AS & A Level Further Mathematics (9231) — May–June 2025, Paper 23
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 e^(1/(x+2)) up to and including the term in x^2.
Answer this question and get it marked →Starting from the definitions of tanh and sech in terms of exponentials, prove that tanh^2(t) + sech^2(t) = 1.
Answer this question and get it marked →The curve C has equation 9y^2 - 3arcsinh(xy) = 1 - 3ln(3). Show that, at the point (4, 1/3) on C, dy/dx = -1/2.
Answer this question and get it marked →Find the particular solution of the differential equation d^2x/dt^2 + dx/dt - 2x = 2t^2 + t - 1, given that, when t = 0, x = dx/dt = 0.
Answer this question and get it marked →Use de Moivre's theorem to show that sec(5theta) = sec^5(theta) / (5sec^4(theta) - 20sec^2(theta) + 16).
Answer this question and get it marked →The diagram shows the curve with equation y = 1/(x^2 + 1) for 0 <= x <= 1, together with a set of n rectangles of width 1/n. The rectangles are drawn on the subintervals between…
Answer this question and get it marked →Find the solution of the differential equation dy/dx - ((2x + 6)/(x^2 + 6x + 5))y = 4, given that y = 0 when x = 0. Give your answer in an exact form.
Answer this question and get it marked →Find the values of a for which the system of equations (3/2)x + 3y + 8z = 1, ax + 3y + 4z = 2, ay - z = 3, does not have a unique solution.
Answer this question and get it marked →