AS & A Level Mathematics (9709) — October–November 2023, Paper 23

7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 3 marks · Trigonometry (compound angle formulae)

It is given that θ is an acute angle in degrees such that sin θ = 2/3. Find the exact value of sin(θ + 60°).

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Question 2 · 5 marks · Differentiation (product rule; trigonometric functions)

A curve has equation y = 3 tan(½x) cos 2x. Find the gradient of the curve at the point for which x = ⅓π.

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Question 3 · 6 marks · Integration (∫ of 1/(ax+b); logarithms)

Find ∫₄¹⁰ 4/(2x − 5) dx, giving your answer in the form ln a, where a is an integer.

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Question 4 · 7 marks · The modulus function (graphs)

Sketch, on the same diagram, the graphs of y = 3x − 5 and y = 2x + 7.

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Question 5 · 9 marks · Algebra (factor and remainder theorems)

The polynomial p(x) is defined by p(x) = 6x³ + ax² + bx − 20, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the remainder is −11 when p(x) is…

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Question 6 · 9 marks · Trigonometry (proving identities; double angle formulae)

Show that cosec θ(3 sin 2θ + 4 sin³ θ) ≡ 4 + 6 cos θ − 4 cos² θ.

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Question 7 · 11 marks · Differentiation (implicit differentiation; stationary points)

The curve with equation e^(2x) − 18x + y³ + y = 11 has a stationary point at (p, q). Find the exact value of p.

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← October–November 2023 Paper 31 · October–November 2023 Paper 22 →

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