AS & A Level Mathematics (9709) — May–June 2023, Paper 32
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Solve the inequality 5x − 3 < 2 3x − 7 .
Answer this question and get it marked →Solve the equation ln(2x² − 3) = 2 ln x − ln 2, giving your answer in an exact form.
Answer this question and get it marked →On an Argand diagram, sketch the locus of points representing complex numbers z satisfying z + 3 − 2i = 2.
Answer this question and get it marked →Solve the equation 2 cos x − cos ½x = 1 for 0 ≤ x ≤ 2π.
Answer this question and get it marked →The complex number 2 + yi is denoted by a, where y is a real number and y < 0. It is given that f(a) = a³ − a² − 2a. Find a simplified expression for f(a) in terms of y.
Answer this question and get it marked →The equation cot ½x = 3x has one root in the interval 0 < x < π, denoted by α. Show by calculation that α lies between 0.5 and 1.
Answer this question and get it marked →The equation of a curve is 3x² + 4xy + 3y² = 5. Show that dy/dx = −(3x + 2y)/(2x + 3y).
Answer this question and get it marked →The variables x and y satisfy the differential equation dy/dx = (4 + 9y²) / e^(2x+1). It is given that y = 0 when x = 1. Solve the differential equation, obtaining an expression…
Answer this question and get it marked →Let f(x) = (2x² + 17x − 17) / ((1 + 2x)(2 − x)²). Express f(x) in partial fractions.
Answer this question and get it marked →The diagram shows the curve y = (x + 5)√(3 − 2x) and its maximum point M. Find the exact coordinates of M.
Answer this question and get it marked →The points A and B have position vectors i + 2j − 2k and 2i − j + k respectively. The line l has equation r = i − j + 3k + μ(2i − 3j + 4k). Show that l does not intersect the line…
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