AS & A Level Mathematics (9709) — May–June 2025, Paper 21
7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Given that y = 6x cos(x^2 + 1), find an expression for dy/dx. [2]
Answer this question and get it marked →Use logarithms to solve the inequality 4^x < 0.05. Give your answer in the form x < a, where the value of a is correct to 3 significant figures. [2]
Answer this question and get it marked →Sketch, on a single diagram, the graphs of y = 3e^(−2x) and y = sec x for values of x such that 0 <= x < (1/2)π. [2]
Answer this question and get it marked →The diagram shows the curve with equation y = 6e^(2x) − e^(3x). The shaded region is bounded by the axes and the curve. Find the exact x-coordinate of the maximum point. [3]
Answer this question and get it marked →The polynomial p(x) is defined by p(x) = ax^3 + bx^2 − ax − 24, where a and b are constants. It is given that (2x − 3) is a factor of p(x) and that the remainder is −15 when p(x)…
Answer this question and get it marked →The parametric equations of a curve are x = (2t + 1)/(3t + 4), y = 2 ln(3t + 4), where t −4/3. Show that dy/dx can be expressed in the form c(3t + 4) and state the value of the…
Answer this question and get it marked →Prove that sin^2(2x) + 4 cos^2(x) cos(2x) ≡ 4 cos^4(x). [3]
Answer this question and get it marked →