Key Summary & High-Yield Concept Takeaways
Curated by senior faculty at Hodu Academy for fast revision, formula derivations, and standard board & competitive exam marking schemes.
- ✓IGCSE Maths Syllabus Topics
- ✓Chapter-wise Formulas & Examples
- ✓Summary Tables & Units
- ✓Key Definitions & Theorems
IGCSE Maths Formulas & Key Facts – Cambridge 0580/0980 (Core & Extended)
IGCSE Mathematics (0580/0980) forms the foundation of advanced problem-solving for exams and real life. Hodu Academy presents the most essential chapter-wise formulas, summaries, worked examples, definitions, and tips—mapped to Cambridge IGCSE Core & Extended syllabus, with step-by-step guidance.
Use this page to master formulae, concepts, calculation shortcuts, and exam strategy for IGCSE Maths. Bookmark for fast revision, formula recall, and error-free working!
? Complete Maths Video Lessons:
Get in-depth explanations and walkthroughs for every chapter on our YouTube Maths Playlist. Perfect for visual learning and step-by-step guidance!
Get in-depth explanations and walkthroughs for every chapter on our YouTube Maths Playlist. Perfect for visual learning and step-by-step guidance!
Table of Content
IGCSE Maths Syllabus Topics (Core & Extended)
| Topic | Key Areas |
|---|---|
| 1. Number | Integers, Fractions, Decimals, Ratio, Percentage, Standard form, Estimation |
| 2. Algebra | Expressions, Equations, Formulae, Graphs, Quadratics, Simultaneous equations |
| 3. Geometry | Angles, Triangles, Circles, Polygons, Transformations, Vectors, Loci |
| 4. Mensuration | Perimeter, Area, Surface Area, Volume (2D & 3D shapes) |
| 5. Trigonometry | Sine, Cosine, Tangent, Pythagoras’ Theorem, 2D/3D Applications |
| 6. Sets & Probability | Set notation, Venn diagrams, Probability, Tree diagrams |
| 7. Statistics | Mean, Median, Mode, Range, Cumulative Frequency, Histograms |
| 8. Functions & Graphs | Function notation, Inverse, Composite, Linear/quadratic/cubic graphs |
IGCSE Maths: Chapter-wise Formulas & Worked Examples
1. Number
- Percentage: value × (percent ÷ 100)
- Ratio: Compare as a:b, convert to fractions if needed
- Standard form: a × 10ⁿ (1 ≤ a < 10, n integer)
- Estimation: Round to 1 significant figure for quick estimate
- LCM & HCF: List or use prime factorization
Worked Example:
Express 0.0037 in standard form.
Solution: 3.7 × 10⁻³
Common Mistakes & Exam Tips:
Express 0.0037 in standard form.
Solution: 3.7 × 10⁻³
- Always show working for rounding/estimation.
- Don’t mix up LCM and HCF methods.
- Check calculator mode (degrees/radians for trig, SD/normal for stats).
2. Algebra
- Expanding: a(b + c) = ab + ac
- Quadratic formula: x = [–b ± √(b²–4ac)] / 2a
- Difference of squares: a² – b² = (a + b)(a – b)
- Simultaneous equations: Solve by substitution/elimination
- Factorizing quadratics: ax² + bx + c = (x + p)(x + q)
Worked Example:
Solve x² – 5x + 6 = 0.
Solution: Factorize: (x–2)(x–3) = 0 ⇒ x = 2 or 3
Common Mistakes & Exam Tips:
Solve x² – 5x + 6 = 0.
Solution: Factorize: (x–2)(x–3) = 0 ⇒ x = 2 or 3
- Always try factorization before using quadratic formula.
- Check for sign errors in expanding and factorizing.
- For graphs, label axes and use correct scale.
3. Geometry
- Angles in triangle: sum = 180°
- Angles on straight line: sum = 180°
- Circle Theorems: Angle at center = 2 × angle at circumference, angles in same segment equal
- Pythagoras’ Theorem: a² + b² = c² (right triangle)
- Polygon: Interior angle = [(n–2) × 180°]/n
- Congruence/Similarity: SSS, SAS, RHS, AA criteria
Worked Example:
Find the hypotenuse if the other two sides are 6 cm and 8 cm.
Solution: c = √(6² + 8²) = √100 = 10 cm
Common Mistakes & Exam Tips:
Find the hypotenuse if the other two sides are 6 cm and 8 cm.
Solution: c = √(6² + 8²) = √100 = 10 cm
- Show all steps in geometric proofs—use clear reasons!
- Don’t confuse similar and congruent triangles.
- Check all working angles total 180°/360° as required.
4. Mensuration
- Area of rectangle: length × width
- Area of triangle: ½ × base × height
- Area of circle: πr²
- Circumference: 2πr or πd
- Volume of cuboid: l × w × h
- Volume of cylinder: πr²h
- Surface area of sphere: 4πr²; Volume: 4/3 πr³
Worked Example:
Find the area of a circle of radius 7 cm (use π = 22/7).
Solution: Area = 22/7 × 7² = 154 cm²
Common Mistakes & Exam Tips:
Find the area of a circle of radius 7 cm (use π = 22/7).
Solution: Area = 22/7 × 7² = 154 cm²
- Always check units—convert cm to m as needed!
- For volume, ensure all dimensions are in same unit.
- Use π = 3.14 unless told to use 22/7 or calculator value.
5. Trigonometry
- Sine: sin θ = opposite / hypotenuse
- Cosine: cos θ = adjacent / hypotenuse
- Tangent: tan θ = opposite / adjacent
- Sine Rule: a/sinA = b/sinB = c/sinC
- Cosine Rule: a² = b² + c² – 2bc cosA
- Area (non-right triangle): ½ ab sinC
Worked Example:
Find the angle if sin θ = 0.5.
Solution: θ = 30° (Check your calculator is in degrees!)
Common Mistakes & Exam Tips:
Find the angle if sin θ = 0.5.
Solution: θ = 30° (Check your calculator is in degrees!)
- Make sure calculator is in DEGREES (not radians) for IGCSE.
- Always label sides and angles carefully.
- For ambiguous case (sine rule), check if two possible triangles.
6. Sets & Probability
- n(A ∪ B): n(A) + n(B) – n(A ∩ B)
- Probability: P = no. of favourable outcomes / total outcomes
- Probability (complement): P(not A) = 1 – P(A)
- Mutually exclusive: P(A ∪ B) = P(A) + P(B)
- Independent: P(A and B) = P(A) × P(B)
Worked Example:
What's the probability of rolling a 4 or 6 on a fair die?
Solution: Favourable: 2, Total: 6 → P = 2/6 = 1/3
Common Mistakes & Exam Tips:
What's the probability of rolling a 4 or 6 on a fair die?
Solution: Favourable: 2, Total: 6 → P = 2/6 = 1/3
- Don't forget to subtract the overlap for "or" in Venn diagrams.
- Probabilities always between 0 and 1—check your answer!
7. Statistics
- Mean: sum of values / number of values
- Median: middle value (arrange in order first)
- Mode: most frequent value
- Range: highest – lowest
- Cumulative frequency: add up frequencies in order
- Grouped mean: (Σfx) / (Σf)
Worked Example:
Find the mean of 5, 8, 12, 15.
Solution: Mean = (5+8+12+15) / 4 = 40/4 = 10
Common Mistakes & Exam Tips:
Find the mean of 5, 8, 12, 15.
Solution: Mean = (5+8+12+15) / 4 = 40/4 = 10
- Always check you used the right formula for grouped/ungrouped data.
- For median, make sure list is ordered!
- Show all workings in frequency tables.
8. Functions & Graphs
- Linear: y = mx + c
- Quadratic: y = ax² + bx + c
- Inverse function: swap x and y, solve for y
- Composite function: f(g(x)) means do g first, then f
- Gradient: change in y / change in x
Worked Example:
Find the gradient of the line through (2,3) and (5,15).
Solution: m = (15–3)/(5–2) = 12/3 = 4
Common Mistakes & Exam Tips:
Find the gradient of the line through (2,3) and (5,15).
Solution: m = (15–3)/(5–2) = 12/3 = 4
- Always plot points carefully on graphs—label axes!
- Check if question wants equation, gradient, or coordinates.
- For quadratic, check for maximum/minimum turning point.
Summary Tables & SI Units
| Quantity | Formula | SI Unit |
|---|---|---|
| Length | - | metre (m) |
| Area | length × width | m² |
| Volume | l × w × h | m³ |
| Angle | - | degree (°) |
| Gradient | Δy / Δx | - |
Key IGCSE Maths Definitions & Theorems
- Prime number: Only divisible by 1 and itself.
- Rational number: Can be written as a fraction.
- Mean: Average of a data set.
- Median: Middle value of ordered data.
- Congruent triangles: Triangles that are exactly equal in shape and size.
- Pythagoras’ Theorem: a² + b² = c² in right-angled triangles.
- Simultaneous equations: Equations with the same variables, solved together.
- Factorize: Write as a product of factors.
- Inverse: Operation that undoes another (e.g. addition and subtraction).
- Complementary angle: Angles that add to 90°.
How to Revise IGCSE Maths Effectively
- Make your own formula sheet for each topic
- Practice exam-style questions, especially word problems
- Show ALL steps—working is required for method marks
- Revise calculator skills (SD, π, square root, etc.)
- Review every error in past papers
- Time yourself—work at exam speed
Tip: Always write units and final answer clearly—neatness earns marks!
Frequently Asked Questions (FAQs) – IGCSE Maths Formulas
- Q1. Do I need to memorize all formulas for IGCSE Maths?
Most are given, but you must remember key area, volume, trigonometry, and quadratic formulas—see syllabus for list. - Q2. What is the best way to practice?
Do past papers, timed quizzes, and always review your errors and mark schemes. - Q3. Are calculators allowed?
Yes, except in paper 1. Practice both with and without calculator. - Q4. How do I get method marks?
Show all steps. Even if answer is wrong, partial method marks are given for correct working.
Bookmark Hodu Academy Maths Resources for regular updates, PDF downloads, and expert revision for every IGCSE Maths chapter!