IGCSE Mathematics 0580 — Complete Syllabus

Identify and use natural numbers, integers, prime numbers, square numbers, cube numbers, common factors, common multiples, rational and irrational numbers, and reciprocals.

Understand and use set language, notation, and Venn diagrams to describe sets, including relationships between sets.

Calculate with squares, square roots, cubes, cube roots, and other powers and roots of numbers.

Recognise equivalence and convert between proper fractions, improper fractions, mixed numbers, decimals, and percentages.

Order quantities by magnitude and demonstrate familiarity with inequality symbols.

Use the four operations for calculations with integers, fractions, and decimals, including order of operations and brackets.

Understand and use indices (positive, zero, and negative integers) and the rules of indices.

Use, convert to and from, and calculate with numbers in standard form (A x 10^n).

Round values to a specified degree of accuracy, make estimates for calculations, and round answers to a reasonable degree of accuracy.

Give upper and lower bounds for data rounded to a specified accuracy.

Understand and use ratio and proportion, including dividing a quantity in a given ratio and using proportional reasoning.

Use common measures of rate, apply other measures of rate, and solve problems involving average speed.

Calculate percentages of quantities, percentage increase/decrease, and work with simple and compound interest.

Use a calculator efficiently, enter values appropriately, and interpret the calculator display correctly.

Calculate with time units, use the 24-hour and 12-hour clock, and read clocks and timetables.

Calculate with money and convert between currencies.

Use exponential growth and decay models for situations like depreciation and population change.

Understand and use surds, including simplifying expressions and rationalising the denominator.

Understand that letters can represent generalised numbers and substitute numbers into expressions and formulas.

Simplify expressions by collecting like terms, expand products of algebraic expressions, and factorise by extracting common factors.

Manipulate and simplify algebraic fractions.

Understand and use indices (positive, zero, negative, and fractional) and the rules of indices.

Solve linear, simultaneous linear, and quadratic equations, and change the subject of formulas.

Represent and interpret inequalities, including on a number line, and solve linear inequalities.

Continue sequences, recognise patterns, and find and use the nth term of linear, quadratic, and cubic sequences.

Express direct and inverse proportion in algebraic terms and use this form to find unknown quantities.

Use and interpret graphs in practical situations, including travel and conversion graphs, and understand rate of change.

Construct tables of values, draw, recognise and interpret graphs for various functions, and solve associated equations graphically.

Recognise, sketch and interpret graphs of linear, quadratic, cubic, reciprocal, and exponential functions.

Estimate gradients of curves, use derivatives of functions, and apply differentiation to gradients and stationary points.

Understand functions, domain and range, and find inverse and composite functions.

Use and interpret Cartesian coordinates in two dimensions.

Draw straight-line graphs for linear equations.

Find the gradient of a straight line, including from the coordinates of two points.

Calculate the length of a line segment and find the coordinates of its midpoint.

Interpret and obtain the equation of a straight-line graph in various forms.

Find the gradient and equation of a straight line parallel to a given line.

Find the gradient and equation of a straight line perpendicular to a given line.

Use and interpret geometrical terms, including vocabulary for triangles, quadrilaterals, polygons, circles, and simple solids.

Measure and draw lines and angles, construct triangles, and draw and interpret nets.

Draw and interpret scale drawings and use and interpret three-figure bearings.

Calculate lengths of similar shapes and use relationships between lengths, areas, and volumes of similar shapes and solids.

Recognise line symmetry and order of rotational symmetry in two dimensions and properties of polygons related to symmetry.

Calculate unknown angles using properties of angles at a point, on a straight line, vertically opposite angles, triangles, quadrilaterals, and parallel lines.

Calculate unknown angles using geometrical properties of circles, including angles in a semicircle, and the angle between a tangent and a radius.

Use symmetry properties of circles, including equal chords, perpendicular bisectors of chords, and tangents from an external point.

Use metric units of mass, length, area, volume, and capacity, and convert between units.

Carry out calculations involving the perimeter and area of rectangles, triangles, parallelograms, and trapeziums.

Calculate circumference, area of circles, arc length, and sector area.

Calculate surface area and volume of cuboids, prisms, cylinders, spheres, pyramids, and cones.

Calculate perimeters, areas, surface areas, and volumes of compound shapes and parts of solids.

Know and use Pythagoras' theorem to find lengths in right-angled triangles.

Use sine, cosine, and tangent ratios for acute angles in right-angled triangles and solve 2D problems.

Know the exact values of sin x, cos x, and tan x for specific angles (0°, 30°, 45°, 60°, 90°).

Recognise, sketch, and interpret graphs of y = sin x, y = cos x, and y = tan x, and solve trigonometric equations.

Use the sine and cosine rules and the area formula (1/2 ab sin C) for any triangle, including obtuse angles and the ambiguous case.

Solve problems in three dimensions using Pythagoras' theorem and trigonometry, including the angle between a line and a plane.

Recognise, describe, and draw transformations including reflection, rotation, enlargement, and translation.

Describe translations using vectors, and add, subtract, and multiply vectors by scalars.

Calculate the magnitude of a vector.

Use vectors to represent directed line segments, position vectors, and solve geometric problems.

Understand and use the probability scale, calculate the probability of a single event, and understand complementary events.

Understand relative frequency as an estimate of probability and calculate expected frequencies.

Calculate the probability of combined events using sample space diagrams, Venn diagrams, and tree diagrams, including with replacement.

Calculate conditional probability using Venn diagrams, tree diagrams, and tables.

Classify and tabulate statistical data using methods like tally tables and two-way tables.

Read, interpret, and draw inferences from tables and statistical diagrams, and compare sets of data.

Calculate and distinguish between mean, median, mode, quartiles, range, and interquartile range for individual and grouped data.

Draw and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, and simple frequency distributions.

Draw and interpret scatter diagrams, understand correlation, and draw and use a line of best fit.

Draw and interpret cumulative frequency diagrams to estimate median, quartiles, and interquartile range.

Draw and interpret histograms, and calculate with frequency density.