IGCSE Mathematics - Additional (0606) — May–June 2025, Paper 13

The diagram shows the graph of y = (2x + a)(x + b)(x + c) where a, b and c are integers. The cubic curve crosses the x-axis at three points: at x = -2, at x = -1, and at x = 1. It…

Find the values of k for which the equation x^2 + 4kx + k + 3 = 0 has two equal roots.

The polynomial p is such that p(x) = x^3 + Ax + 30, where A is a constant. When p(x) is divided by x + 2 the remainder is 84. Write p(x) as a product of linear factors.

Solve the equation 2 / (logx 10) - lg(x + 4) = lg 2 for x 0.

Solutions by accurate drawing will not be accepted. A circle, C, has equation (x - 5)^2 + (y - 12)^2 = 100. Find the equation of the tangent to C at the point (11, 4). Give your…

Find the x-coordinates of the points of intersection of the following curves. y = 4 ln x and y = 5 - 3 / ln(x^2) Give your answers in exact form.

In this question, all lengths are in centimetres and all angles are in radians. The diagram shows a sector of a circle with centre O and radius 6. The two radii OA and OB each…

The diagram shows part of the curve y = 3 / (x + 1) - (x - 2) / x. The points A and B lie on the curve such that the x-coordinate of A is 1 and the x-coordinate of B is 2. A line…

The function f is defined by f(x) = -2x^2 + 9x - 10 for 0 <= x <= 3. Write f(x) in the form a + b(x + c)^2 where a, b and c are constants.

The diagram shows four points, O, A, B and C. A, B and C lie in a straight line and are such that AB/AC = 1/3. Vector OA = a and vector OB = b. (In the diagram, a points from O to…

A particle P moves in a straight line and passes through a fixed point O. At time t seconds, its displacement from O, s metres, is given by s = t + 6t^2 - t^3 for 0 <= t <= 3 s =…

The normal to the curve y = 4 / x^2 + ax + 7 at the point where x = 2 has equation x + 4y = b. Find the values of a and b.