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The official Cambridge 0580 syllabus, unit by unit — exactly the way school numbers it. Click any line to jump straight to that lesson. Amber = on your Unit Assessment (Maths paper Mon 21 Sep).
E1 · Number
E1.1 Types of number Knowing what natural numbers, integers, primes, squares, cubes, rationals, irrationals and reciprocals are, and using prime factors to find the HCF and LCM of two numbers. E1.2 Sets UNIT EXAM · MON 21 SEP Set language, notation and Venn diagrams for up to three sets, including union, intersection, complement, subsets and the empty set. 🎙 Tutor Live — a voice lesson on this topic Talks you through sets and Venn diagrams step by step, asks you questions, and draws a new picture when you are stuck. Pilot — tell Appa what you think. E1.3 Powers and roots Working with squares, cubes and their roots (and other powers), including recalling squares up to 15 and the common cubes from memory. E1.4 Fractions, decimals and percentages Naming and converting between proper and improper fractions, mixed numbers, decimals and percentages, including turning recurring decimals into fractions and back. E1.5 Ordering Putting quantities in order of size and using the symbols =, ≠, >, <, ⩾ and ⩽ correctly. E1.6 The four operations Adding, subtracting, multiplying and dividing integers, fractions and decimals in the right order, with brackets and negative numbers. E1.7 Indices I Using powers that are positive, zero, negative or fractional, and applying the rules of indices to work out values. E1.8 Standard form Writing numbers as A × 10ⁿ, converting into and out of standard form, and calculating with numbers written this way. E1.9 Estimation Rounding to decimal places and significant figures, and estimating the answer to a messy calculation by rounding each number to 1 significant figure first. E1.10 Limits of accuracy Giving the upper and lower bounds of a rounded measurement, and then finding the bounds of an answer calculated from rounded values (such as a perimeter, area or speed). E1.11 Ratio and proportion Simplifying ratios, sharing a quantity in a given ratio, and using proportional reasoning in real contexts like recipes, map scales and best value. E1.12 Rates Calculating with rates such as pay per hour, exchange rates, flow rate, density and pressure, and solving average speed problems using distance ÷ time. E1.13 Percentages UNIT EXAM · MON 21 SEP Percentage of an amount, one amount as a percentage of another, percentage increase and decrease, simple and compound interest, and reverse percentages. 🎙 Tutor Live — a voice lesson on this topic Walks you through all five percentage question types, including the reverse one that trips everybody up. E1.14 Using a calculator Using a calculator efficiently, entering values correctly and reading the display sensibly — for example not rounding until the very end. E1.15 Time UNIT EXAM · MON 21 SEP Calculating with seconds, minutes, hours, days and years, reading 12- and 24-hour clocks and timetables, and handling time zones and time differences. 🎙 Tutor Live — a voice lesson on this topic The counting-up method for durations, the next-day trap, and how to read a timetable without slipping a column. E1.16 Money UNIT EXAM · MON 21 SEP Doing calculations with money and converting an amount from one currency to another. 🎙 Tutor Live — a voice lesson on this topic Best value, currency both ways, and percentage profit — all of it is really about matching the units first. E1.17 Exponential growth and decay [Extended only] Handling situations where something grows or shrinks by the same percentage repeatedly, such as depreciation of a car or a growing population. E1.18 Surds [Extended only] Working with exact square roots — simplifying them, adding and subtracting them, and rationalising the denominator so no root is left on the bottom.
E2 · Algebra and graphs
E2.1 Introduction to algebra Using letters to stand for numbers, and substituting numbers into expressions and formulas. E2.2 Algebraic manipulation Collecting like terms, expanding brackets (including three at once), factorising fully by grouping, difference of two squares and quadratics, and completing the square. E2.3 Algebraic fractions [Extended only] Adding, subtracting, multiplying and dividing fractions that contain letters, and cancelling them down by factorising the top and bottom. E2.4 Indices II Using the index rules on algebraic terms and solving equations where the unknown is in the power, such as 32ˣ = 2. Logarithms are not needed. E2.5 Equations Building and solving equations: linear, fractional, simultaneous (including one linear and one non-linear), quadratics by factorising, completing the square and the formula, plus rearranging formulas. E2.6 Inequalities Showing inequalities on a number line, solving linear inequalities, shading regions on a graph and writing down the inequalities that describe a region. E2.7 Sequences Continuing a sequence, spotting the term-to-term rule and finding the nth term for linear, quadratic, cubic and exponential sequences. E2.8 Proportion [Extended only] Writing direct and inverse proportion as an equation (including square, square root, cube and cube root versions) and using it to find missing values. E2.9 Graphs in practical situations Reading and drawing travel and conversion graphs, using gradient as a rate of change, finding acceleration and getting distance from the area under a speed–time graph. E2.10 Graphs of functions Making a table of values and plotting curves of the form axⁿ and abˣ + c, then using the graph to solve equations and to model growth and decay. E2.11 Sketching curves Recognising and sketching the shape of linear, quadratic, cubic, reciprocal and exponential graphs, including turning points, roots, symmetry and asymptotes. E2.12 Differentiation [Extended only] Finding dy/dx for terms like axⁿ, using it to get the gradient at a point and to locate turning points, then deciding whether each is a maximum or a minimum. E2.13 Functions [Extended only] Function notation, domain and range, finding the inverse function f⁻¹(x) and forming composite functions such as gf(x).
E3 · Coordinate geometry
E4 · Geometry
E4.1 Geometrical terms The vocabulary of shapes: points, lines, planes, bearings, types of angle, similar and congruent, plus the names and parts of triangles, quadrilaterals, polygons, solids, nets and circles. E4.2 Geometrical constructions Measuring and drawing lines and angles, constructing a triangle from three sides with compasses (leaving the arcs showing), and drawing and using nets. E4.3 Scale drawings Drawing and reading scale drawings, and using three-figure bearings measured clockwise from north. E4.4 Similarity Finding missing lengths in similar shapes, using the area and volume scale factors (k² and k³), and explaining why two triangles are similar. E4.5 Symmetry Line symmetry and order of rotational symmetry in 2D, and symmetry properties (planes and axes) of prisms, cylinders, pyramids and cones. E4.6 Angles Calculating unknown angles with reasons: angles at a point and on a line, vertically opposite, triangle and quadrilateral sums, parallel line rules, and interior and exterior angles of polygons. E4.7 Circle theorems I The angle theorems for circles — angle in a semicircle, tangent meets radius at 90°, angle at the centre is double, same segment, cyclic quadrilateral, and the alternate segment theorem. E4.8 Circle theorems II [Extended only] The symmetry theorems for circles — equal chords are the same distance from the centre, the perpendicular bisector of a chord goes through the centre, and tangents from a point are equal.
E5 · Mensuration
E5.1 Units of measure Using metric units of mass, length, area, volume and capacity and converting between them, including tricky ones like cm² to m² and m³ to litres. E5.2 Area and perimeter Perimeter and area of rectangles, triangles, parallelograms and trapeziums — only the triangle formula is given, the rest must be known. E5.3 Circles, arcs and sectors Circumference and area of a circle, and arc length and sector area as a fraction of the whole circle. Answers may be left in terms of π. E5.4 Surface area and volume Surface area and volume of cuboids, prisms, cylinders, spheres, pyramids and cones, using the formulas given on the formula page. E5.5 Compound shapes and parts of shapes Areas, perimeters, surface areas and volumes of shapes and solids made by joining pieces together or cutting them apart, such as a frustum.
E6 · Trigonometry
E6.1 Pythagoras’ theorem Using a² + b² = c² to find a missing side of a right-angled triangle. E6.2 Right-angled triangles Using sine, cosine and tangent to find sides and angles in right-angled triangles, including angles of elevation and depression and shortest-distance problems. E6.3 Exact trigonometric values [Extended only] Knowing by heart the exact values of sin and cos for 0°, 30°, 45°, 60° and 90°, and tan for 0°, 30°, 45° and 60°. E6.4 Trigonometric functions [Extended only] Recognising and sketching the sine, cosine and tangent graphs from 0° to 360°, and using them to find all the solutions of an equation such as 2 cos x + 1 = 0. E6.5 Non-right-angled triangles [Extended only] Using the sine rule, the cosine rule and area = ½ ab sin C in any triangle, including obtuse angles and the ambiguous case. E6.6 Pythagoras’ theorem and trigonometry in 3D [Extended only] Applying Pythagoras and trigonometry inside solids, such as finding a diagonal of a cuboid or the angle between a line and a plane.
E7 · Transformations and vectors
E8 · Probability
E8.1 Introduction to probability The 0-to-1 probability scale, probability notation, working out the chance of a single event, and using P(A′) = 1 − P(A). E8.2 Relative and expected frequencies Using experimental results as an estimate of probability, calculating how many times you would expect an outcome, and understanding fair, biased and random. E8.3 Probability of combined events Finding probabilities for two or more events using sample space diagrams, Venn diagrams and tree diagrams, with and without replacement. E8.4 Conditional probability [Extended only] Finding the probability of one event given that another has already happened, using Venn diagrams, tree diagrams and tables. The P(A|B) formula is not needed.
E9 · Statistics
E9.1 Classifying statistical data Sorting data into tally tables and two-way tables. E9.2 Interpreting statistical data Reading tables and statistical diagrams, comparing two data sets using averages and spread, and knowing the limits of what the data can tell you. E9.3 Averages and measures of spread Mean, median, mode, quartiles, range and interquartile range, plus estimating the mean of grouped data and identifying the modal class. E9.4 Statistical charts and diagrams Drawing and reading bar charts (including stacked and dual), pie charts, pictograms, stem-and-leaf diagrams with a key, and simple frequency distributions. E9.5 Scatter diagrams Plotting scatter diagrams, describing positive, negative or zero correlation, and drawing and using a line of best fit by eye. E9.6 Cumulative frequency diagrams [Extended only] Building cumulative frequency tables, plotting the smooth curve, and reading off the median, quartiles, percentiles and interquartile range. E9.7 Histograms [Extended only] Drawing and interpreting histograms with unequal class widths, using frequency density = frequency ÷ class width.