AS & A Level Mathematics (9709) — May–June 2023, Paper 31
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 3e^(2x) − 4e^(−2x) = 5. Give the answer correct to 3 decimal places.
Answer this question and get it marked →Sketch the graph of y = 2x + 3 .
Answer this question and get it marked →Find the coefficient of x³ in the binomial expansion of (3 + x)√(1 + 4x).
Answer this question and get it marked →Show that the equation sin 2θ + cos 2θ = 2 sin² θ can be expressed in the form cos² θ + 2 sin θ cos θ − 3 sin² θ = 0.
Answer this question and get it marked →The equation of a curve is x²y − ay² = 4a³, where a is a non-zero constant. Show that dy/dx = 2xy / (2ay − x²).
Answer this question and get it marked →Relative to the origin O, the points A, B and C have position vectors given by (as column vectors) OA = (2, 1, 3), OB = (4, 3, 2) and OC = (3, −2, −4). The quadrilateral ABCD is a…
Answer this question and get it marked →The variables x and y satisfy the differential equation cos 2x (dy/dx) = 4 tan 2x / sin² 3y, where 0 ⩽ x < ¼π. It is given that y = 0 when x = ⅙π. Solve the differential equation…
Answer this question and get it marked →Let f(x) = (3 − 3x²) / ((2x + 1)(x + 2)²). Express f(x) in partial fractions.
Answer this question and get it marked →The constant a is such that ∫₀ᵃ x e^(−2x) dx = 1/8. Show that a = ½ ln(4a + 2).
Answer this question and get it marked →The polynomial x³ + 5x² + 31x + 75 is denoted by p(x). Show that (x + 3) is a factor of p(x).
Answer this question and get it marked →