AS & A Level Further Mathematics (9231) — May–June 2023, Paper 12
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Let A = ( 3, 0 ; 1, 1 ) (the 2x2 matrix with first row [3, 0] and second row [1, 1]). Prove by mathematical induction that, for all positive integers n, 2A^n = ( 23^n, 0 ; 3^n -…
Answer this question and get it marked →The cubic equation x^3 + 4x^2 + 6x + 1 = 0 has roots alpha, beta, gamma. Find the value of alpha^2 + beta^2 + gamma^2.
Answer this question and get it marked →Use the method of differences to find sum{r=1}^{n} 1/( (kr + 1)(kr - k + 1) ) in terms of n and k, where k is a positive constant.
Answer this question and get it marked →The matrix M is given by M = ( a, b^2 ; c^2, a ) (the 2x2 matrix with first row [a, b^2] and second row [c^2, a]), where a, b, c are real constants and b != 0. Show that M does…
Answer this question and get it marked →The curve C has polar equation r^2 = 1/(theta^2 + 1), for 0 <= theta <= pi. Sketch C and state the polar coordinates of the point of C furthest from the pole.
Answer this question and get it marked →The curve C has equation y = (x^2 + 2x - 15)/(x - 2). Find the equations of the asymptotes of C.
Answer this question and get it marked →The plane Pi1 has equation r = -4j - 3k + lambda(i - j + k) + mu(i + j - k). Obtain an equation of Pi1 in the form px + qy + rz = d.
Answer this question and get it marked →