AS & A Level Mathematics (9709) — May–June 2023, Paper 21
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Use logarithms to solve the equation 12^x = 3^(2x+1). Give your answer correct to 3 significant figures. [4]
Answer this question and get it marked →A curve has equation y = (2 + 3 ln x) / (1 + 2x). Find the equation of the tangent to the curve at the point (1, 2/3). Give your answer in the form ax + by + c = 0, where a, b and…
Answer this question and get it marked →It is given that ∫₀ᵃ (3e^(2x) − 1) dx = 12, where a is a positive constant. Show that a = (1/2) ln(9 + (2/3)a). [4]
Answer this question and get it marked →The polynomial p(x) is defined by p(x) = 2x^3 + 3x^2 + kx − 30, where k is a constant. It is given that (x − 3) is a factor of p(x). Find the value of k. [2]
Answer this question and get it marked →The diagram shows the curve with parametric equations x = 4e^(2t), y = 5e^(−t) cos 2t, for −(1/4)π ≤ t ≤ (1/4)π. The curve has a maximum point M. Find an expression for dy/dx in…
Answer this question and get it marked →Show that ∫ from (1/4)π to (1/3)π of (4 cos^2 2x + 1/cos^2 x) dx = (3/4)√3 + (1/6)π − 1. [7]
Answer this question and get it marked →Express 7 cos θ + 24 sin θ in the form R cos(θ − α), where R 0 and 0° < α < 90°. Give the value of α correct to 2 decimal places. [3]
Answer this question and get it marked →