IGCSE Mathematics - Additional (0606) — October–November 2024, Paper 12

The curve y = a cos bx + c, where a, b and c are integers, passes through the points (−π/6, −2) and (π/9, 1/2). The curve has a period of 2π/3. Find the values of a, b and c.

It is given that y = f(x), where f(x) = (2x − 5)(x − 1)². Find the coordinates of the stationary points on the curve y = f(x).

In this question, all lengths are in centimetres and all angles are in radians. The diagram shows a circle with centre O and radius 12, and a circle with centre C and radius 5.…

The function f is such that f(x) = 4 ln(3x − 2), for x a, where a is as small as possible. Write down the value of a.

Show that (1 + cot²θ)/cot²θ = sec²θ.

Find, in descending powers of x, the first 3 terms in the expansion of (x + 2/x²)¹⁰. Simplify each term as far as possible.

It is given that y = ln(3x² − 1)/(x + 2), for x 1/√3. When x = 1, y is increasing at the rate of h units per second. Find, in terms of h, the corresponding rate of change in x,…

The tangent to the curve y = e^x(2x + 5)^(1/2) at the point where x = 2 meets the x-axis at the point X and the y-axis at the point Y. Find the coordinates of the mid-point of XY,…

The diagram shows part of the curve y = 4/(2x + 1) and the straight line 2y = 6x + 1. Find the area of the shaded region, giving your answer in the form ln a + b, where a is an…

The first 3 terms of an arithmetic progression are 2 tan 2x, 5 tan 2x, 8 tan 2x. Find the values of x, where −180° ≤ x ≤ 180°, for which the sum to 30 terms is 455√3.