AS & A Level Mathematics (9709) — May–June 2025, Paper 33
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Sketch the graph of y = 3x − 2a , where a is a positive constant.
Answer this question and get it marked →Solve the equation 2 ln(2x + 3) − ln(2x + 5) = ln(3x).
Answer this question and get it marked →Find the exact value of the integral from (1/5)π to (1/4)π of 3 cos²(5x) dx, i.e. ∫{(1/5)π}^{(1/4)π} 3 cos²(5x) dx.
Answer this question and get it marked →It is given that z1 = r1 e^(iθ1) and z2 = r2 e^(iθ2). Show that (z1 z2) = z1 z2.
Answer this question and get it marked →The equation of a curve is xy + y² e^(−x) = 4. Show that dy/dx = (y² − y e^x) / (x e^x + 2y).
Answer this question and get it marked →Find the complex numbers z for which (z + 4)/(z + 4i) is real and z = √10. Give your answers in the form z = x + iy, where x and y are real.
Answer this question and get it marked →Let f(x) = (3a − 5x) / ((3a + 2x)(2a − x)), where a is a positive constant. Express f(x) in partial fractions.
Answer this question and get it marked →Prove the identity cot²θ − tan²θ ≡ 4 cot 2θ cosec 2θ.
Answer this question and get it marked →With respect to the origin O, the points A, B and C have position vectors given by OA = i + 2j, OB = i + 3j − 2k, and OC = 2i − j + 3k. The line l passes through B and C. Find a…
Answer this question and get it marked →The variables x and y satisfy the differential equation sin 4y (dy/dx) = x sin 2y sin 3x. It is given that y = (1/12)π when x = (1/2)π. Solve the differential equation, obtaining…
Answer this question and get it marked →The diagram shows the curve y = √x sin 2x for 0 ⩽ x ⩽ (1/2)π. The curve has a maximum point at M, where x = a. Show that tan 2a = −4a.
Answer this question and get it marked →