AS & A Level Further Mathematics (9231) — May–June 2023, Paper 13
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Prove by mathematical induction that, for all positive integers n, 5^(3n) + 32^n - 33 is divisible by 31.
Answer this question and get it marked →Use standard results from the list of formulae (MF19) to show that sum{r=1}^{n} (6r^2 + 6r - 5) = an^3 + bn^2 + cn, where a, b and c are integers to be determined.
Answer this question and get it marked →The equation x^4 - x^2 + 2x + 5 = 0 has roots alpha, beta, gamma, delta. Find a quartic equation whose roots are alpha^2, beta^2, gamma^2, delta^2 and state the value of alpha^2 +…
Answer this question and get it marked →The matrix M is given by M = ( cos 2theta, -sin 2theta ; sin 2theta, cos 2theta )( 1, k ; 0, 1 ), where 0 < theta < pi and k is a non-zero constant. The matrix M represents a…
Answer this question and get it marked →Show that the curve with Cartesian equation x^2 - y^2 = a, where a is a positive constant, has polar equation r^2 = asec 2theta.
Answer this question and get it marked →The points A, B, C have position vectors i + j, -i + 2j + 4k, -2i + j + 3k, respectively, relative to the origin O. Find the equation of the plane ABC, giving your answer in the…
Answer this question and get it marked →The curve C has equation y = (x^2 + 2x + 1)/(x - 3). Find the equations of the asymptotes of C.
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