O-Level / IGCSE Mathematics (0580)
Original practice questions with long-form, step-by-step worked solutions, organised by the Cambridge 0580 syllabus strands. Everything here is free to read.
- Subject code
- 0580
- Tier
- Core & Extended
- Topics
- 15
- Worked questions
- 57
Official Cambridge references: 0580 syllabus ↗ · past papers ↗
Number
Standard Form
Write numbers in the form a × 10ⁿ (with 1 ≤ a < 10 and integer n), convert between ordinary numbers and standard form, and calculate with values written in…
Percentages
Find a percentage of a quantity; percentage increase/decrease; express one quantity as a percentage of another; reverse percentages and repeated percentage…
Ratio and Proportion
Use ratio notation; divide a quantity in a given ratio; relate ratios to fractions; solve problems involving direct and inverse proportion.
Algebra and graphs
Quadratic Equations
Factorise quadratic expressions and solve quadratic equations by factorising, by completing the square, and by using the quadratic formula.
Linear Equations and Inequalities
Solve linear equations in one unknown and simultaneous linear equations in two unknowns; solve and represent linear inequalities.
Sequences and the nth Term
Continue sequences; find and use the nth term of linear and simple quadratic sequences; recognise patterns in number sequences.
Coordinate geometry
Geometry
Angles and Polygons
Calculate unknown angles using angles at a point, on a line, in triangles and quadrilaterals, on parallel lines, and the interior/exterior angles of polygons.
Circle Theorems
Use circle theorems (angle at centre, angle in a semicircle, angles in the same segment, cyclic quadrilaterals, tangents) to find unknown angles and lengths.