IGCSE Maths syllabus checklist

CoreEvery candidate

• 1.1Identify and use natural numbers, integers (positive, zero and negative), prime numbers, square numbers, cube numbers, common factors, common multiples, rational and irrational numbers, and reciprocals.
• 1.1Use number types in context: convert between numbers and words, express a number as a product of its prime factors, and find the highest common factor and lowest common multiple of two numbers.
• 1.2Understand and use set language, notation and Venn diagrams limited to two sets, including n(A) for the number of elements, A′ for the complement, and union and intersection.
• 1.3Calculate with squares, square roots, cubes, cube roots and other powers and roots, recalling squares and roots up to 15² and cubes of 1, 2, 3, 4, 5 and 10.
• 1.5Order quantities by magnitude and use the symbols =, ≠, >, <, ⩾ and ⩽ correctly.
• 1.5Order exact values given in different forms — integers, fractions and decimals — by converting to a common form; ordering surds and powers extends this with Extended-only number types.

ExtendedExtended candidates only

• 1.2Extend set notation with the element symbols ∈ and ∉, the empty set ∅, and subset notation; use Venn diagrams with up to three sets.
• 1.3Evaluate fractional powers such as 16^(1/2) and 8^(1/3) and negative powers of whole numbers in exact form.

CoreEvery candidate

• 1.4Use the language and notation of proper fractions, improper fractions, mixed numbers, decimals and percentages, writing fractions in their simplest form.
• 1.4Recognise equivalence and convert between fractions, decimals and percentages.
• 1.6Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets, negative numbers, improper fractions and mixed numbers.
• 1.13Calculate a given percentage of a quantity, express one quantity as a percentage of another, and calculate percentage increase or decrease.
• 1.13Calculate with simple and compound interest (formulas are not given).
• 1.14Use a calculator efficiently: do not round values mid-calculation, enter times and money appropriately, and interpret displays (excluded from the non-calculator papers).
• 1.15Calculate with units of time, use the 12-hour and 24-hour clock, and read clocks and timetables, including time zones.
• 1.16Calculate with money and convert from one currency to another.

ExtendedExtended candidates only

• 1.4Use recurring decimal notation and convert between recurring decimals and fractions.
• 1.13Solve problems with repeated percentage change and reverse percentages, and apply percentages to deposits, discounts, profit and loss, earnings and percentages over 100%.
• 1.17Use exponential growth and decay, e.g. depreciation and population change (no e required).

CoreEvery candidate

• 1.11Understand and use ratio to give ratios in their simplest form, divide a quantity in a given ratio, and use proportional reasoning and ratios in context such as recipes, map scales and best value.
• 1.12Use common measures of rate, e.g. hourly rates of pay, exchange rates between currencies, flow rates and fuel consumption.
• 1.12Apply other measures of rate, e.g. pressure, density and population density, using formulas given in the question.
• 1.12Solve problems involving average speed, using speed = distance ÷ time.

ExtendedExtended candidates only

• E2.8Express direct and inverse proportion in algebraic terms, including linear, square, square root, cube and cube root proportion, and use the form to find unknown quantities. The symbol ∝ is required. (Extended)

CoreEvery candidate

• 1.7Understand and use indices with positive, zero and negative integer powers, and use the rules of indices.
• 1.8Use standard form A × 10ⁿ where n is a positive or negative integer and 1 ⩽ A < 10, and convert numbers into and out of standard form.
• 1.8Calculate with values in standard form (Core candidates are expected to calculate with standard form only on Paper 3).

ExtendedExtended candidates only

• 1.7Understand and use fractional indices, e.g. 16^(1/2) and 8^(1/3), alongside the index laws. (Extended)
• 1.18Understand and use surds, including simplifying expressions such as √20 = 2√5 and √200 − √32 = 6√2. (Extended)
• 1.18Rationalise the denominator of a fraction involving a surd. (Extended)

CoreEvery candidate

• 1.9Round values to a specified degree of accuracy, including decimal places and significant figures.
• 1.9Make estimates for calculations involving numbers, quantities and measurements, e.g. by rounding each number to 1 significant figure.
• 1.9Round answers to a reasonable degree of accuracy in the context of a given problem.
• 1.10Give upper and lower bounds for data rounded to a specified accuracy.

ExtendedExtended candidates only

• 1.10Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy, e.g. bounds of a perimeter, area or speed. (Extended)

CoreEvery candidate

• 2.1Use letters to generalise numbers, and substitute numbers into expressions and formulas.
• 2.2Collect like terms, and expand brackets: two brackets of the form (x ± a)(x ± b) at Core, three brackets with two variables at Extended.
• 2.2Factorise by taking out common factors, and factorise quadratic expressions including the difference of two squares.

ExtendedExtended candidates only

• 2.2Factorise expressions of the form ax² + bx + c and ax³ + bx² + cx, and complete the square for quadratic expressions. (Extended)
• 2.3Add, subtract, multiply and divide algebraic fractions, and simplify rational expressions by factorising and cancelling a common factor. (Extended)

CoreEvery candidate

• 2.5Construct expressions, equations and formulas, and solve linear equations, including those with brackets and fractions.
• 2.5Derive and solve simultaneous linear equations in two unknowns.
• 2.6Represent and solve linear inequalities in one variable, and show solutions on a number line.

ExtendedExtended candidates only

• 2.5Solve quadratic equations by factorising, completing the square and using the quadratic formula (given); solve one linear and one non-linear equation simultaneously; change the subject of formulas, including cases with powers, roots and two steps. (Extended)
• 2.6Represent and interpret inequalities in two variables graphically, listing the inequalities that define a region. (Extended)

CoreEvery candidate

• 2.7Continue a given sequence and describe its term-to-term rule, including patterns of shapes or objects.
• 2.7Find and use the nth term of a linear sequence and of simple quadratic and cubic sequences.
• 2.7Express a general term from a context — matchstick or dot patterns — and decide whether a value can be a term.

ExtendedExtended candidates only

• 2.7Find and use the nth term of exponential (geometric) patterns, and of sequences built from combinations of rules. (Extended)

CoreEvery candidate

• 2.9Interpret and use conversion graphs and travel (distance–time) graphs, with gradient as a rate of change.
• 2.10Draw and read graphs of linear functions, quadratic functions and the reciprocal function a⁄x from tables of values; Extended candidates also draw sums of powers and exponential graphs.
• 2.10Use graphs to solve equations, including finding roots and intersections with drawn lines.

ExtendedExtended candidates only

• 2.9Work with speed–time graphs, including acceleration and deceleration as gradients, and distance as the area under the graph (linear sections only). (Extended)
• 2.11Sketch and interpret linear and quadratic graphs (roots and symmetry), and — at Extended — cubic, reciprocal and exponential graphs, with turning points and asymptotes.

ExtendedExtended candidates only

• 2.13Use function notation, and determine the domain and range of a function. (Extended)
• 2.13Find the inverse of a one-one function and form composite functions such as gf(x) = g(f(x)). (Extended)
• 2.12Differentiate sums of multiples of powers of x, and use the dy⁄dx notation. (Extended)
• 2.12Find the gradient of a curve at a point, and the equation of a tangent at that point. (Extended)
• 2.12Find and classify stationary points as maxima or minima, using a sketch, the second derivative or the gradient either side. (Extended)

CoreEvery candidate

• 3.1Use Cartesian coordinates in two dimensions to describe and locate points.
• 3.2Draw and interpret straight-line graphs of the form y = mx + c, and read gradients from a grid; rearrange equations like ax + by = c to find the gradient. (Extended for two-point gradients and ax + by = c)
• 3.5Find the equation of a straight line from its gradient and a point on it, in the form y = mx + c.
• 3.6Find the gradient and equation of parallel lines.

ExtendedExtended candidates only

• 3.4Calculate the length and the coordinates of the midpoint of a line segment. (Extended)
• 3.7Use perpendicular gradients (products of −1) and find the equation of a perpendicular bisector. (Extended)

CoreEvery candidate

• 4.6Use angle properties: angles at a point (360°), angles on a straight line (180°), vertically opposite angles, angles of triangles and quadrilaterals.
• 4.6Use angle properties of parallel lines — corresponding, alternate and co-interior — giving reasons.
• 4.6Use interior and exterior angles of regular polygons, including the sums 180(n − 2) and 360.
• 4.5Recognise line and rotational symmetry in 2-D shapes.
• 4.3Interpret scale drawings and use three-figure bearings measured clockwise from north.

ExtendedExtended candidates only

• 4.4Use similarity: calculate unknown lengths in similar shapes, and — at Extended — areas (× length²) and volumes (× length³).

CoreEvery candidate

• 4.7Use the angle in a semicircle (90°) and the perpendicularity of a tangent and the radius at the point of contact.

ExtendedExtended candidates only

• 4.7Use the angle at the centre (twice the angle at the circumference on the same arc) and angles in the same segment. (Extended)
• 4.7Use opposite angles of a cyclic quadrilateral summing to 180° and the alternate segment theorem. (Extended)
• 4.8Use properties of chords: the perpendicular from the centre bisects a chord, and equal chords are equidistant from the centre. (Extended)
• 4.8Use equal tangents from an external point and the isosceles triangles formed by radii. (Extended)

CoreEvery candidate

• 7.1Reflect in horizontal and vertical lines, rotate about the origin through multiples of 90°, translate by a vector, and enlarge from a centre with positive and fractional scale factors.

ExtendedExtended candidates only

• 7.1Reflect in any straight line, enlarge with negative scale factors, and describe combined transformations. (Extended)
• 7.2Use column-vector notation, adding and subtracting vectors and multiplying by scalars. (Extended)
• 7.3Calculate the magnitude of a vector as √(x² + y²). (Extended)
• 7.4Use directed line segments and position vectors, express vectors in terms of two others, and prove lines parallel or collinear. (Extended)

CoreEvery candidate

• 5.1Use metric units of length (mm, cm, m, km), mass (g, kg, tonne), time, area (mm² to km²), volume (mm³ to m³) and capacity (ml, litres); convert between them, including area units such as cm² ↔ m² and volume ↔ capacity such as m³ ↔ litres.
• 5.2Carry out calculations of perimeter and area of rectangles, triangles, parallelograms and trapeziums (only the triangle area formula is given on the formula sheet).
• 5.3Calculate the circumference and area of a circle; calculate arc length and sector area as fractions of the circle (Core: sector angles that are factors of 360°).
• 5.4Carry out calculations of the surface area and volume of cuboids, prisms and cylinders.
• 5.5Carry out calculations of perimeter and area of compound shapes, and volume and surface area of compound solids. (Extended for parts of solids such as hemispheres and frustums.)

ExtendedExtended candidates only

• 5.3Calculate arc length and sector area for any angle, and distinguish minor and major sectors; give answers in terms of π where asked. (Extended)
• 5.4Carry out calculations of the surface area and volume of spheres, pyramids and right circular cones, including curved surface areas. (Extended)

CoreEvery candidate

• 6.1Know and use Pythagoras’ theorem in right-angled triangles.
• 6.2Use sine, cosine and tangent in right-angled triangles to find sides and angles, and solve 2-D problems; give angles to 1 decimal place.

ExtendedExtended candidates only

• 6.2Use trigonometry for the shortest distance from a point to a line, and for angles of elevation and depression. (Extended)
• 6.3Know the exact values of sin and cos at 0°, 30°, 45°, 60° and 90°, and of tan at 0°, 30°, 45° and 60°. (Extended)
• 6.4Sketch y = sin x, y = cos x and y = tan x for 0° ⩽ x ⩽ 360°, and solve simple trigonometric equations in that interval. (Extended)
• 6.5Use the sine and cosine rules (formulas given) in non-right-angled triangles, including obtuse cases, and use area = ½ab sin C. (Extended)
• 6.6Use Pythagoras’ theorem and trigonometry in 3-D, including the angle between a line and a plane. (Extended)

CoreEvery candidate

• 8.1Place events on the probability scale from 0 (impossible) to 1 (certain); calculate the probability of a single event as a fraction, decimal or percentage; use P(not A) = 1 − P(A); read probabilities from tables, graphs and two-set Venn diagrams.
• 8.2Use relative frequency as an estimate of probability and calculate expected frequency; use the language of fair, biased and random.
• 8.3List outcomes with sample space diagrams and Venn diagrams; calculate probabilities of two combined events using tree diagrams with replacement.

ExtendedExtended candidates only

• 8.1Use P(A) and P(A′) notation and interpret Venn diagrams with more than two sets. (Extended)
• 8.3Use tree diagrams with and without replacement, and combine events with and-and-or structure, multiplying along branches and adding between them. (Extended)
• 8.4Work out conditional probabilities from Venn diagrams, tree diagrams and two-way tables. (Extended)

CoreEvery candidate

• 9.1Collect, classify and tabulate statistical data, including tally charts and two-way tables.
• 9.2Read, interpret and compare sets of data from tables and diagrams, recognising the limitations of conclusions. (Extended also compares measures of spread.)
• 9.3Calculate the mean, median, mode and range of ungrouped data, and the mean, median and mode from an ungrouped frequency table.
• 9.4Draw and interpret bar charts (composite and dual), pie charts, pictograms, stem-and-leaf diagrams (ordered, with a key) and simple frequency distributions.
• 9.5Draw and interpret scatter diagrams; describe positive, negative or zero correlation; draw and use a line of best fit by eye across the whole data set.

ExtendedExtended candidates only

• 9.3Calculate an estimate of the mean of grouped data using class midpoints, and identify the modal class; use quartiles and the interquartile range. (Extended)
• 9.6Draw and interpret cumulative frequency diagrams, reading estimates of the median, quartiles, interquartile range and percentiles from the curve. (Extended)
• 9.7Draw and interpret histograms, including those with unequal class intervals using frequency density. (Extended)