AS & A Level Further Mathematics (9231) — October–November 2023, Paper 22
8 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Find the Maclaurin's series for ln(x + 2) + ln(x^2 + 5) up to and including the term in x^2.
Answer this question and get it marked →It is given that x = 1 + 1/t and y = te^t. Show that dy/dx = -e^t(t^3 + t^2).
Answer this question and get it marked →Use de Moivre's theorem to show that cos 5theta = 16 cos^5 theta - 20 cos^3 theta + 5 cos theta.
Answer this question and get it marked →Find the solution of the differential equation dy/dx + 3y = sin x for which y = 1 when x = 0. Give your answer in the form y = f(x).
Answer this question and get it marked →The diagram shows part of the curve y = x sech^2(x) and its maximum point M. Show that, at M, 2x tanh x - 1 = 0 and verify that this equation has a root between 0.7 and 0.8.
Answer this question and get it marked →The matrix P is given by P = ( 1 -1 1 ) ( 0 2 1 ) ( 0 0 -1 ). State the eigenvalues of P.
Answer this question and get it marked →Starting from the definitions of cosh and sinh in terms of exponentials, prove that 2 sinh^2 A = cosh 2A - 1.
Answer this question and get it marked →It is given that v = y^4 and y^3 (d^2y/dx^2) + 3y^2 (dy/dx)^2 + y^3 (dy/dx) + y^4 = e^(-2x). Show that d^2v/dx^2 + dv/dx + 4v = 4 e^(-2x).
Answer this question and get it marked →← October–November 2023 Paper 23 · October–November 2023 Paper 21 →