AS & A Level Mathematics (9709) — October–November 2023, Paper 12
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →The coefficient of x³ in the expansion of (3 + 2ax)⁵ is six times the coefficient of x² in the expansion of (2 + ax)⁶. Find the value of the constant a.
Answer this question and get it marked →Find the exact solution of the equation (1/6)π + tan⁻¹(4x) = −cos⁻¹((1/2)√3).
Answer this question and get it marked →The equation of a curve is such that dy/dx = (1/2)x + 72/x⁴. The curve passes through the point P(2, 8). Find the equation of the normal to the curve at P.
Answer this question and get it marked →The diagram shows the shape of a coin. The three arcs AB, BC and CA are parts of circles with centres C, A and B respectively. ABC is an equilateral triangle with sides of length…
Answer this question and get it marked →The first, second and third terms of a geometric progression are sin θ, cos θ and 2 − sin θ respectively, where θ radians is an acute angle. Find the value of θ.
Answer this question and get it marked →The equation of a curve is y = x² − 8x + 5. Find the coordinates of the minimum point of the curve.
Answer this question and get it marked →Verify the identity (2x − 1)(4x² + 2x − 1) ≡ 8x³ − 4x + 1.
Answer this question and get it marked →Functions f and g are defined by f(x) = (x + a)² − a for x ≤ −a, g(x) = 2x − 1 for x ∈ ℝ, where a is a positive constant. Find an expression for f⁻¹(x).
Answer this question and get it marked →The diagram shows curves with equations y = 2x^(1/2) + 13x^(−1/2) and y = 3x^(−1/2) + 12. The curves intersect at points A and B. Find the coordinates of A and B.
Answer this question and get it marked →The equation of a curve is y = f(x), where f(x) = (4x − 3)^(5/3) − (20/3)x. Find the x-coordinates of the stationary points of the curve and determine their nature.
Answer this question and get it marked →The coordinates of points A, B and C are (6, 4), (p, 7) and (14, 18) respectively, where p is a constant. The line AB is perpendicular to the line BC. Given that p < 10, find the…
Answer this question and get it marked →← October–November 2023 Paper 13 · October–November 2023 Paper 11 →