AS & A Level Further Mathematics (9231) — May–June 2025, Paper 13
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →The matrix M represents the sequence of two transformations in the x-y plane given by a stretch parallel to the x-axis, scale factor 14, followed by a rotation anticlockwise about…
Answer this question and get it marked →Prove by mathematical induction that 2025^n + 47^n - 2 is divisible by 46 for all positive integers n.
Answer this question and get it marked →The quartic equation x^4 + 7x^2 + 3x + 22 = 0 has roots alpha, beta, gamma, delta. Find the value of alpha^2 + beta^2 + gamma^2 + delta^2.
Answer this question and get it marked →Let wr = r(r+1)(r+2)...(r+9). Show that w{r+1} - wr = 10(r+1)(r+2)...(r+9).
Answer this question and get it marked →The plane Pi has equation r = 2i + 3j - 2k + lambda(i - 2j - k) + mu(3i + 2j - 2k). Find a Cartesian equation of Pi, giving your answer in the form ax + by + cz = d.
Answer this question and get it marked →The curve C has equation y = (x^2 + a)/(x + a), where a is a positive constant. Find the equations of the asymptotes of C.
Answer this question and get it marked →The curve C has polar equation r^2 = e^(sin(theta)) cos(theta), for -(1/2)pi <= theta <= (1/2)pi. Find the polar coordinates of the point on C that is furthest from the pole,…
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