AS & A Level Mathematics (9709) — May–June 2024, Paper 21
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →A curve has equation y = 2 tan x − 5 sin x for 0 ≤ x < (1/2)π. Find the x-coordinate of the stationary point of the curve. Give your answer correct to 3 significant figures. [3]
Answer this question and get it marked →A curve has equation x² ln y + y² + 4x = 9. Find the gradient of the curve at the point (2, 1). [5]
Answer this question and get it marked →Sketch on the same diagram the graphs of y = 3x − 8 and y = 5 − x. [2]
Answer this question and get it marked →Show that 3 tan 2θ + tan(θ + 45°) ≡ (tan²θ + 8 tan θ + 1)/(1 − tan²θ). [4]
Answer this question and get it marked →A curve has equation y = (1 + e^(2x))/(1 + 3x). The curve has exactly one stationary point P. Find dy/dx and hence show that the x-coordinate of P satisfies the equation x = 1/6 +…
Answer this question and get it marked →The diagram shows the curve with equation y = √(sin 2x + sin² 2x) for 0 ≤ x ≤ (1/6)π. The shaded region is bounded by the curve and the straight lines x = (1/6)π and y = 0. Use…
Answer this question and get it marked →The polynomial p(x) is defined by p(x) = 9x³ + 6x² + 12x + k, where k is a constant. Find the quotient when p(x) is divided by (3x + 2) and show that the remainder is (k − 8). [3]
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