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Learn/ A Level Mathematics/ Past Papers/ 2020/ Oct/Nov 2020 /Paper 1 (Variant 2)

Pure Mathematics 1 — Variant 2

A Level Mathematics · 9709/12 · Oct/Nov 2020

Question Paper

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Mark Scheme

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Questions

6 of 11 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]
The coefficient of x3x^{3} in the expansion of (1+kx)(1−2x)5(1 + kx)(1 - 2x)^{5} is 20. Find the value of the constant kk.
2 [5]
The first, second and third terms of a geometric progression are 2p+62p + 6, −2p-2p and p+2p + 2 respectively, where pp is positive. Find the sum to infinity of the progression.
3 [5]
The equation of a curve is y=2x2+m(2x+1)y = 2x^{2} + m(2x + 1), where mm is a constant, and the equation of a line is y=6x+4y = 6x + 4. Show that, for all values of mm, the line intersects the curve at two distinct points.
4 [5]
The sum, SnS_{n}, of the first nn terms of an arithmetic progression is given by Sn=n2+4nS_{n} = n^{2} + 4n. The kkth term in the progression is greater than 200. Find the smallest possible value of kk.
5
Functions f and g are defined by f(x)=4x−2f(x) = 4x - 2, for x∈Rx \in \mathbb{R}, g(x)=4x+1g(x) = \frac{4}{x + 1}, for x∈Rx \in \mathbb{R}, x≠−1x \neq -1.
5(a) [1]
Find the value of fg(7)fg(7).
5(b) [5]
Find the values of xx for which f−1(x)=g−1(x)f^{-1}(x) = g^{-1}(x).
7
The point (4,7)(4, 7) lies on the curve y=f(x)y = f(x) and it is given that f′(x)=6x−12−4x−32f'(x) = 6x^{-\frac{1}{2}} - 4x^{-\frac{3}{2}}.
7(a) [3]
A point moves along the curve in such a way that the xx-coordinate is increasing at a constant rate of 0.12 units per second. Find the rate of increase of the yy-coordinate when x=4x = 4.
7(b) [4]
Find the equation of the curve.

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