AS & A Level Mathematics (9709) — May–June 2024, Paper 33
10 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Solve the equation 8^(3 − 6x) = 4 × 5^(−2x). Give your answer correct to 3 decimal places.
Answer this question and get it marked →Find the exact coordinates of the stationary point of the curve y = e^(2x) sin 2x for 0 ⩽ x ⩽ ½π.
Answer this question and get it marked →The square roots of 24 − 7i can be expressed in the Cartesian form x + iy, where x and y are real and exact. By first forming a quartic equation in x or y, find the square roots…
Answer this question and get it marked →The variables x and y satisfy the equation ky = e^(cx), where k and c are constants. The graph of ln y against x is a straight line passing through the points (2.80, 0.372) and…
Answer this question and get it marked →Express (6x² − 2x + 2) / ((x − 1)(2x + 1)) in partial fractions.
Answer this question and get it marked →On an Argand diagram shade the region whose points represent complex numbers z which satisfy both the inequalities z − 4 − 3i ⩽ 2 and arg(z − 2 − i) ⩾ ⅓π.
Answer this question and get it marked →Let f(x) = 8x³ + 54x² − 17x − 21. Show that x + 7 is a factor of f(x).
Answer this question and get it marked →Express 3 cos 2x − √3 sin 2x in the form R cos(2x + α), where R 0 and 0 < α < ½π. Give the exact values of R and α.
Answer this question and get it marked →A container in the shape of a cuboid has a square base of side x and a height of (10 − x). It is given that x varies with time, t, where t 0. The container decreases in volume at…
Answer this question and get it marked →The equations of two straight lines are r = i + j + 2ak + λ(3i + 4j + ak) and r = −3i − j + 4k + μ(−i + 2j + 2k), where a is a constant. Given that the acute angle between the…
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