AS & A Level Further Mathematics (9231) — May–June 2024, 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 A is given by A = ( k, 1, 0 ; 6, 5, 2 ; -1, 3, -k ), where k is a real constant. Show that A is non-singular.
Answer this question and get it marked →The cubic equation x^3 + 2x^2 + 3x + 1 = 0 has roots alpha, beta, gamma. Find a cubic equation whose roots are alpha^2 + 1, beta^2 + 1, gamma^2 + 1.
Answer this question and get it marked →The matrix M is given by M = ( 1, 2 ; 0, 1 )( 7, 0 ; 0, 1 ). The matrix M represents a sequence of two geometrical transformations in the x-y plane. Give full details of each…
Answer this question and get it marked →Prove by mathematical induction that, for all positive integers n, sum{r=1}^{n} r^2 = (1/6) n(n+1)(2n+1).
Answer this question and get it marked →The lines l1 and l2 have equations r = i + 4j - k + lambda(j - 2k) and r = -3i + 4j + mu(i + 2j + k) respectively. Find the shortest distance between l1 and l2.
Answer this question and get it marked →The curve C has equation y = (x + 1)/(x^2 + 3). Show that C has no vertical asymptotes and state the equation of the horizontal asymptote.
Answer this question and get it marked →The curve C has polar equation r^2 = sin(2theta) cos(theta), for 0 <= theta <= pi. Sketch C and state the equation of the line of symmetry. (Answer on the grid provided in the…
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