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Learn/ A Level Mathematics/ Past Papers/ 2021/ Oct/Nov 2021 /Paper 1 (Variant 1)

Pure Mathematics 1 — Variant 1

A Level Mathematics · 9709/11 · Oct/Nov 2021

Question Paper

PDF · 130 KB · 20 pages

Mark Scheme

PDF · 386 KB · 19 pages

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Questions

4 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
1(a) [1]
Expand (1−12x)2(1 - \frac{1}{2x})^{2}.
1(b) [2]
Find the first four terms in the expansion, in ascending powers of xx, of (1+2x)6(1 + 2x)^{6}.
1(c) [2]
Hence find the coefficient of xx in the expansion of (1−12x)2(1+2x)6(1 - \frac{1}{2x})^{2} (1 + 2x)^{6}.
2 [5]
A curve has equation y=kx2+2x−ky = kx^{2} + 2x - k and a line has equation y=kx−2y = kx - 2, where kk is a constant. Find the set of values of kk for which the curve and line do not intersect.
3 [4]
Solve, by factorising, the equation 6cos⁡θtan⁡θ−3cos⁡θ+4tan⁡θ−2=06\cos\theta\tan\theta - 3\cos\theta + 4\tan\theta - 2 = 0, for 0∘⩽θ⩽180∘0^\circ \leqslant \theta \leqslant 180^\circ.
9
A curve has equation y=f(x)y = \mathrm{f}(x), and it is given that f′(x)=2x2−7−4x2\mathrm{f}'(x) = 2x^{2} - 7 - \frac{4}{x^{2}}.
9(a) [4]
Given that f(1)=−13\mathrm{f}(1) = -\frac{1}{3}, find f(x)\mathrm{f}(x).
9(b) [5]
Find the coordinates of the stationary points on the curve.
9(c) [1]
Find f′′(x)\mathrm{f}''(x).
9(d) [2]
Hence, or otherwise, determine the nature of each of the stationary points.

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