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Year 10: Cambridge IGCSE Mathematics 0580

Listed Mathematics subject content statements at Extended, in the words of the Cambridge Assessment International Education, with the practice on this site that covers it. Checked against the source on 3 September 2026.

Extended subject content, which contains all of the Core content. The subject content is unchanged in the 2028-2030 version of the syllabus.

  • 72subject content statements
  • 135skills mapped
  • 97%have practice

Coverage is the percentage of listed subject content statements with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one subject content statement, so some appear more than once below.

Number

  1. E1.1Types of numberIdentify and use: • natural numbers • integers (positive, zero and negative) • prime numbers • square numbers • cube numbers • common factors • common multiples • rational and irrational numbers • reciprocals.

  2. E1.2SetsUnderstand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets.

  3. E1.3Powers and rootsCalculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers.

  4. E1.4Fractions, decimals and percentages1 Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages. 2 Recognise equivalence and convert between these forms.

  5. E1.5OrderingOrder quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽.

  6. E1.6The four operationsUse the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets.

  7. E1.7Indices I1 Understand and use indices (positive, zero, negative, and fractional). 2 Understand and use the rules of indices.

  8. E1.8Standard form1 Use the standard form A × 10ⁿ where n is a positive or negative integer and 1 ⩽ A < 10. 2 Convert numbers into and out of standard form. 3 Calculate with values in standard form.

  9. E1.9Estimation1 Round values to a specified degree of accuracy. 2 Make estimates for calculations involving numbers, quantities and measurements. 3 Round answers to a reasonable degree of accuracy in the context of a given problem.

  10. E1.10Limits of accuracy1 Give upper and lower bounds for data rounded to a specified accuracy. 2 Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy.

  11. E1.11Ratio and proportionUnderstand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context.

  12. E1.12Rates1 Use common measures of rate. 2 Apply other measures of rate. 3 Solve problems involving average speed.

  13. E1.13Percentages1 Calculate a given percentage of a quantity. 2 Express one quantity as a percentage of another. 3 Calculate percentage increase or decrease. 4 Calculate with simple and compound interest. 5 Calculate using reverse percentages.

  14. E1.14Using a calculator1 Use a calculator efficiently. 2 Enter values appropriately on a calculator. 3 Interpret the calculator display appropriately.

    No practice for this one yet.

  15. E1.15Time1 Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units. 2 Calculate times in terms of the 24-hour and 12-hour clock. 3 Read clocks and timetables.

  16. E1.16Money1 Calculate with money. 2 Convert from one currency to another.

  17. E1.17Exponential growth and decayUse exponential growth and decay.

  18. E1.18Surds1 Understand and use surds, including simplifying expressions. 2 Rationalise the denominator.

Algebra and graphs

  1. E2.1Introduction to algebra1 Know that letters can be used to represent generalised numbers. 2 Substitute numbers into expressions and formulas.

  2. E2.2Algebraic manipulation1 Simplify expressions by collecting like terms. 2 Expand products of algebraic expressions. 3 Factorise by extracting common factors. 4 Factorise expressions of the form: • ax + bx + kay + kby • a2 x2 − b2y2 • a2 + 2ab + b2 • ax2 + bx + c • ax3 + bx2 + cx. 5 Complete the square for expressions in the form ax2 + bx + c.

  3. E2.3Algebraic fractions1 Manipulate algebraic fractions. 2 Factorise and simplify rational expressions.

  4. E2.4Indices II1 Understand and use indices (positive, zero, negative and fractional). 2 Understand and use the rules of indices.

  5. E2.5Equations1 Construct expressions, equations and formulas. 2 Solve linear equations in one unknown. 3 Solve fractional equations with numerical and linear algebraic denominators. 4 Solve simultaneous linear equations in two unknowns. 5 Solve simultaneous equations, involving one linear and one non-linear. 6 Solve quadratic equations by factorisation, completing the square and by use of the quadratic formula. 7 Change the subject of formulas.

  6. E2.6Inequalities1 Represent and interpret inequalities, including on a number line. 2 Construct, solve and interpret linear inequalities. 3 Represent and interpret linear inequalities in two variables graphically. 4 List inequalities that define a given region.

  7. E2.7Sequences1 Continue a given number sequence or pattern. 2 Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences. 3 Find and use the nth term of sequences.

  8. E2.8ProportionExpress direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.

  9. E2.9Graphs in practical situations1 Use and interpret graphs in practical situations including travel graphs and conversion graphs. 2 Draw graphs from given data. 3 Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration. 4 Calculate distance travelled as area under a speed–time graph.

  10. E2.10Graphs of functions1 Construct tables of values, and draw, recognise and interpret graphs for functions of the following forms: • axⁿ (includes sums of no more than three of these) • abx + c where n = –2, –1, − 2 , 0, 2 , 1, 2, 3; a and c are 1 1 rational numbers; and b is a positive integer. 2 Solve associated equations graphically, including finding and interpreting roots by graphical methods. 3 Draw and interpret graphs representing exponential growth and decay problems.

  11. E2.11Sketching curvesRecognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic (c) cubic (d) reciprocal (e) exponential.

  12. E2.12Differentiation1 Estimate gradients of curves by drawing tangents. 2 Use the derivatives of functions of the form axⁿ, where a is a rational constant and n is a positive integer or zero, and simple sums of not more than three of these. 3 Apply differentiation to gradients and stationary points (turning points). 4 Discriminate between maxima and minima by any method.

  13. E2.13Functions1 Understand functions, domain and range and use function notation. 2 Understand and find inverse functions f⁻¹(x). 3 Form composite functions as defined by gf(x) = g(f(x)).

Coordinate geometry

  1. E3.1CoordinatesUse and interpret Cartesian coordinates in two dimensions.

  2. E3.2Drawing linear graphsDraw straight-line graphs for linear equations.

  3. E3.3Gradient of linear graphs1 Find the gradient of a straight line. 2 Calculate the gradient of a straight line from the coordinates of two points on it.

  4. E3.4Length and midpoint1 Calculate the length of a line segment. 2 Find the coordinates of the midpoint of a line segment.

  5. E3.5Equations of linear graphsInterpret and obtain the equation of a straight-line graph.

  6. E3.6Parallel linesFind the gradient and equation of a straight line parallel to a given line.

  7. E3.7Perpendicular linesFind the gradient and equation of a straight line perpendicular to a given line.

Geometry

  1. E4.1Geometrical terms1 Use and interpret the following geometrical terms: • point • vertex • line • plane • parallel • perpendicular • perpendicular bisector • bearing • right angle • acute, obtuse and reflex angles • interior and exterior angles • similar • congruent • scale factor. 2 Use and interpret the vocabulary of: • triangles • special quadrilaterals • polygons • nets • solids. 3 Use and interpret the vocabulary of a circle.

  2. E4.2Geometrical constructions1 Measure and draw lines and angles. 2 Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only. 3 Draw, use and interpret nets.

    No practice for this one yet.

  3. E4.3Scale drawings1 Draw and interpret scale drawings. 2 Use and interpret three-figure bearings.

  4. E4.4Similarity1 Calculate lengths of similar shapes. 2 Use the relationships between lengths and areas of similar shapes and lengths, surface areas and volumes of similar solids. 3 Solve problems and give simple explanations involving similarity.

  5. E4.5Symmetry1 Recognise line symmetry and order of rotational symmetry in two dimensions. 2 Recognise symmetry properties of prisms, cylinders, pyramids and cones.

  6. E4.6Angles1 Calculate unknown angles and give simple explanations using the following geometrical properties: • sum of angles at a point = 360° • sum of angles at a point on a straight line = 180° • vertically opposite angles are equal • angle sum of a triangle = 180° and angle sum of a quadrilateral = 360°. 2 Calculate unknown angles and give geometric explanations for angles formed within parallel lines: • corresponding angles are equal • alternate angles are equal • co-interior angles sum to 180° (supplementary). 3 Know and use angle properties of regular and irregular polygons.

  7. E4.7Circle theorems ICalculate unknown angles and give explanations using the following geometrical properties of circles: • angle in a semicircle = 90° • angle between tangent and radius = 90° • angle at the centre is twice the angle at the circumference • angles in the same segment are equal • opposite angles of a cyclic quadrilateral sum to 180° (supplementary) • alternate segment theorem.

  8. E4.8Circle theorems IIUse the following symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the centre • tangents from an external point are equal in length.

Mensuration

  1. E5.1Units of measureUse metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units.

  2. E5.2Area and perimeterCarry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium.

  3. E5.3Circles, arcs and sectors1 Carry out calculations involving the circumference and area of a circle. 2 Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle.

  4. E5.4Surface area and volumeCarry out calculations and solve problems involving the surface area and volume of a: • cuboid • prism • cylinder • sphere • pyramid • cone.

  5. E5.5Compound shapes and parts of shapes1 Carry out calculations and solve problems involving perimeters and areas of: • compound shapes • parts of shapes. 2 Carry out calculations and solve problems involving surface areas and volumes of: • compound solids • parts of solids.

Trigonometry

  1. E6.1Pythagoras' theoremKnow and use Pythagoras' theorem.

  2. E6.2Right-angled triangles1 Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. 2 Solve problems in two dimensions using Pythagoras' theorem and trigonometry. 3 Know that the perpendicular distance from a point to a line is the shortest distance to the line. 4 Carry out calculations involving angles of elevation and depression.

  3. E6.3Exact trigonometric valuesKnow the exact values of: 1 sin x and cos x for x = 0°, 30°, 45°, 60° and 90°. 2 tan x for x = 0°, 30°, 45° and 60°.

  4. E6.4Trigonometric functions1 Recognise, sketch and interpret the following graphs for 0° ⩽ x ⩽ 360°: • y = sin x • y = cos x • y = tan x. 2 Solve trigonometric equations involving sin x, cos x or tan x, for 0° ⩽ x ⩽ 360°.

  5. E6.5Non-right-angled triangles1 Use the sine and cosine rules in calculations involving lengths and angles for any triangle. 2 Use the formula area of triangle = ½ ab sin C.

  6. E6.6Pythagoras' theorem and trigonometry in 3DCarry out calculations and solve problems in three dimensions using Pythagoras' theorem and trigonometry, including calculating the angle between a line and a plane.

Transformations and vectors

  1. E7.1TransformationsRecognise, describe and draw the following transformations: 1 Reflection of a shape in a straight line. 2 Rotation of a shape about a centre through multiples of 90°. 3 Enlargement of a shape from a centre by a scale factor. JN x 4 Translation of a shape by a vector KK OO . y LP

  2. E7.2Vectors in two dimensions1 Describe a translation using a vector represented by a column vector, AB or a. 2 Add and subtract vectors. 3 Multiply a vector by a scalar.

  3. E7.3Magnitude of a vectorCalculate the magnitude of a column vector as the square root of x squared plus y squared.

  4. E7.4Vector geometry1 Represent vectors by directed line segments. 2 Use position vectors. 3 Use the sum and difference of two or more vectors to express given vectors in terms of two coplanar vectors. 4 Use vectors to reason and to solve geometric problems.

Probability

  1. E8.1Introduction to probability1 Understand and use the probability scale from 0 to 1. 2 Understand and use probability notation. 3 Calculate the probability of a single event. 4 Understand that the probability of an event not occurring = 1 – the probability of the event occurring.

  2. E8.2Relative and expected frequencies1 Understand relative frequency as an estimate of probability. 2 Calculate expected frequencies.

  3. E8.3Probability of combined eventsCalculate the probability of combined events using, where appropriate: • sample space diagrams • Venn diagrams • tree diagrams.

  4. E8.4Conditional probabilityCalculate conditional probability using Venn diagrams, tree diagrams and tables.

Statistics

  1. E9.1Classifying statistical dataClassify and tabulate statistical data.

  2. E9.2Interpreting statistical data1 Read, interpret and draw inferences from tables and statistical diagrams. 2 Compare sets of data using tables, graphs and statistical measures. 3 Appreciate restrictions on drawing conclusions from given data.

  3. E9.3Averages and measures of spread1 Calculate the mean, median, mode, quartiles, range and interquartile range for individual data and distinguish between the purposes for which these are used. 2 Calculate an estimate of the mean for grouped discrete or grouped continuous data. 3 Identify the modal class from a grouped frequency distribution.

  4. E9.4Statistical charts and diagramsDraw and interpret: (a) bar charts (b) pie charts (c) pictograms (d) stem-and-leaf diagrams (e) simple frequency distributions.

  5. E9.5Scatter diagrams1 Draw and interpret scatter diagrams. 2 Understand what is meant by positive, negative and zero correlation. 3 Draw by eye, interpret and use a straight line of best fit.

  6. E9.6Cumulative frequency diagrams1 Draw and interpret cumulative frequency tables and diagrams. 2 Estimate and interpret the median, percentiles, quartiles and interquartile range from cumulative frequency diagrams.

  7. E9.7Histograms1 Draw and interpret histograms. 2 Calculate with frequency density.

Other Year 10 skills

Year 10 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.

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