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.
Start with Question 1 →Solve the equation 6 sin θ = 1 + 2/(sin θ) for −180° < θ < 180°.
Answer this question and get it marked →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.
Answer this question and get it marked →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.…
Answer this question and get it marked →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…
Answer this question and get it marked →Find the first three terms, in ascending powers of x, in the expansion of each of the following expressions. (2 − px)^5
Answer this question and get it marked →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…
Answer this question and get it marked →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…
Answer this question and get it marked →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…
Answer this question and get it marked →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…
Answer this question and get it marked →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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