AS & A Level Further Mathematics (9231) — May–June 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 →Show that the system of equations x + 2y + 3z = 1, 4x + 5y + 6z = 1, 7x + 8y + 9z = 1, does not have a unique solution.
Answer this question and get it marked →Use the substitution z = x + y to find the solution of the differential equation dy/dx = (1 + 3x + 3y) / (3x + 3y - 1) for which y = 0 when x = 1. Give your answer in the form…
Answer this question and get it marked →By considering the binomial expansion of (z + z^(-1))^4, where z = cos(theta) + isin(theta), use de Moivre's theorem to show that cos^4(theta) = (1/8)(cos(4theta) + 4cos(2theta) +…
Answer this question and get it marked →The integral In is defined by In = integral from 0 to 1 of (1 + x^5)^n dx. By considering (d/dx)(x(1 + x^5)^n), or otherwise, show that (5n + 1)In = 2^n + 5nI{n-1}.
Answer this question and get it marked →The matrix A is given by A = ( 18 5 -11 ; 8 6 -4 ; 32 10 -20 ) (that is, the rows of A are (18, 5, -11), (8, 6, -4) and (32, 10, -20)). Show that the characteristic equation of A…
Answer this question and get it marked →Find the particular solution of the differential equation d^2x/dt^2 - 12(dx/dt) + 36x = 37sin(t), given that, when t = 0, x = dx/dt = 0.
Answer this question and get it marked →Use the substitution u = x^2 - 1 to find the integral of x / sqrt(x^2 - 1) dx.
Answer this question and get it marked →Starting from the definitions of sech and tanh in terms of exponentials, prove that 1 - sech^2(t) = tanh^2(t).
Answer this question and get it marked →