Free Practice Questions for IGCSE Additional Mathematics

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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 review concepts for the IGCSE Additional Mathematics exam. 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.

Exam sponsor: Cambridge International (CAIE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

100 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 / Certification Fees

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

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

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

Preparing for 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 / certification fees: £50-£100 per subject (school-set entry fee) Official sources

Using Our Practice Resources

Work through all 100 available questions
Review every answer and explanation
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IGCSE Additional Mathematics: Suggested Study Strategy

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.