AS & A Level Further Mathematics (9231) — May–June 2025, Paper 24
8 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Find the values of k for which the system of equations x + 2y + 3z = 1, kx + 5y + 6z = 2, 7x + 2ky + 9z = 3, does not have a unique solution.
Answer this question and get it marked →Find the exact value of integral from 1 to 5/2 of 1/sqrt(x^2 - 2x + 5) dx, giving your answer in logarithmic form.
Answer this question and get it marked →Find the particular solution of the differential equation d^2y/dx^2 + 4 dy/dx + 5y = 13 e^{3x} given that y = 1 and dy/dx = 0 when x = 0.
Answer this question and get it marked →A curve has parametric equations x = t^3 - t^2 + t - 1 and y = t e^t. Show that 1 is the only real value of t for which x = 0.
Answer this question and get it marked →Use de Moivre's theorem to show that sin 7θ = -64 sin^7 θ + 112 sin^5 θ - 56 sin^3 θ + 7 sin θ.
Answer this question and get it marked →Find the solution of the differential equation x dy/dx - y = 2x^2 tan^{-1} x for which y = (1/2)π when x = 1. Give your answer in the form y = f(x).
Answer this question and get it marked →The matrix A is given by A = ( 1 7 11 ; 0 2 5 ; 0 0 -3 ) (a 3x3 matrix with rows [1, 7, 11], [0, 2, 5], [0, 0, -3]). Find a matrix P and a diagonal matrix D such that A^6 = P D…
Answer this question and get it marked →The curve C has equation y = tanh x for x = 0. Sketch C and state the equation of the asymptote.
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