IGCSE Mathematics - Additional (0606) — October–November 2024, Paper 22

Solve the following simultaneous equations: y/x = 3/2 and y⁴/x⁵ = 27/16.

Variables x and y are related by the equation y = x√(1 + 2x). Find dy/dx.

DO NOT USE A CALCULATOR IN THIS QUESTION. The polynomial p is defined by p(x) = ax³ − 3x² − 3x + b, where a and b are constants. Given that x = 2 and x = −1 are roots of the…

Use a graphical method to solve the inequality 2x − 8 4.

Solve the equation log₂ x² + log₁₆ x = 18.

DO NOT USE A CALCULATOR IN THIS QUESTION. Write (5 − √3)(√6 + √2)⁻² in the form a + b√3, where a and b are constants.

A class of 10 students includes Abby and Ben. A group of 5 students is to be selected from the class. Find the number of possible groups when there are no restrictions.

Solve the equation cot²2θ + 3 cosec 2θ = 9 for −90° ≤ θ ≤ 90°.

In this question time is measured in seconds. A particle is moving in a straight line with constant velocity of 6 m s⁻¹. At time t = 0, it passes a fixed point A. At time t = 5 it…

The diagram shows part of the curve y = x − x²/4 and the line y = −4. The curve and the line intersect at the point A. The maximum point on the curve is at a perpendicular…

In this question i is a unit vector in the positive x-direction and j is a unit vector in the positive y-direction. Time is in seconds and distances are in metres. Particle A…

A metal tank is in the shape of a cuboid with a square base of side x m and an open top. The tank has a volume of 5 m³. Given that x can vary, and that the area of the metal used…