AS & A Level Further Mathematics (9231) — October–November 2023, Paper 23
8 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Show that the system of equations 14x - 4y + 6z = 5, x + y + kz = 3, -21x + 6y - 9z = 14, where k is a constant, does not have a unique solution and interpret this situation…
Answer this question and get it marked →Find the roots of the equation (z + 5i)^3 = 4 + 4 sqrt(3) i, giving your answers in the form r cos(theta) + i(r sin(theta) - 5), where r 0 and 0 < theta < 2pi.
Answer this question and get it marked →Find the first three terms in the Maclaurin's series for tanh^(-1)((1/2) e^x) in the form (1/2) ln(a) + b x + c x^2, giving the exact values of the constants a, b and c.
Answer this question and get it marked →Find the particular solution of the differential equation d^2y/dx^2 + 2 dy/dx + 3y = 27 x^2, given that, when x = 0, y = 2 and dy/dx = -8.
Answer this question and get it marked →The curve C has parametric equations x = (2/3) t^(3/2) - 2 t^(1/2) and y = 2t + 5, for 0 < t <= 3. Find the exact length of C.
Answer this question and get it marked →Starting from the definitions of cosh and sinh in terms of exponentials, prove that sinh(2x) = 2 sinh(x) cosh(x).
Answer this question and get it marked →The matrix A is the 3x3 upper-triangular matrix with rows (-6, 2, 13), (0, -2, 5) and (0, 0, 8). Find a matrix P and a diagonal matrix D such that A^(-1) = P D P^(-1).
Answer this question and get it marked →State the sum of the series 1 + z + z^2 + ... + z^(n-1), for z != 1.
Answer this question and get it marked →← October–November 2023 Paper 31 · October–November 2023 Paper 22 →