Specification points
Cambridge Cambridge IGCSE Mathematics 0580
344 points in 11 topics, with Cambridge's codes and titles.
Grade boundaries·Cambridge command words
Codes and titles are read by a script from Cambridge's published specification and have not been checked by a person. What each point covers is in the specification itself: Cambridge’s specification.
1 Number
- C1.1 Types of number (Core)
- C1.2 Sets (Core)
- C1.3 Powers and roots (Core)
- C1.4 Fractions, decimals and percentages (Core)
- C1.4.1 Fractions, decimals and percentages notation
- C1.4.2 Equivalence and conversion between forms
- C1.5 Ordering (Core)
- C1.6 The four operations (Core)
- C1.7 Indices I (Core)
- C1.7.1 Indices
- C1.7.2 Rules of indices
- C1.8 Standard form (Core)
- C1.8.1 Standard form notation
- C1.8.2 Converting to and from standard form
- C1.8.3 Calculating in standard form
- C1.9 Estimation (Core)
- C1.9.1 Rounding to decimal places and significant figures
- C1.9.2 Estimating calculations
- C1.9.3 Rounding answers sensibly in context
- C1.10 Limits of accuracy (Core)
- C1.11 Ratio and proportion (Core)
- C1.12 Rates (Core)
- C1.12.1 Common measures of rate
- C1.12.2 Other measures of rate
- C1.12.3 Average speed problems
- C1.13 Percentages (Core)
- C1.13.1 Percentage of a quantity
- C1.13.2 One quantity as a percentage of another
- C1.13.3 Percentage increase and decrease
- C1.13.4 Simple and compound interest
- C1.14 Using a calculator (Core)
- C1.14.1 Using a calculator efficiently
- C1.14.2 Entering values on a calculator
- C1.14.3 Interpreting the calculator display
- C1.15 Time (Core)
- C1.15.1 Calculating with units of time
- C1.15.2 24-hour and 12-hour clock
- C1.15.3 Clocks and timetables
- C1.16 Money (Core)
- C1.16.1 Calculating with money
- C1.16.2 Currency conversion
- E1.1 Types of number (Extended)
- E1.2 Sets (Extended)
- E1.3 Powers and roots (Extended)
- E1.4 Fractions, decimals and percentages (Extended)
- E1.4.1 Fractions, decimals and percentages notation
- E1.4.2 Equivalence and conversion, including recurring decimals
- E1.5 Ordering (Extended)
- E1.6 The four operations (Extended)
- E1.7 Indices I (Extended)
- E1.7.1 Indices, including fractional
- E1.7.2 Rules of indices
- E1.8 Standard form (Extended)
- E1.8.1 Standard form notation
- E1.8.2 Converting to and from standard form
- E1.8.3 Calculating in standard form
- E1.9 Estimation (Extended)
- E1.9.1 Rounding to decimal places and significant figures
- E1.9.2 Estimating calculations
- E1.9.3 Rounding answers sensibly in context
- E1.10 Limits of accuracy (Extended)
- E1.10.1 Upper and lower bounds of rounded data
- E1.10.2 Bounds of calculated results
- E1.11 Ratio and proportion (Extended)
- E1.12 Rates (Extended)
- E1.12.1 Common measures of rate
- E1.12.2 Other measures of rate
- E1.12.3 Average speed problems
- E1.13 Percentages (Extended)
- E1.13.1 Percentage of a quantity
- E1.13.2 One quantity as a percentage of another
- E1.13.3 Percentage increase and decrease
- E1.13.4 Simple and compound interest, including repeated change
- E1.13.5 Reverse percentages
- E1.14 Using a calculator (Extended)
- E1.14.1 Using a calculator efficiently
- E1.14.2 Entering values on a calculator
- E1.14.3 Interpreting the calculator display
- E1.15 Time (Extended)
- E1.15.1 Calculating with units of time
- E1.15.2 24-hour and 12-hour clock
- E1.15.3 Clocks and timetables
- E1.16 Money (Extended)
- E1.16.1 Calculating with money
- E1.16.2 Currency conversion
- E1.17 Exponential growth and decay (Extended)
- E1.18 Surds (Extended)
- E1.18.1 Surds and simplifying surd expressions
- E1.18.2 Rationalising the denominator
2 Algebra and graphs
- C2.1 Introduction to algebra (Core)
- C2.1.1 Letters as generalised numbers
- C2.1.2 Substitution into expressions and formulas
- C2.2 Algebraic manipulation (Core)
- C2.2.1 Collecting like terms
- C2.2.2 Expanding products
- C2.2.3 Factorising by common factors
- C2.4 Indices II (Core)
- C2.4.1 Indices in algebra
- C2.4.2 Rules of indices in algebra
- C2.5 Equations (Core)
- C2.5.1 Constructing expressions, equations and formulas
- C2.5.2 Linear equations in one unknown
- C2.5.3 Simultaneous linear equations
- C2.5.4 Changing the subject of simple formulas
- C2.6 Inequalities (Core)
- C2.7 Sequences (Core)
- C2.7.1 Continuing sequences and patterns
- C2.7.2 Patterns in sequences and term-to-term rules
- C2.7.3 nth term of linear, quadratic and cubic sequences
- C2.9 Graphs in practical situations (Core)
- C2.9.1 Travel and conversion graphs
- C2.9.2 Drawing graphs from data
- C2.10 Graphs of functions (Core)
- C2.10.1 Tables of values and graphs of functions
- C2.10.2 Solving equations graphically
- C2.11 Sketching curves (Core)
- E2.1 Introduction to algebra (Extended)
- E2.1.1 Letters as generalised numbers
- E2.1.2 Substitution into expressions and formulas
- E2.2 Algebraic manipulation (Extended)
- E2.2.1 Collecting like terms
- E2.2.2 Expanding products, including two brackets
- E2.2.3 Factorising by common factors
- E2.2.4 Factorising expressions of various forms
- E2.2.5 Completing the square
- E2.3 Algebraic fractions (Extended)
- E2.3.1 Algebraic fractions
- E2.3.2 Rational expressions
- E2.4 Indices II (Extended)
- E2.4.1 Indices in algebra, including fractional
- E2.4.2 Rules of indices in algebra
- E2.5 Equations (Extended)
- E2.5.1 Constructing expressions, equations and formulas
- E2.5.2 Linear equations in one unknown
- E2.5.3 Fractional equations
- E2.5.4 Simultaneous linear equations
- E2.5.5 Simultaneous equations, one linear and one non-linear
- E2.5.6 Quadratic equations
- E2.5.7 Changing the subject of formulas
- E2.6 Inequalities (Extended)
- E2.6.1 Inequalities on a number line
- E2.6.2 Linear inequalities
- E2.6.3 Graphing linear inequalities in two variables
- E2.6.4 Inequalities defining a region
- E2.7 Sequences (Extended)
- E2.7.1 Continuing sequences and patterns
- E2.7.2 Patterns in sequences, including exponential
- E2.7.3 nth term of sequences
- E2.8 Proportion (Extended)
- E2.9 Graphs in practical situations (Extended)
- E2.9.1 Travel and conversion graphs
- E2.9.2 Drawing graphs from data
- E2.9.3 Rate of change in kinematics graphs
- E2.9.4 Distance as area under a speed–time graph
- E2.10 Graphs of functions (Extended)
- E2.10.1 Tables of values and graphs of further functions
- E2.10.2 Solving equations graphically
- E2.10.3 Exponential growth and decay graphs
- E2.11 Sketching curves (Extended)
- E2.12 Differentiation (Extended)
- E2.12.1 Gradients of curves by tangents
- E2.12.2 Derivatives of power functions
- E2.12.3 Differentiation for gradients and turning points
- E2.12.4 Maxima and minima
- E2.13 Functions (Extended)
- E2.13.1 Functions, domain, range and notation
- E2.13.2 Inverse functions
- E2.13.3 Composite functions
3 Coordinate geometry
- C3.1 Coordinates (Core)
- C3.2 Drawing linear graphs (Core)
- C3.3 Gradient of linear graphs (Core)
- C3.5 Equations of linear graphs (Core)
- C3.6 Parallel lines (Core)
- E3.1 Coordinates (Extended)
- E3.2 Drawing linear graphs (Extended)
- E3.3 Gradient of linear graphs (Extended)
- E3.3.1 Gradient of a straight line
- E3.3.2 Gradient from two points
- E3.4 Length and midpoint (Extended)
- E3.4.1 Length of a line segment
- E3.4.2 Midpoint of a line segment
- E3.5 Equations of linear graphs (Extended)
- E3.6 Parallel lines (Extended)
- E3.7 Perpendicular lines (Extended)
4 Geometry
- C4.1 Geometrical terms (Core)
- C4.1.1 Geometrical terms
- C4.1.2 Vocabulary of triangles, quadrilaterals, polygons and solids
- C4.1.3 Vocabulary of a circle
- C4.2 Geometrical constructions (Core)
- C4.2.1 Measuring and drawing lines and angles
- C4.2.2 Constructing triangles
- C4.2.3 Nets
- C4.3 Scale drawings (Core)
- C4.3.1 Scale drawings
- C4.3.2 Three-figure bearings
- C4.4 Similarity (Core)
- C4.5 Symmetry (Core)
- C4.6 Angles (Core)
- C4.6.1 Angle properties at points, lines and shapes
- C4.6.2 Angles in parallel lines
- C4.6.3 Angles in regular polygons
- C4.7 Circle theorems (Core)
- E4.1 Geometrical terms (Extended)
- E4.1.1 Geometrical terms
- E4.1.2 Vocabulary of triangles, quadrilaterals, polygons and solids
- E4.1.3 Vocabulary of a circle
- E4.2 Geometrical constructions (Extended)
- E4.2.1 Measuring and drawing lines and angles
- E4.2.2 Constructing triangles
- E4.2.3 Nets
- E4.3 Scale drawings (Extended)
- E4.3.1 Scale drawings
- E4.3.2 Three-figure bearings
- E4.4 Similarity (Extended)
- E4.4.1 Lengths of similar shapes
- E4.4.2 Lengths, areas and volumes of similar shapes
- E4.4.3 Problems involving similarity
- E4.5 Symmetry (Extended)
- E4.5.1 Line and rotational symmetry
- E4.5.2 Symmetry of prisms, cylinders, pyramids and cones
- E4.6 Angles (Extended)
- E4.6.1 Angle properties at points, lines and shapes
- E4.6.2 Angles in parallel lines
- E4.6.3 Angles in regular and irregular polygons
- E4.7 Circle theorems I (Extended)
- E4.8 Circle theorems II (Extended)
5 Mensuration
- C5.1 Units of measure (Core)
- C5.2 Area and perimeter (Core)
- C5.3 Circles, arcs and sectors (Core)
- C5.3.1 Circumference and area of a circle
- C5.3.2 Arc length and sector area
- C5.4 Surface area and volume (Core)
- C5.5 Compound shapes and parts of shapes (Core)
- C5.5.1 Perimeter and area of compound shapes
- C5.5.2 Surface area and volume of compound solids
- E5.1 Units of measure (Extended)
- E5.2 Area and perimeter (Extended)
- E5.3 Circles, arcs and sectors (Extended)
- E5.3.1 Circumference and area of a circle
- E5.3.2 Arc length and sector area, including major sectors
- E5.4 Surface area and volume (Extended)
- E5.5 Compound shapes and parts of shapes (Extended)
- E5.5.1 Perimeter and area of compound shapes
- E5.5.2 Surface area and volume of compound solids
6 Trigonometry
- C6.1 Pythagoras’ theorem (Core)
- C6.2 Right-angled triangles (Core)
- C6.2.1 Sine, cosine and tangent in right-angled triangles
- C6.2.2 Pythagoras and trigonometry in two dimensions
- E6.1 Pythagoras’ theorem (Extended)
- E6.2 Right-angled triangles (Extended)
- E6.2.1 Sine, cosine and tangent in right-angled triangles
- E6.2.2 Pythagoras and trigonometry in two dimensions
- E6.2.3 Perpendicular distance from a point to a line
- E6.2.4 Angles of elevation and depression
- E6.3 Exact trigonometric values (Extended)
- E6.3.1 Exact values of sine and cosine
- E6.3.2 Exact values of tangent
- E6.4 Trigonometric functions (Extended)
- E6.4.1 Graphs of sine, cosine and tangent
- E6.4.2 Trigonometric equations
- E6.5 Non-right-angled triangles (Extended)
- E6.5.1 Sine and cosine rules
- E6.5.2 Area of a triangle using sine
- E6.6 Pythagoras’ theorem and trigonometry in 3D (Extended)
7 Transformations and vectors
- C7.1 Transformations (Core)
- C7.1.1 Reflection in vertical or horizontal lines
- C7.1.2 Rotation through multiples of 90°
- C7.1.3 Enlargement
- C7.1.4 Translation by a vector
- E7.1 Transformations (Extended)
- E7.1.1 Reflection in a straight line
- E7.1.2 Rotation about a centre
- E7.1.3 Enlargement, including negative scale factors
- E7.1.4 Translation by a vector
- E7.2 Vectors in two dimensions (Extended)
- E7.2.1 Describing translations with vectors
- E7.2.2 Adding and subtracting vectors
- E7.2.3 Multiplying a vector by a scalar
- E7.3 Magnitude of a vector (Extended)
- E7.4 Vector geometry (Extended)
- E7.4.1 Vectors as directed line segments
- E7.4.2 Position vectors
- E7.4.3 Expressing vectors in terms of two coplanar vectors
- E7.4.4 Vector reasoning and geometric problems
8 Probability
- C8.1 Introduction to probability (Core)
- C8.1.1 The probability scale
- C8.1.2 Probability of a single event
- C8.1.3 Probability of an event not occurring
- C8.2 Relative and expected frequencies (Core)
- C8.2.1 Relative frequency
- C8.2.2 Expected frequencies
- C8.3 Probability of combined events (Core)
- E8.1 Introduction to probability (Extended)
- E8.1.1 The probability scale
- E8.1.2 Probability notation
- E8.1.3 Probability of a single event
- E8.1.4 Probability of an event not occurring
- E8.2 Relative and expected frequencies (Extended)
- E8.2.1 Relative frequency
- E8.2.2 Expected frequencies
- E8.3 Probability of combined events (Extended)
- E8.4 Conditional probability (Extended)
9 Statistics
- C9.1 Classifying statistical data (Core)
- C9.2 Interpreting statistical data (Core)
- C9.2.1 Interpreting tables and statistical diagrams
- C9.2.2 Comparing sets of data
- C9.2.3 Limits of conclusions from data
- C9.3 Averages and range (Core)
- C9.4 Statistical charts and diagrams (Core)
- C9.5 Scatter diagrams (Core)
- C9.5.1 Scatter diagrams
- C9.5.2 Positive, negative and zero correlation
- C9.5.3 Line of best fit
- E9.1 Classifying statistical data (Extended)
- E9.2 Interpreting statistical data (Extended)
- E9.2.1 Interpreting tables and statistical diagrams
- E9.2.2 Comparing sets of data, including spread
- E9.2.3 Limits of conclusions from data
- E9.3 Averages and measures of spread (Extended)
- E9.3.1 Averages, quartiles, range and interquartile range
- E9.3.2 Estimated mean for grouped data
- E9.3.3 Modal class
- E9.4 Statistical charts and diagrams (Extended)
- E9.5 Scatter diagrams (Extended)
- E9.5.1 Scatter diagrams
- E9.5.2 Positive, negative and zero correlation
- E9.5.3 Line of best fit
- E9.6 Cumulative frequency diagrams (Extended)
- E9.6.1 Cumulative frequency tables and diagrams
- E9.6.2 Median, percentiles and quartiles from cumulative frequency
- E9.7 Histograms (Extended)
- E9.7.1 Histograms
- E9.7.2 Frequency density