IGCSE Mathematics - Additional (0606) — October–November 2024, Paper 23

The diagram shows the graph of y = (x + 1)(x − 1)(x − 2). Use the graph to solve the inequality (x + 1)(x − 1)(x − 2) < 1.

The function f is defined by f(x) = 1 − 4x − x² for all real values of x. Write f(x) in the form a − (x + b)², where a and b are constants.

Show that (2 tan θ + sec θ)(2 tan θ − sec θ) = 3 tan²θ − 1.

The diagram shows a design for a logo. The logo is a sector of a circle, radius r cm, with angle α radians. The area of the logo is 9 cm². Show that the perimeter, P cm, of the…

The tangent to the curve y = √(x + 1)/x at the point where x = 3 meets the line y = x − 16 at the point A. Find the coordinates of A.

Find ∫ 1/√(3x + 2) dx.

In the expansion of (x + x²)⁸ in ascending powers of x, the 3rd and 6th terms are equal. Find the value of x.

Solve the equation sin 4x = 1/2 for 0 ≤ x ≤ π/4, giving your answers in terms of π.

DO NOT USE A CALCULATOR IN THIS QUESTION. Write (16 + 11√10)/(2 + √10) + 1 in the form p + q√10, where p and q are integers.

Suzma is training for a marathon. In the first week she runs 10 km. Then each week she runs a distance that is 10% greater than the week before. The total distance that Suzma has…

There are 3 girls and 2 boys standing in a straight line. Find the number of possible orders if no girls are next to each other.

A particle moves in a straight line. Its velocity, v m s⁻¹, at time t seconds is given by v = cos t − sin t. Find the acceleration, a m s⁻², when t = π/3.