AS & A Level Mathematics (9709) — May–June 2025, Paper 32
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Solve the equation (e^x + 2e^(-x)) / (e^x - 3) = 4. Give your answer correct to 3 decimal places. [5]
Answer this question and get it marked →Expand (6 - x)(1 - 2x)^(-3/2) in ascending powers of x, up to and including the term in x^2, simplifying the coefficients. [4]
Answer this question and get it marked →On an Argand diagram shade the region whose points represent complex numbers z which satisfy both the inequalities z - 3i <= 2 and (1/4)pi <= arg(z - 1 - 2i) <= (3/4)pi. [5]
Answer this question and get it marked →Solve the equation 3 cot x - 4 cot 2x = 3 for 0 degrees <= x <= 180 degrees. [6]
Answer this question and get it marked →The square roots of -1 - 4 sqrt(5) i can be expressed in the Cartesian form x + iy, where x and y are real and exact. By first forming a quartic equation in x or y, find the…
Answer this question and get it marked →By sketching a suitable pair of graphs, show that the equation x - 2 = 2 sin((1/2)x) has only one root in the interval 0 < x < pi. [2]
Answer this question and get it marked →Express 7 sin theta + 24 cos theta in the form R cos(theta - alpha), where R 0 and 0 < alpha < (1/2)pi. Give the value of alpha correct to 4 decimal places. [3]
Answer this question and get it marked →The variables x and theta satisfy the differential equation sin 2theta (dx/dtheta) = (4x + 3) cos 2theta, and x = 0 when theta = (1/12)pi. Solve the differential equation and…
Answer this question and get it marked →With respect to the origin O, the points A, B and C have position vectors given by OA = (1, -4, 2), OB = (-2, 1, 3) and OC = (2, 3, 5) (each written as a column vector). Find a…
Answer this question and get it marked →Find the quotient and remainder when x^2 is divided by 1 + 4x^2. [2]
Answer this question and get it marked →The diagram shows the graph of y = 5 sin 2x cos^2 x for 0 <= x <= (1/2)pi and its maximum point M. Find the exact x-coordinate of M. [6]
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