CIE GCSE Mathematics Revision
Explore CIE GCSE Mathematics revision topics. Check the official specification for complete requirements for your exam year and route.
Course details
Assessment The assessment includes Paper 1 and Paper 2; see the official specification for the full structure.
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Reviewed course guidance
Revision points, with the explanation beside them
Open a point to read what to know, how to use it in an assessment, a plain-language explanation and a self-check. Answers stay hidden until you choose to reveal them.
Options and source
Cambridge IGCSE syllabus route
- Core route (Papers 1 and 3)
- Extended route (Papers 2 and 4)
0580 syllabus route and assessment overview: Core papers 1 and 3; Extended papers 2 and 4
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Topic group
Reviewed requirements
- Core
Scope: Core · Cambridge IGCSE syllabus route: Core route (Papers 1 and 3) · Core subject content §1 Number, C1.1 Types of number — identify and use integers (positive, zero and negative)
Open revision guidance
What to know
- An integer has no fractional or decimal part. Positive integers are greater than zero, zero is neither positive nor negative, and negative integers are less than zero.
What to do in an assessment
- Classify a value by its sign and place it correctly on a number line. Use zero as the boundary between positive and negative integers; do not include non-integers such as 2.5 in an integer list.
In plain language
The whole-number line extends in both directions from zero: …, −3, −2, −1, 0, 1, 2, 3, …. A minus sign puts a non-zero integer to the left of zero. Fractions and decimals can be negative too, but they are not integers because they have a part between whole-number positions.
Self-check
Which of −4, 0, 3 and 3.5 are integers, and which are negative?
Show the answer
−4, 0 and 3 are integers; −4 is the only negative integer. 3.5 is not an integer.
- Core
Scope: Core · Cambridge IGCSE syllabus route: Extended route (Papers 2 and 4) · Extended subject content §1 Number, E1.1 Types of number — identify and use integers (positive, zero and negative)
Open revision guidance
What to know
- An integer has no fractional or decimal part. Positive integers are greater than zero, zero is neither positive nor negative, and negative integers are less than zero.
What to do in an assessment
- Classify a value by its sign and place it correctly on a number line. Use zero as the boundary between positive and negative integers; do not include non-integers such as 2.5 in an integer list.
In plain language
The whole-number line extends in both directions from zero: …, −3, −2, −1, 0, 1, 2, 3, …. A minus sign puts a non-zero integer to the left of zero. Fractions and decimals can be negative too, but they are not integers because they have a part between whole-number positions.
Self-check
Which of −4, 0, 3 and 3.5 are integers, and which are negative?
Show the answer
−4, 0 and 3 are integers; −4 is the only negative integer. 3.5 is not an integer.
- Core
Scope: Core · Cambridge IGCSE syllabus route: Extended route (Papers 2 and 4) · Extended subject content §1 Number, E1.18 Surds — simplify surds and rationalise denominators; all syllabus examples included
Open revision guidance
What to know
- A surd is kept in exact root form. Extract square factors to simplify it, combine like surds only, and multiply by a suitable surd or conjugate to rationalise a denominator.
What to do in an assessment
- Simplify each radical first; then combine matching surds. For a single-root denominator multiply by that root, and for a binomial denominator use its conjugate so the denominator becomes a rational difference of squares.
In plain language
The syllabus examples give √20=2√5 and √200−√32=10√2−4√2=6√2. For 10/√5, multiply top and bottom by √5 to get 2√5. For 1/(−1+√3), multiply by the conjugate 1+√3: the denominator is 3−1=2, so the result is (1+√3)/2. These are exact values, so do not replace them with rounded decimals during the working. The Extended selection is essential: this is not being relabelled as a UK Higher-tier point.
Self-check
Simplify √45 and rationalise 3/√3.
Show the answer
√45=3√5 and 3/√3=√3.
Earlier topic checklist
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Mathematics topic list
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