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Learn/ A Level Mathematics/ Past Papers/ 2024/ May/June 2024 /Paper 1 (Variant 1)

Pure Mathematics 1 — Variant 1

A Level Mathematics · 9709/11 · May/June 2024

Question Paper

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Mark Scheme

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Questions

4 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
1(a) [2]
Express 3y2−12y−153y^{2} - 12y - 15 in the form 3(y+a)2+b3(y+a)^{2} + b, where aa and bb are constants.
1(b) [3]
Hence find the exact solutions of the equation 3x4−12x2−15=03x^{4} - 12x^{2} - 15 = 0.
3
The coefficient of x3x^{3} in the expansion of (3+ax)6(3 + ax)^{6} is 160160.
3(a) [2]
Find the value of the constant aa.
3(b) [3]
Hence find the coefficient of x3x^{3} in the expansion of (3+ax)6(1−2x)(3 + ax)^{6}(1 - 2x).
8
8(a) [4]
The first three terms of an arithmetic progression are 2525, 4p−14p - 1 and 13−p13 - p, where pp is a constant. Find the value of the tenth term of the progression.
8(b) [4]
The first three terms of a geometric progression are 2525, 4q−14q - 1 and 13−q13 - q, where qq is a positive constant. Find the sum to infinity of the progression.
10 [8]
The equation of a circle is (x−3)2+y2=18(x - 3)^{2} + y^{2} = 18. The line with equation y=mx+cy = mx + c passes through the point (0,−9)(0, -9) and is a tangent to the circle. Find the two possible values of mm and, for each value of mm, find the coordinates of the point at which the tangent touches the circle.

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