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Learn/ A Level Mathematics/ Past Papers/ 2023/ Oct/Nov 2023 /Paper 2 (Variant 2)

Pure Mathematics 2 — Variant 2

A Level Mathematics · 9709/22 · Oct/Nov 2023

Question Paper

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Mark Scheme

PDF · 307 KB · 11 pages

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Questions

4 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 [2]
When the polynomial ax3+4ax2−7x−5ax^{3} + 4ax^{2} - 7x - 5 is divided by (x+2)(x + 2), the remainder is 3333. Find the value of the constant aa.
2 [5]
Solve the equation sec⁡θcos⁡(θ−60∘)=4\sec \theta \cos(\theta - 60^\circ) = 4 for −180∘<θ<180∘-180^\circ < \theta < 180^\circ.
4
4(a) [2]
Sketch, on the same diagram, the graphs of y=∣3−x∣y = |3 - x| and y=9−2xy = 9 - 2x.
4(b) [3]
Solve the inequality ∣3−x∣>9−2x|3 - x| > 9 - 2x.
4(c) [3]
Use logarithms to solve the inequality 23x−10<5002^{3x - 10} < 500. Give your answer in the form x<ax < a, where the value of aa is given correct to 3 significant figures.
4(d) [1]
List the integers that satisfy both of the inequalities ∣3−x∣>9−2x|3 - x| > 9 - 2x and 23x−10<5002^{3x - 10} < 500.
5
5(a) [3]
Find the quotient when 6x3−5x2−24x−46x^{3} - 5x^{2} - 24x - 4 is divided by (2x+1)(2x + 1), and show that the remainder is 66.
5(b) [5]
Hence find ∫276x3−5x2−24x−42x+1 dx\int_{2}^{7} \frac{6x^{3} - 5x^{2} - 24x - 4}{2x + 1} \, \mathrm{d}x, giving your answer in the form a+ln⁡ba + \ln b, where aa and bb are integers.

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