IGCSE Maths practice papers

The exam

Cambridge IGCSE Mathematics (0580) has two tiers. Core: Paper 1 (no calculator) and Paper 3 (calculator), 1 hour 30 minutes and 80 marks each, grades C to G. Extended: Paper 2 (no calculator) and Paper 4 (calculator), 2 hours and 100 marks each, grades A* to E. Every question is a written answer, and you show your working.

How the marking works

• The right answer gets all the marks of a part.
• Wrong answer? Each right line of your working gets a method mark, and a line that follows from a wrong one still counts (follow-through), as in the exams.
• Drawings, constructions and proofs: you see the mark scheme and tick the marks your work earns.

Learn the topics

Every question links to the lesson that teaches it.

Number

Bounds in calculations · Compound and continuous interest · Decimals · Density, pressure, population density · Exchange rates · Exponential models from words · Factors and multiples · Fractions · Fractions and decimals · Motion with an unknown speed · Negative numbers in real life · Order of operations · Percent · Percent · Percent · Percents and money · Rational exponents · Rationalising a two-term bottom with its partner · Ratios with units · Repeating decimals to fractions · Scientific notation · Sets · Sharing in a ratio · Significant figures and estimating · Simple interest · Simplifying square roots · Upper and lower bounds of a measurement · Venn diagrams with numbers · Word problems part 2

Algebra and graphs

Adding and subtracting rational expressions · Changing the subject when it appears twice · Completing the square · Composition and inverse functions · Composition order · Compound inequalities · Direct and inverse variation · Evaluate expressions · Expanding three brackets · Exponent rules · Exponential equations and logarithms · Exponential models from words · Factoring · Graphing with a table · Inequalities · Linear equations · Linear equations · Literal equations · Nonlinear systems · Polynomials · Quadratic equations · Quadratic sequences · Rational equations · Rational expressions · Sequences · Simplify expressions · Speed-time graphs · Systems of equations · Systems of inequalities · Tangent lines · The power rule · The second derivative test · Tickets with a link · Vertex form by completing the square · Word problems part 1

Coordinate geometry

Distance between two points · Equation of a line through two points · Midpoint · Parallel and perpendicular lines · Slope from two points

Geometry

Angle facts · Angles in a polygon · Chords · Circle rules · Constructions with a ruler and compasses · Cyclic quadrilaterals · Exterior angles · Intersecting chords, secants and tangents · Loci · Pythagoras · Pythagoras in 3D · Scale drawings and maps · Similar triangles · The alternate segment theorem

Mensuration

Arc length, sector area and perimeter as a part of the circle · Cones · Parallelogram and trapezoid · Perimeter and area · Similar shapes and solids · Spheres and hemispheres · Volume and surface area · Volume of a frustum

Trigonometry

Angles of elevation and depression · Area of a triangle with sine · Bearings with trigonometry and Pythagoras · Right-triangle trigonometry · The law of cosines · The law of sines · Trig equations · Trigonometry in 3D

Transformations and vectors

Adding, subtracting, × a number · Dilations about the origin · Reflections · Rotations about the origin · Translations · Two moves in a row · Vector geometry

Probability

Conditional probability · Probability · Probability with and · Probability with counting · Sample spaces · Samples and predictions · Venn and tree diagrams

Statistics

Cumulative frequency · Histograms with unequal class widths · Mean of grouped data · Mean, median, mode, range · Scatter plots and correlation