IGCSE Mathematics - Additional (0606) — May–June 2025, Paper 22

10 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 4 marks · Equations, inequalities and graphs - modulus inequalities

Solve the inequality 5x + 2 = 3.

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Question 2 · 10 marks · Kinematics - displacement-time graphs

In this question, all lengths are in metres and time is in seconds. A particle P moves in a straight line such that its displacement s from a fixed point O at time t is given by s…

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Question 3 · 4 marks · Functions - composite functions and equations

Functions f and g are such that f(x) = 3x / (x + 4) for x 0 g(x) = sqrt(x + 2) for x -2. Solve the equation fg(x) = 1.

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Question 4 · 9 marks · Differentiation - product rule and trigonometric functions

Given that y = 4 sin 2x cos 2x, find the value of dy/dx when x = pi/6.

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Question 5 · 8 marks · Permutations and combinations

A 4-digit number is to be formed using the digits 0, 2, 4, 5, 6 and 8. The 4-digit number must not start with 0. Any digit may be used at most once in the 4-digit number. Find how…

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Question 6 · 6 marks · Differentiation - related rates of change

The volume, V, of a sphere is increasing at the constant rate of 2pi cm^3 s^-1. Find the rate of change of the surface area, S, of this sphere when the volume of the sphere is…

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Question 7 · 9 marks · Series - arithmetic progressions and logarithms

The first three terms of an arithmetic progression can be written as 2 ln(x^3), 5 ln(x^2), 2 ln(x^7). Given that x 1, find the least number of terms for the sum of this…

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Question 8 · 11 marks · Integration - area between a curve and a line

The diagram shows part of the curve y = 15/x - 5/x^2. The curve meets the x-axis at the point A. The curve has a maximum at the point B. Find the area of the shaded region…

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Question 9 · 10 marks · Trigonometry - solving equations with reciprocal ratios

Solve the equation 3 sec 3x = sqrt(3) cosec 3x for -120 degrees <= x <= 120 degrees.

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Question 10 · 9 marks · Series - binomial expansion

The first three terms, in descending powers of x, in the expansion of (3x^2 - a)^n (1 + 1/x^2)^2 can be written as 729 x^12 + 972 x^10 + b x^8, where a, b and n are constants.…

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