AS & A Level Further Mathematics (9231) — October–November 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 →Use standard results from the list of formulae (MF19) to find sum{r=1}^{n} (3r^2 + 3r + 1), simplifying your answer.
Answer this question and get it marked →Prove by mathematical induction that, for all positive integers n, (d^n/dx^n)(x^2 e^x) = (x^2 + 2nx + n(n-1)) e^x.
Answer this question and get it marked →The matrix M is given by M = ( k, 0 ; 0, 1 )( 1, 0 ; 1, 1 ), where k is a constant and k != 0 and k != 1. (Here M is the product of the 2x2 matrix with first row [k, 0], second…
Answer this question and get it marked →The cubic equation 27x^3 + 18x^2 + 6x - 1 = 0 has roots alpha, beta, gamma. Show that a cubic equation with roots 3alpha + 1, 3beta + 1, 3gamma + 1 is y^3 - y^2 + y - 2 = 0.
Answer this question and get it marked →The plane Pi1 has equation r = i - j - 2k + lambda(i - 2j - 3k) + mu(3i - k). Find an equation for Pi1 in the form ax + by + cz = d.
Answer this question and get it marked →The curve C has polar equation r = e^(-theta) - e^(-(1/2)pi), where 0 <= theta <= (1/2)pi. Sketch C and state, in exact form, the greatest distance of a point on C from the pole.
Answer this question and get it marked →The curve C has equation y = f(x), where f(x) = x^2 / (x + 1). Find the equations of the asymptotes of C.
Answer this question and get it marked →← October–November 2023 Paper 13 · October–November 2023 Paper 11 →