AS & A Level Further Mathematics (9231) — May–June 2024, Paper 12
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →The cubic equation 2x^3 + x^2 - px - 5 = 0, where p is a positive constant, has roots alpha, beta, gamma. State, in terms of p, the value of alphabeta + betagamma + gammaalpha.
Answer this question and get it marked →Prove by mathematical induction that 6^(4n) + 38^n - 2 is divisible by 74 for all positive integers n.
Answer this question and get it marked →Use standard results from the list of formulae (MF19) to show that sum{r=1}^{N} r(r+1)(3r+4) = (1/12)N(N+1)(N+2)(9N+19).
Answer this question and get it marked →The matrix M is given by M = ( 1/2, -(1/2)sqrt(3) ; (1/2)sqrt(3), 1/2 )( 14, 0 ; 0, 1 ) (the product of the 2x2 matrix with first row [1/2, -(1/2)sqrt(3)] and second row…
Answer this question and get it marked →The points A, B, C have position vectors 2i + 2j + 4k, 2i + 4j - k, -3i - 3j + 4k, respectively, relative to the origin O. Find the equation of the plane ABC, giving your answer…
Answer this question and get it marked →The curve C has equation y = (x^2 + ax + 1)/(x + 2), where a 5/2. Find the equations of the asymptotes of C.
Answer this question and get it marked →The curve C has polar equation r^2 = (pi - theta)arctan(pi - theta), for 0 <= theta <= pi. Sketch C and state the polar coordinates of the point of C furthest from the pole.
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