AS & A Level Mathematics (9709) — May–June 2025, Paper 15

The equation of a curve is such that dy/dx = 12(2x − 5)^2 + 8x. It is given that the curve passes through the point (2, 4). Find an equation of the curve. [4]

In the expansion of (3 + ax)^5 + (6 − x)^4, the coefficient of x^2 is six times the coefficient of x. Find the possible values of the constant a. [5]

Use completing the square to find the exact solutions of the equation 4x^2 − 4x − 1 = 0. [2]

The diagram shows part of the curve y = x^2 − 1/x^2. The shaded region is bounded by the curve, the line x = 2 and the x-axis. Find the volume formed when the shaded region is…

The diagram shows a sector ABD of a circle with centre A and radius 10 cm. The perpendicular bisector of AB passes through D. (In the diagram, A and B are the ends of a horizontal…

Each year, on her birthday, Ananya receives some money from each of her parents. On Ananya's first birthday, her father gives her $10. Every subsequent year, her father gives her…

In the parallelogram ABCD, the coordinates of A are (3, 7), the coordinates of B are (6, p) and the coordinates of D are (1, p). It is given that the gradient of AB is −2/3. Find…

The equation of a curve is y = x^3 + ax^2 + bx + 5. The curve has a stationary point at (1, 9). Find the values of the constants a and b. [5]

Functions f and g are defined as follows. f(x) = cos x for 0 ⩽ x ⩽ π g(x) = 3 cos(x − π) + 2 for π ⩽ x ⩽ 2π Describe fully the transformations that have been combined to transform…

The equation of a circle is x^2 + y^2 + 4x − 8y − 12 = 0. Find an equation of the tangent to the circle at the point (2, 8), giving your answer in the form ax + by + c = 0. [4]