AS & A Level Further Mathematics (9231) — May–June 2024, 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 roots of the equation z^3 = -108sqrt(3) + 108i, giving your answers in the form r(cos(theta) + isin(theta)), where r 0 and 0 < theta < 2pi.
Answer this question and get it marked →Find the Maclaurin's series for e^(1 + x^2) + e^(1 - x) up to and including the term in x^2.
Answer this question and get it marked →It is given that x = sin^(-1)(t) and y = tcos^(-1)(t), for 0 <= t < 1. Show that dy/dx = -t + sqrt(1 - t^2)cos^(-1)(t).
Answer this question and get it marked →It is given that, for n = 0, In = integral from 0 to ln(3) of sech^n(x) dx. Show that, for n = 2, (n - 1)In = (3/5)^(n-2)(4/5) + (n - 2)I(n-2). [You may use the result that…
Answer this question and get it marked →The diagram shows the curve with equation y = 2x - x^2 for 0 <= x <= 1, together with a set of n rectangles of width 1/n. By considering the sum of the areas of these rectangles,…
Answer this question and get it marked →Show that (cosh(x) + sinh(x))^(1/2) = e^((1/2)x).
Answer this question and get it marked →Use the substitution u = 1 + x^2 to find integral of x/sqrt(1 + x^2) dx.
Answer this question and get it marked →Find the set of values of a for which the system of equations 6x + ay = 3, 2x - y = 1, x + 5y + 4z = 2 has a unique solution.
Answer this question and get it marked →