x−18=04x^{3} + 17x^{2} + 9x - 18 = 0.
3 [6]
It is given that ∫a3a22x−5 dx=ln⁡72\int_{a}^{3a} \frac{2}{2x - 5} \, \mathrm{d}x = \ln \frac{7}{2}. Find the value of the positive constant aa.
4 [6]
A curve has equation 3x2−y2−4ln⁡(2y+3)=263x^{2} - y^{2} - 4\ln(2y + 3) = 26. Find the equation of the tangent to the curve at the point (3,−1)(3, -1).
5
5(a) [3]
Sketch, on the same diagram, the graphs of y=∣x+2k∣y = |x + 2k| and y=∣2x−3k∣y = |2x - 3k|, where kk is a positive constant. Give, in terms of kk, the coordinates of the points where each graph meets the axes.
5(b) [4]
Find, in terms of kk, the coordinates of each of the two points where the graphs intersect.
5(c) [2]
Find, in terms of kk, the largest value of tt satisfying the inequality ∣2t+2k∣⩾∣2t+1−3k∣|2^{t} + 2k| \geqslant |2^{t+1} - 3k|.

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