AS & A Level Further Mathematics (9231) — October–November 2023, Paper 11
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →By considering (r + 1)^2 - r^2, use the method of differences to prove that sum{r=1}^{n} r = (1/2) n (n + 1).
Answer this question and get it marked →Prove by mathematical induction that, for all positive integers n, 1 + 2x + 3x^2 + ... + n x^(n-1) = (1 - (n + 1) x^n + n x^(n+1)) / (1 - x)^2.
Answer this question and get it marked →The quartic equation x^4 + b x^3 + c x^2 + d x - 2 = 0 has roots alpha, beta, gamma, delta. It is given that alpha + beta + gamma + delta = 3, alpha^2 + beta^2 + gamma^2 + delta^2…
Answer this question and get it marked →The lines l1 and l2 have equations r = -2i - 3j - 5k + lambda(-4i + 3j + 5k) and r = 2i - 2j + 3k + mu(2i - 3j + k) respectively. Find the shortest distance between l1 and l2.
Answer this question and get it marked →Let k be a constant. The matrices A, B and C are given by A = [[1, k, 3], [2, 1, 3], [3, 2, 5]] (rows (1, k, 3), (2, 1, 3), (3, 2, 5)), B = [[0, -2], [-1, 3], [0, 0]] (rows (0,…
Answer this question and get it marked →Show that the curve with Cartesian equation (x - 1/2)^2 + y^2 = 1/4 has polar equation r = cos theta.
Answer this question and get it marked →The curve C has equation y = f(x), where f(x) = (x^2 + 2) / (x^2 - x - 2). Find the equations of the asymptotes of C.
Answer this question and get it marked →