100+ Free IGCSE Additional Mathematics Practice Questions

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Solve 2^(x+1) = 16.

x = 4

x = 3

x = 7

x = 8

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2026 Statistics

Key Facts: IGCSE Additional Mathematics Exam

A*-E

Grading scale

Cambridge International

2 papers

Assessment structure

CAIE 0606 syllabus

0606

Cambridge syllabus code

Cambridge International

100

Free practice questions here

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Cambridge IGCSE Additional Mathematics (0606) is assessed through two 2-hour written papers — Paper 1 is non-calculator and Paper 2 allows a scientific calculator. The syllabus covers algebra, functions, trigonometry, vectors and calculus on the 2025-2027 specification used for the 2026 series.

Sample IGCSE Additional Mathematics Practice Questions

Try these sample questions to test your IGCSE Additional Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1The function f is defined by f(x) = 3x - 2 for all real x. Find f^-1(x).

A.(x + 2)/3

B.(x - 2)/3

C.3/(x - 2)

D.(2 - x)/3

Explanation: Let y = 3x - 2 and swap x and y: x = 3y - 2, so 3y = x + 2 and y = (x + 2)/3. The inverse is f^-1(x) = (x + 2)/3.

2Given f(x) = 2x + 1 and g(x) = x^2, find fg(x).

A.2x^2 + 1

B.(2x + 1)^2

C.2x^2 + 2x + 1

D.4x^2 + 4x + 1

Explanation: fg(x) means f(g(x)). Compute g(x) = x^2 first, then apply f: f(x^2) = 2(x^2) + 1 = 2x^2 + 1.

3The function f is defined by f(x) = 5 - 2x for x in the real numbers. State the range of f when the domain is 0 <= x <= 4.

A.-3 <= f(x) <= 5

B.0 <= f(x) <= 4

C.-3 <= f(x) <= 4

D.5 <= f(x) <= 13

Explanation: f is decreasing, so the endpoints map to the extreme values. f(0) = 5 and f(4) = 5 - 8 = -3, giving the range -3 <= f(x) <= 5.

4Solve |2x - 5| = 7.

A.x = 6 or x = -1

B.x = 6 only

C.x = -1 only

D.x = 6 or x = 1

Explanation: |2x - 5| = 7 gives the two cases 2x - 5 = 7 and 2x - 5 = -7. The first gives x = 6; the second gives 2x = -2, so x = -1.

5The function f(x) = (x - 1)/(x + 2) is defined for x not equal to -2. Find f^-1(x).

A.(2x + 1)/(1 - x)

B.(x + 2)/(x - 1)

C.(2x - 1)/(1 - x)

D.(1 - x)/(2x + 1)

Explanation: Let y = (x - 1)/(x + 2). Cross multiply: y(x + 2) = x - 1, so xy + 2y = x - 1, giving x(y - 1) = -1 - 2y, hence x = (2y + 1)/(1 - y). So f^-1(x) = (2x + 1)/(1 - x).

6Given f(x) = x + 3 and g(x) = 2x - 1, find gf(2).

A.9

B.7

C.5

D.11

Explanation: gf(2) means g(f(2)). First f(2) = 2 + 3 = 5; then g(5) = 2(5) - 1 = 9.

7Solve |3x + 1| < 7.

A.-8/3 < x < 2

B.x < -8/3 or x > 2

C.-2 < x < 8/3

D.x > 2 only

Explanation: |3x + 1| < 7 means -7 < 3x + 1 < 7. Subtract 1: -8 < 3x < 6. Divide by 3: -8/3 < x < 2.

8The graph of y = |x - 3| meets the line y = 5 at two points. Find the sum of the x-coordinates of these points.

A.6

B.8

C.-2

D.10

Explanation: Solve |x - 3| = 5: x - 3 = 5 gives x = 8, and x - 3 = -5 gives x = -2. The sum is 8 + (-2) = 6.

9Find the largest possible domain of f(x) = sqrt(4 - x^2) considering only real values.

A.-2 <= x <= 2

B.x >= 0

C.-4 <= x <= 4

D.x <= 2 only

Explanation: We need 4 - x^2 >= 0, so x^2 <= 4 and -2 <= x <= 2. This is the natural domain of the square-root function with input 4 - x^2.

10Given f(x) = x^2 + 1 with domain x >= 0, find f^-1(x).

A.sqrt(x - 1)

B.sqrt(x) - 1

C.(x - 1)^2

D.+/- sqrt(x - 1)

Explanation: Let y = x^2 + 1, so x^2 = y - 1 and x = +/- sqrt(y - 1). The domain x >= 0 forces the positive root, so f^-1(x) = sqrt(x - 1).

About the IGCSE Additional Mathematics Exam

Cambridge IGCSE Additional Mathematics (0606) is offered by Cambridge International (CAIE) and bridges between IGCSE Mathematics and AS-Level Mathematics. The course covers functions, quadratics, indices and surds, logarithms and exponentials, straight-line graphs, circular measure, trigonometry, series, vectors, and differentiation and integration.

Questions

100 scored questions

Time Limit

Paper 1: 2 hours (no calculator); Paper 2: 2 hours (calculator allowed)

Passing Score

Grades A* to E available, with A* the highest and E the minimum pass

Exam Fee

£50-£100 per subject (school-set entry fee) (Cambridge International (CAIE))

IGCSE Additional Mathematics Exam Content Outline

15%

Functions

Domain and range, function notation, composite and inverse functions, modulus function and graphs

15%

Quadratic Functions and Equations

Completing the square, max/min, discriminant, quadratic inequalities, factor theorem, sum and product of roots

10%

Indices and Surds

Index laws including negative and fractional indices, rationalising surd denominators

10%

Logarithmic and Exponential Functions

Laws of logarithms, change of base, e^x and ln x, solving exponential equations

10%

Straight-Line Graphs

Parallel and perpendicular lines, perpendicular distance, transforming non-linear relations to linear form

10%

Circular Measure

Radians, arc length s = r theta, sector area A = (1/2) r^2 theta

15%

Trigonometry

Trig graphs, exact values, identities, sec/csc/cot, double angle and addition formulae, equations in radians

10%

Series

Binomial expansion (1+x)^n, arithmetic and geometric progressions, sum to infinity

Vectors in Two Dimensions

Vector arithmetic, magnitudes, position vectors, parallel and collinear vectors, simple kinematics

10%

Differentiation and Integration

Power, chain, product and quotient rules; stationary points; integration; area and kinematics

How to Pass the IGCSE Additional Mathematics Exam

What You Need to Know

Passing score: Grades A* to E available, with A* the highest and E the minimum pass
Exam length: 100 questions
Time limit: Paper 1: 2 hours (no calculator); Paper 2: 2 hours (calculator allowed)
Exam fee: £50-£100 per subject (school-set entry fee)

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

IGCSE Additional Mathematics Study Tips from Top Performers

1Practise Paper 1 questions without a calculator to build algebra and surd fluency

2Memorise the calculus rules — no formula sheet is provided for differentiation and integration

3Use Cambridge past papers from 2020 onwards; the question style is highly consistent year on year

4Always show working — 2026 mark schemes reward intermediate steps, not just final answers

Frequently Asked Questions

Who is Cambridge IGCSE Additional Mathematics 0606 for?

It is designed for high-ability learners targeting A*/A/B at IGCSE Mathematics. The syllabus bridges between IGCSE Mathematics and AS-Level Mathematics and is widely taken alongside the 0580 IGCSE Mathematics.

How is Cambridge IGCSE 0606 assessed?

Two written papers, each 2 hours and 80 marks. Paper 1 is non-calculator and Paper 2 allows a scientific calculator. There is no coursework component.

What is the 2026 syllabus version?

The 2026 exams use the 2025-2027 syllabus (0606). Mark schemes have been updated to award more marks for working, in line with other Cambridge Mathematics qualifications.

Is a formula sheet provided?

A List of formulas is provided for selected topics such as the quadratic formula and trigonometry, but no formulas are given for the calculus section — these must be memorised.