AS & A Level Mathematics (9709) — May–June 2024, Paper 32
10 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Sketch the graph of y = x - 2a , where a is a positive constant. [1]
Answer this question and get it marked →Express (6x^2 - 9x - 16) / (2x^2 - 5x - 12) in partial fractions. [5]
Answer this question and get it marked →The variables x and y satisfy the equation a^(2y - 1) = b^(x - y), where a and b are constants. Show that the graph of y against x is a straight line. [3]
Answer this question and get it marked →The equation of a curve is ye^(2x) + y^2 e^x = 6. Find the gradient of the curve at the point where y = 1. [6]
Answer this question and get it marked →It is given that the equation e^(2x) = 5 + cos 3x has only one root. Show by calculation that this root lies in the interval 0.7 < x < 0.8. [2]
Answer this question and get it marked →The diagram shows the curve y = xe^(-ax), where a is a positive constant, and its maximum point M. Find the exact coordinates of M. [4]
Answer this question and get it marked →Show that cos^4 theta - sin^4 theta is identically equal to cos 2theta. [3]
Answer this question and get it marked →The points A, B and C have position vectors OA = -2i + j + 4k, OB = 5i + 2j and OC = 8i + 5j - 3k, where O is the origin. The line l1 passes through B and C. Find a vector…
Answer this question and get it marked →The complex numbers z and w are defined by z = 1 - i and w = -3 + 3sqrt(3) i. Express zw in the form a + bi, where a and b are real and in exact surd form. [1]
Answer this question and get it marked →By writing y = sec^3 theta as 1/(cos^3 theta), show that dy/dtheta = 3 sin theta sec^4 theta. [2]
Answer this question and get it marked →