AS & A Level Mathematics (9709) — May–June 2024, Paper 13

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

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Question 1 · 4 marks · Series (binomial expansion)

Find the coefficient of x^2 in the expansion of (2 − 5x)(1 + 3x)^10.

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Question 2 · 5 marks · Trigonometry (graphs)

The diagram shows the curve y = k cos(x − (1/6)π) where k is a positive constant and x is measured in radians. The curve crosses the x-axis at point A and B is a minimum point.…

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Question 3 · 6 marks · Circular measure

The diagram shows a sector of a circle with centre C. The radii CA and CB each have length r cm and the size of the reflex angle ACB is θ radians. The sector, shaded in the…

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Question 4 · 6 marks · Trigonometry (identities and equations)

Show that the equation cos θ(7 tan θ − 5 cos θ) = 1 can be written in the form a sin^2 θ + b sin θ + c = 0, where a, b and c are integers to be found.

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Question 5 · 7 marks · Differentiation

The equation of a curve is y = 2x^2 − 1/(2x) + 3. Find the coordinates of the stationary point.

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Question 6 · 7 marks · Integration

A curve passes through the point (4/5, −3) and is such that dy/dx = −20/(5x − 3)^2. Find the equation of the curve.

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Question 7 · 7 marks · Series (arithmetic progression)

The first term of an arithmetic progression is 1.5 and the sum of the first ten terms is 127.5. Find the common difference.

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Question 8 · 8 marks · Coordinate geometry (circles and tangents)

A circle with equation x^2 + y^2 − 6x + 2y − 15 = 0 meets the y-axis at the points A and B. The tangents to the circle at A and B meet at the point P. Find the coordinates of P.

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Question 9 · 8 marks · Differentiation (tangents)

The diagram shows the curve with equation y = √(2x^3 + 10). Find the equation of the tangent to the curve at the point where x = 3. Give your answer in the form ax + by + c = 0…

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Question 10 · 8 marks · Series (geometric progression)

The geometric progression a₁, a₂, a₃, … has first term 2 and common ratio r where r 0. It is given that (9/2)a₅ + 7a₃ = 8. Find the value of r.

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Question 11 · 9 marks · Functions (range, completing the square)

The function f is defined by f(x) = 10 + 6x − x^2 for x ∈ ℝ. By completing the square, find the range of f.

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← May–June 2024 Paper 21 · May–June 2024 Paper 12 →

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