AS & A Level Further Mathematics (9231) — May–June 2025, Paper 11
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Use standard results from the list of formulae (MF19) to show that sum{r=1}^{n} (2 - 3r)(5 - 3r) = an^3 + bn^2 + cn, where a, b and c are integers to be determined.
Answer this question and get it marked →The cubic equation x^3 + 2x + 1 = 0 has roots alpha, beta, gamma. Find a cubic equation whose roots are alpha^3 - 1, beta^3 - 1, gamma^3 - 1.
Answer this question and get it marked →The sequence u1, u2, u3, ... is such that u1 = 5 and u{n+1} = 6un + 5 for n = 1. Prove by induction that un = 6^n - 1 for all positive integers n.
Answer this question and get it marked →The matrix M is given by M = (1 2; 0 1)(cos theta, -sin theta; sin theta, cos theta), where 0 < theta < 2pi. The matrix M represents a sequence of two geometrical transformations…
Answer this question and get it marked →The curve C has polar equation r = theta e^((1/8) theta), for 0 <= theta <= 2pi. Sketch C.
Answer this question and get it marked →The points A, B, C have position vectors i - 2k, i + 2j + 2k, 2i - j - k, respectively. Find the equation of the plane ABC, giving your answer in the form ax + by + cz = d.
Answer this question and get it marked →The curve C has equation y = (2x^2 - 5x)/(2x^2 - 7x - 4). Find the equations of the asymptotes of C.
Answer this question and get it marked →