AS & A Level Further Mathematics (9231) — October–November 2024, 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 set of values of k for which the system of equations x + 5y + 6z = 1, kx + 2y + 2z = 2, -3x + 4y + 8z = 3, has a unique solution and interpret this situation…
Answer this question and get it marked →It is given that x = 1 + 1/t and y = arccos(t) (that is, y = cos^(-1) t) for 0 < t < 1. Show that dy/dx = t^2 / sqrt(1 - t^2).
Answer this question and get it marked →A curve has equation y = e^x for ln(4/3) <= x <= ln(12/5). The area of the surface generated when the curve is rotated through 2pi radians about the x-axis is denoted by A. Use…
Answer this question and get it marked →The matrix A is given by A = [ -11 1 8 ; 0 -2 0 ; -16 1 13 ]. Show that the column vector (1, 1, 1)^T is an eigenvector of A and state the corresponding eigenvalue.
Answer this question and get it marked →Find the particular solution of the differential equation 6 d^2x/dt^2 - 5 dx/dt + x = t^2 + t + 1, given that, when t = 0, x = 12 and dx/dt = -6.
Answer this question and get it marked →The diagram shows the curve with equation y = (1/2)^x for 0 <= x <= 1, together with a set of N rectangles each of width 1/N. By considering the sum of the areas of these…
Answer this question and get it marked →Show that an appropriate integrating factor for sqrt(x^2 + 16) dy/dx + y = x sqrt(x^2 + 16) is (1/4)x + (1/4) sqrt(x^2 + 16).
Answer this question and get it marked →By considering the binomial expansion of (z + 1/z)^7, where z = cos(theta) + i sin(theta), use de Moivre's theorem to show that cos^7(theta) = a cos(7 theta) + b cos(5 theta) + c…
Answer this question and get it marked →← October–November 2024 Paper 31 · October–November 2024 Paper 22 →