IGCSE Math RevisionCambridge IGCSE Maths 0580 scheme of work
A complete plan for Cambridge IGCSE Maths 0580: 65 weeks, 260 lessons, with a quick check most weeks and a test at the end of each unit. Here is the whole plan at a glance and one lesson in full.
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A sample lesson, in full
The course at a glance
FA = a short formative check in that week; SA = an end-of-unit test.
Extended (two years)
65 weeks · 260 lessons · 14 unit tests (SA)
| Week | Lessons | Checks |
|---|---|---|
| Topic 1 · Number | ||
| 1 | Baseline check: number and algebra from earlier years · Types of number: natural numbers, integers, primes, squares and cubes · Factors and multiples: prime factors, HCF and LCM · Rational and irrational numbers; reciprocals | |
| 2 | Powers and roots: squares, cubes and their roots · The four operations with integers; order of operations and brackets · Fractions: the four operations without a calculator · Decimals: the four operations without a calculator | |
| 3 | Equivalent fractions, decimals and percentages · Converting recurring decimals to fractions · Ordering quantities; the symbols =, ≠, <, >, ≤ and ≥ · Indices I: the laws of indices | |
| 4 | Zero, negative and fractional indices · Standard form: writing numbers and converting back · Calculating with standard form, with and without a calculator · Rounding to decimal places and significant figures | |
| 5 | Estimating calculations and rounding answers in context · Using a calculator efficiently and reading the display · Limits of accuracy: upper and lower bounds · Upper and lower bounds of calculations | |
| 6 | Ratio: simplest form and sharing in a given ratio · Proportional reasoning in context · Rates: density, pressure and population density · Average speed and converting units of rate | |
| 7 | Percentages of quantities; one quantity as a percentage of another · Percentage increase and decrease · Simple and compound interest · Reverse percentages: finding the original amount | |
| 8 | Exponential growth and decay in context · Money: calculating with money and converting currencies · Time: 24-hour clock, timetables and time zones · Half-term Test 1 (Number) | SA1 |
| 9 | Surds: simplifying expressions with surds · Surds: rationalising the denominator · Sets: notation, n(A), complement, union and intersection · Venn diagrams with two and three sets; set-builder notation | |
| Topic 2 · Algebra and graphs | ||
| 10 | Letters for numbers; substituting into expressions and formulas · Simplifying by collecting like terms · Expanding single and double brackets · Expanding products of three brackets | |
| 11 | Factorising: common factors and grouping · Factorising quadratics and the difference of two squares · Indices II: the laws of indices in algebra · Fractional and negative indices in algebra | |
| 12 | Constructing expressions, equations and formulas · Solving linear equations · Fractional equations with numerical and linear denominators · Simultaneous linear equations | |
| 13 | Changing the subject of a formula · Changing the subject: when it appears twice or as a power or root · Inequalities: number lines, solving and interpreting · End-of-term Test 1 (Number and algebra) | SA2 |
| 14 | Sequences: term-to-term rules and the nth term of linear sequences · Quadratic and cubic sequences · Exponential sequences and combinations of sequences · Travel graphs and conversion graphs | |
| Topic 3 · Coordinate geometry | ||
| 15 | Coordinates and drawing straight-line graphs · Gradient from a graph and from the coordinates of two points · Equations of straight lines: y = mx + c and x = k · Lines in the form ax + by = c; the line through two points | |
| 16 | Length and midpoint of a line segment · Parallel lines: gradient and equation · Perpendicular lines and perpendicular bisectors · Half-term Test 2 (Algebra and coordinate geometry) | SA3 |
| Topic 4 · Geometry | ||
| 17 | Geometrical terms: angles, lines, polygons, circles and solids · Measuring and drawing; constructing a triangle from three sides · Drawing, using and interpreting nets · Scale drawings and three-figure bearings | |
| 18 | Angles on lines, at points, in triangles and quadrilaterals · Angles with parallel lines · Interior and exterior angles of polygons · Symmetry of 2D shapes; planes and axes of symmetry of solids | |
| 19 | Similar shapes: calculating lengths · Circle theorems: angle in a semicircle; tangent and radius · Circle theorems: angle at the centre, same segment, cyclic quadrilateral · The alternate segment theorem | |
| Topic 5 · Mensuration | ||
| 20 | Units of measure: converting length, area, volume and capacity · Perimeter and area of rectangles, triangles, parallelograms and trapezia · Circumference and area of a circle · Arc length and sector area | |
| 21 | Surface area and volume of cuboids, prisms and cylinders · Surface area and volume of pyramids, cones and spheres · Compound shapes and parts of shapes · Compound solids, frustums and hemispheres | |
| Topic 6 · Trigonometry | ||
| 22 | Pythagoras' theorem · Right-angled trigonometry: finding sides · Right-angled trigonometry: finding angles; elevation and depression · Bearings and problems in two dimensions | |
| 23 | Exact trigonometric values · Problem solving: mensuration and trigonometry · End-of-term Test 2 (Geometry, mensuration and trigonometry) · Test review: correcting errors and closing gaps | SA4 |
| Topic 8 · Probability | ||
| 24 | The probability scale; P(not A) = 1 − P(A) · Relative frequency and expected frequency · Combined events: sample space and Venn diagrams · Tree diagrams, with and without replacement | |
| 25 | Conditional probability · Classifying and tabulating data · Averages and range from lists and frequency tables · Estimated mean and modal class of grouped data | |
| Topic 9 · Statistics | ||
| 26 | Bar charts, pie charts and pictograms · Stem-and-leaf diagrams and frequency distributions · Interpreting and comparing sets of data · Scatter diagrams and correlation | |
| 27 | Lines of best fit · Quartiles and interquartile range · Cumulative frequency tables and diagrams · Median, quartiles and percentiles from a cumulative frequency diagram | |
| 28 | Histograms with equal class widths · Histograms with unequal class widths: frequency density · Half-term Test 3 (Probability and statistics) · Statistics problem solving: choosing a diagram and an average | SA5 |
| Topic 7 · Transformations and vectors | ||
| 29 | Reflections and rotations · Translations and enlargements · Enlargements with fractional and negative scale factors · Describing transformations fully | |
| 30 | Vectors: notation, adding, subtracting and multiplying by a scalar · The magnitude of a vector · Vector geometry: expressing vectors in terms of others · Vector geometry: parallel lines and collinear points | |
| Revision and exam practice | ||
| 31 | Year 10 revision: number, algebra and coordinate geometry · Year 10 revision: geometry, mensuration and statistics · End-of-year exam: Paper 2 style (non-calculator) · End-of-year exam: Paper 4 style (calculator) | SA7 |
| Topic 4 · Geometry | ||
| 32 | Exam review: common errors and corrections · Similar shapes: areas and volumes · Circle theorems II: chords and tangents from an external point · Circle theorems problem solving | |
| Topic 2 · Algebra and graphs | ||
| 33 | Completing the square · Quadratic equations by factorising · Quadratic equations by completing the square and the formula · Year 10 review and Year 11 readiness check | |
| 34 | Quadratic equations in context · Simultaneous equations: one linear, one non-linear · Algebraic fractions: simplifying by factorising · Algebraic fractions: add, subtract, multiply and divide | |
| 35 | Equations with algebraic fractions · Linear inequalities in two variables: regions on a graph · Inequalities problem solving · Direct and inverse proportion | |
| 36 | Proportion: forming equations and finding unknowns · Graphs of linear, quadratic and reciprocal functions · Graphs of cubics and powers of x · Graphs of exponential functions | |
| 37 | Solving equations graphically, including where a curve meets a line · Sketching curves: roots, turning points and symmetry · Sketching cubics, reciprocals and exponentials; asymptotes · Speed-time graphs: acceleration and distance travelled | |
| Quadratic equations: completing the square and the formula in context · Sketching curves: turning points by completing the square · Graphs of exponential functions and growth and decay · Review: algebra and graphs before Half-term Test 4 | ||
| 38 | Functions: notation, domain and range · Composite functions · Inverse functions · Half-term Test 4 (Algebra and graphs) | SA8 |
| 39 | Estimating gradients of curves by drawing tangents · Differentiating axⁿ and sums of terms · Gradients of curves at a point · Stationary points: maxima and minima | |
| Differentiation: stationary points, maximum or minimum? · Differentiation: the point where the gradient has a given value · Differentiation: expanding brackets before differentiating · Speed-time graphs: acceleration and distance in context | ||
| Topic 6 · Trigonometry | ||
| 40 | Exact trigonometric values without a calculator · Graphs of sine, cosine and tangent · Solving trigonometric equations for 0° ≤ x ≤ 360° · The sine rule | |
| 41 | The sine rule: obtuse angles and the ambiguous case · The cosine rule · Area of a triangle = ½ab sin C · Pythagoras and trigonometry in three dimensions | |
| 42 | The angle between a line and a plane · Trigonometry problem solving: choosing the method · End-of-term Test 3 (Differentiation and trigonometry) · Test review: correcting errors and closing gaps | SA9 |
| Topic 4 · Geometry | ||
| 43 | Similarity: problems and explanations · Sectors: major and minor, finding the angle or radius · Mensuration problem solving in exam style · Bearings and scale drawing problems | |
| Similarity: areas and volumes of similar shapes and solids · Similarity: explaining why shapes are similar · Circle theorems: centre, same segment and cyclic quadrilaterals · Circle theorems: the alternate segment theorem | ||
| Circle theorems II: chords and tangents from a point · Harder parts of solids: frustums and hemispheres · Symmetry of solids: planes and axes of symmetry · Angles of elevation and depression | ||
| Topic 7 · Transformations and vectors | ||
| 44 | Transformations: reflections in y = x and y = −x · Vector geometry: exam-style problems · Combined events: problem solving · Conditional probability from tables | |
| Topic 9 · Statistics | ||
| Cumulative frequency: median, quartiles and percentiles · Histograms: unequal class widths and frequency density · Grouped data: estimated mean and modal class · Review: geometry, vectors, probability and statistics before Half-term Test 5 | ||
| 45 | Cumulative frequency: interpreting and comparing · Histograms: frequency density problems · Comparing distributions in words · Half-term Test 5 (Geometry, vectors, probability and statistics) | SA10 |
| Revision and exam practice | ||
| 46 | Non-calculator skills: fractions, decimals and percentages · Non-calculator skills: indices and surds · Non-calculator skills: standard form and estimation · Non-calculator skills: exact values and answers in terms of π | |
| 47 | Revision: manipulation and equations · Revision: inequalities and sequences · Revision: graphs and sketching curves · Revision: functions and differentiation | |
| Exam practice: surds, indices and standard form without a calculator · Exam practice: reverse percentages and exponential growth and decay · Exam practice: bounds of calculations · Exam practice: recurring decimals, ratio and rates | ||
| 48 | Mock exam: Paper 2 (non-calculator) · Mock exam: Paper 4 (calculator) · Review of the Paper 2 mock · Review of the Paper 4 mock | SA12 |
| 49 | Revision: bounds, percentages and growth · Revision: coordinate geometry · Revision: angles and circle theorems · Revision: surface area and volume | |
| Exam practice: algebraic fractions and quadratic equations · Exam practice: simultaneous equations, linear and non-linear · Exam practice: functions, inverse and composite · Exam practice: differentiation and stationary points | ||
| 50 | Revision: trigonometry · Revision: transformations and vectors · Revision: probability · Revision: statistics | |
| Exam practice: coordinate geometry · Exam practice: circle theorems with reasons · Exam practice: similar shapes and solids · Exam practice: arcs, sectors and harder solids | ||
| 51 | Exam technique: accuracy, 3 significant figures and showing working · Revision: sets, sequences and proportion · Timed practice: Paper 2 style · Timed practice: Paper 4 style | |
| 52 | Mock exam 2: Paper 2 (non-calculator) · Mock exam 2: Paper 4 (calculator) · Review of the second Paper 2 mock · Review of the second Paper 4 mock | SA14 |
| 53 | Revision: rates, time and money · Revision: geometrical terms, nets and symmetry · Revision: charts, stem-and-leaf and scatter diagrams · Revision: powers, ordering and ratio | |
| Exam practice: sine rule, cosine rule and area of a triangle · Exam practice: exact values and trigonometry in 3D · Exam practice: trigonometric graphs and equations · Exam practice: transformations and vectors | ||
| 54 | Revision: substitution, indices and practical graphs · Revision: straight-line graphs · Revision: units, area and Pythagoras · Revision: probability and interpreting data | |
| Exam practice: tree diagrams and conditional probability · Exam practice: cumulative frequency and histograms · Exam practice: inequalities, sequences and proportion · Exam practice: averages, spread and comparing data | ||
| 55 | Final revision: your weakest topics (Paper 2) · Final revision: your weakest topics (Paper 4) · Exam-day preparation · Final questions and answers | |
The full plan: every lesson with its objective, starters, practice and homework links, your own order and dates, and a tick to mark each lesson taught.
Get the full editable scheme of work — free for teachersWhat the course covers
Every syllabus point in plain English, with practice for each: Cambridge IGCSE Maths 0580 syllabus checklist.