AS & A Level Mathematics (9709) — May–June 2023, Paper 11
12 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →Solve the equation 4 sin θ + tan θ = 0 for 0° < θ < 180°.
Answer this question and get it marked →Find the first three terms in the expansion, in ascending powers of x, of (2 + 3x)⁴.
Answer this question and get it marked →The diagram shows two piecewise-linear graphs drawn on a grid (x from about −8 to 6, y from about −6 to 6), with equations y = f(x) and y = g(x). The graph y = f(x) lies mainly in…
Answer this question and get it marked →The diagram shows a sector ABC of a circle with centre A and radius 8 cm. In the diagram C is at the top, B is at the lower left with a right angle marked at B, and A is at the…
Answer this question and get it marked →The line with equation y = kx − k, where k is a positive constant, is a tangent to the curve with equation y = −1/(2x). Find, in either order, the value of k and the coordinates…
Answer this question and get it marked →The first three terms of an arithmetic progression are p²/6, 2p − 6 and p. Given that the common difference of the progression is not zero, find the value of p.
Answer this question and get it marked →A curve has equation y = 2 + 3 sin(½x) for 0 ⩽ x ⩽ 4π. State the greatest and least values of y.
Answer this question and get it marked →The functions f and g are defined by f(x) = 1 + 2a/(x − a) for x a and g(x) = bx − 2 for x ∈ ℝ, where a and b are constants. Given that f(7) = 5/2 and gf(5) = 4, find the values…
Answer this question and get it marked →Water is poured into a tank at a constant rate of 500 cm³ per second. The depth of water is h cm at time t seconds and the volume is V = (4/3)(25 + h)³ − 62500/3 cm³. Find the…
Answer this question and get it marked →The diagram shows part of the curve y = 4/(2x − 1)² and parts of the lines x = 1 and y = 1; the curve passes through A(1, 4) and B(3/2, 1), and the shaded region is bounded by the…
Answer this question and get it marked →The equation of a curve is such that dy/dx = 6x² − 30x + 6a, where a is a positive constant. The curve has a stationary point at (a, −15). Find the value of a.
Answer this question and get it marked →The diagram shows a circle P with centre (0, 2) and radius 10 and the tangent to the circle at the point A(6, 10). A second circle Q has centre at the point where this tangent…
Answer this question and get it marked →