IGCSE Mathematics - Additional (0606) — May–June 2025, Paper 11

Given that vector PQ = (-3, 7) (column vector) and 4 × vector PR = (-2, 8) (column vector), find vector RQ.

Solve the inequality (3 − x)(5x + 8) ≥ 9 − 3x.

Point A has coordinates (3, −1). A circle has equation (x − 4)^2 + (y + 3)^2 = 5. Show that A lies on the circumference of the circle.

Solve the equation x^(1/3) − x^(1/6) = 2.

Solve the equation 5 2x − 1 + 8 = 23.

A curve has equation y = ((x^2 − 1)/(x^2 + 1))^4. Show that dy/dx can be written as A x (x^2 − 1)^3 / (x^2 + 1)^5, where A is a positive integer to be found.

Solutions to this question by accurate drawing will not be accepted. Find the x-coordinates of the points where the curve y = (2x − 9)(x^2 + 5) + 42 cuts the x-axis.

Write down the set of values of x for which log5 (12x − 4) exists.

The point A with x-coordinate 2 lies on the curve y = sqrt(4x + 1). The diagram shows part of this curve and the tangent to the curve at A. Find the area of the shaded region…

Given that 0 ≤ θ < π/2, show that sin θ / sqrt(cosec^2 θ − 1) + 1 / sqrt(1 + tan^2 θ) can be written as sec θ.

An arithmetic progression has common difference d. The 3rd term of this progression is 10. Write down expressions for the 1st term and the 2nd term of this progression. Give your…

In this question n ≥ 6. Use an algebraic method to show that (n choose 5) − (n−1 choose 5) can be written as (n−1 choose 4). [In standard notation: nC5 − (n−1)C5 = (n−1)C4.]