AS & A Level Mathematics (9709) — May–June 2025, Paper 11

10 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 · Trigonometry

Solve the equation 6 sin θ = 1 + 2/(sin θ) for −180° < θ < 180°.

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Question 2 · 6 marks · Differentiation

The equation of a curve is such that dy/dx = 4(2x − 5)^3 − 9x^(1/2). The curve passes through the point A(4, −11/2). Find the gradient of the normal to the curve at the point A.

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Question 3 · 7 marks · Series

The third term of a geometric progression is 18 and the sum of the first three terms is 26. It is given that the common ratio is negative. Find the tenth term of the progression.…

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Question 4 · 5 marks · Integration

The diagram shows the curve with equation y = 5x^(3/2) − 20x and the line with equation y = x − 16. The x-coordinates of the points of intersection of the curve and line are 1 and…

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Question 5 · 7 marks · Binomial expansion

Find the first three terms, in ascending powers of x, in the expansion of each of the following expressions. (2 − px)^5

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Question 6 · 9 marks · Quadratics

The equation of a curve is 2x^2 − kxy + 2 = 0 and the equation of a line is y = px + 3, where k and p are constants. Given that k = 2 and p = 11, find the coordinates of the…

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Question 7 · 9 marks · Differentiation

The equation of a curve is y = 4x^2 + 9/(x^2) − 8. A point P is moving along the curve in such a way that its y-coordinate is decreasing at 5 units per second. Find the rate at…

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Question 8 · 8 marks · Coordinate geometry

The circle with equation x^2 + y^2 − 6x + 10y − 27 = 0 intersects the line x = −2 at the points P and Q. Find the area of the triangle formed by the tangents to the circle at P…

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Question 9 · 8 marks · Trigonometry

The diagram shows a sector ABC of a circle with centre A and radius r cm. The angle BAC is α radians, where 0 < α < (1/2)π. It is given that the area of the triangle ABC is 4 cm^2…

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Question 10 · 12 marks · Functions

The functions f and g are defined by f(x) = √x for x ⩾ 0, g(x) = 3√(x + 2) − 5 for x ⩾ −2. Describe fully a sequence of transformations which transforms the graph of y = f(x) to…

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