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Learn/ A Level Mathematics/ Past Papers/ 2020/ Oct/Nov 2020 /Paper 2 (Variant 2)

Pure Mathematics 2 — Variant 2

A Level Mathematics · 9709/22 · Oct/Nov 2020

Question Paper

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Mark Scheme

PDF · 258 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 [3]
Solve the equation 7cot⁡θ=3cosec⁡θ7 \cot \theta = 3 \operatorname{cosec} \theta for 0∘<θ<90∘0^\circ < \theta < 90^\circ.
2 [5]
Given that 23x+2+823x−7=5\frac{2^{3x+2} + 8}{2^{3x} - 7} = 5, find the value of 23x2^{3x} and hence, using logarithms, find the value of xx correct to 4 significant figures.
3
3(a) [2]
Sketch, on a single diagram, the graphs of y=∣12x−a∣y = |\frac{1}{2}x - a| and y=32x−12ay = \frac{3}{2}x - \frac{1}{2}a, where aa is a positive constant.
3(b) [3]
Find the coordinates of the point of intersection of the two graphs.
3(c) [1]
Deduce the solution of the inequality ∣12x−a∣>32x−12a|\frac{1}{2}x - a| > \frac{3}{2}x - \frac{1}{2}a.
5
The equation of a curve is 2e2xy−y3+4=02\mathrm{e}^{2x}y - y^{3} + 4 = 0.
5(a) [4]
Show that dydx=4e2xy3y2−2e2x\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{4\mathrm{e}^{2x}y}{3y^{2} - 2\mathrm{e}^{2x}}.
5(b) [3]
The curve passes through the point (0,2)(0, 2). Find the equation of the tangent to the curve at this point, giving your answer in the form ax+by+c=0ax + by + c = 0.
5(c) [2]
Show that the curve has no stationary points.
6
6(a) [4]
Find ∫(84x+1+8cos⁡2(4x+1))dx\int \left( \frac{8}{4x+1} + \frac{8}{\cos^{2}(4x+1)} \right) \mathrm{d}x.
6(b) [6]
It is given that ∫012π(3+4cos⁡212x+ksin⁡2x) dx=10\int_{0}^{\frac{1}{2}\pi} (3 + 4\cos^{2} \frac{1}{2}x + k \sin 2x) \, \mathrm{d}x = 10. Find the exact value of the constant kk.

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