Northern Ireland · CCEASyllabus
Maths syllabus, dot point by dot point
Every dot point in the Northern Ireland Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Algebra
Module overview →- How do you simplify, expand, factorise and rearrange algebraic expressions?Collect like terms, substitute into expressions and formulae, expand single and double brackets, factorise into single brackets and quadratics, simplify algebraic fractions and change the subject of a formula.11 min answer →
- How do you recognise, plot and interpret quadratic, cubic, reciprocal and other graphs?Plot and recognise quadratic, cubic, reciprocal and exponential graphs, read roots and turning points, use graphs to solve equations, and recognise the equation of a circle and real-life graphs (Higher tier for non-linear).11 min answer →
- How do you solve linear equations and inequalities and represent the solutions?Solve linear equations including those with brackets, fractions and the unknown on both sides, form equations from contexts, and solve and represent linear inequalities on a number line.10 min answer →
- How do you solve quadratic equations by factorising, the formula and completing the square?Solve quadratic equations by factorising, by the quadratic formula and by completing the square, and form and solve quadratics from problems (Higher tier for formula and completing the square).11 min answer →
- How do you continue a sequence and find the nth term of linear and quadratic sequences?Continue sequences using a term-to-term rule, find and use the nth term of a linear sequence, recognise quadratic and special sequences, and find the nth term of a quadratic sequence (Higher tier).10 min answer →
- How do you solve two simultaneous equations by elimination, substitution and graphically?Solve a pair of linear simultaneous equations by elimination and substitution, solve a linear and a quadratic simultaneously, and interpret the solution as the intersection of two graphs (Higher tier for non-linear).11 min answer →
- How do you find and use the equation of a straight line, including gradient and intercept?Plot and recognise straight-line graphs, find the gradient and y-intercept, use , find the equation of a line through given points, and use parallel and perpendicular gradient conditions.11 min answer →
Geometry and Measures
Module overview →- How do angle rules at points, lines, triangles, parallel lines and polygons work?Use angle facts at a point, on a line and in triangles and quadrilaterals, apply the angle properties of parallel lines, and find interior and exterior angles of polygons.10 min answer →
- How do you find circle measurements and apply the circle theorems?Find the circumference and area of circles, the length of an arc and area of a sector, and apply the circle theorems about angles, tangents and cyclic quadrilaterals (theorems at Higher tier).11 min answer →
- How do you carry out ruler-and-compass constructions and find loci that satisfy a condition?Construct perpendicular bisectors, perpendiculars from a point and angle bisectors with ruler and compasses, and find loci and regions defined by distance conditions, including bearings.10 min answer →
- How do you find perimeter, area, surface area and volume of plane shapes and solids?Find the perimeter and area of triangles, quadrilaterals and compound shapes, the surface area and volume of prisms, cylinders, pyramids, cones and spheres, and convert between units of area and volume.11 min answer →
- How do Pythagoras' theorem and right-angled trigonometry find missing sides and angles?Use Pythagoras' theorem in two and three dimensions, use the sine, cosine and tangent ratios to find sides and angles in right-angled triangles, and use exact trigonometric values.11 min answer →
- How do the sine and cosine rules solve any triangle, and how is its area found using trigonometry?Use the sine rule and cosine rule to find sides and angles in any triangle, and use the formula for the area of a triangle as one half a b sine C (Higher tier).11 min answer →
- How do you describe and perform transformations, and use congruence and similarity?Perform and describe reflections, rotations, translations and enlargements (including negative and fractional scale factors), and use congruence and similarity, including area and volume scale factors (Higher tier).11 min answer →
- How do you use column vectors to add, subtract and scale, and prove geometric results?Use column vector notation, add and subtract vectors, multiply by a scalar, find the magnitude of a vector, and use vectors to prove geometric facts such as collinearity (Higher tier).11 min answer →
Number
Module overview →- How do you round, estimate, and find the upper and lower bounds of a rounded quantity?Round to decimal places and significant figures, estimate by rounding to one significant figure, and find and use upper and lower bounds, including in calculations with compound measures.10 min answer →
- How do you calculate with fractions, decimals and percentages and convert freely between them?Carry out the four operations with fractions, convert between fractions, decimals and percentages, find percentages of amounts, work with percentage change, reverse percentages, compound interest and depreciation.11 min answer →
- How do the laws of indices work, including negative and fractional powers, and how is standard form used?Use the laws of indices for positive, negative and fractional powers, evaluate powers and roots, and write numbers in standard form and calculate with them.10 min answer →
- How do place value, the four operations and the order of operations work with integers and decimals?Read, write and order integers and decimals, use the four operations with directed numbers and decimals, apply the order of operations (BIDMAS), and use factors, multiples, primes, the HCF and the LCM.10 min answer →
- How do you simplify and use ratio, share in a given ratio, and solve direct and inverse proportion problems?Simplify ratios, divide a quantity in a given ratio, use the unitary method, solve best-buy and scale problems, and work with direct and inverse proportion including compound measures.10 min answer →
- How do you simplify surds, calculate with them, and rationalise a denominator?Simplify surds, carry out the four operations with surds, expand brackets containing surds, and rationalise the denominator of a fraction (Higher tier).10 min answer →
Probability
Module overview →- How do you measure probability, use the probability scale, and handle mutually exclusive and combined events?Use the probability scale from 0 to 1, find probabilities of single events, use that probabilities sum to 1, apply the mutually exclusive addition rule, and list outcomes with sample space diagrams.10 min answer →
- How do you estimate probability from experiments and predict expected outcomes?Use relative frequency to estimate probability from experimental data, understand how estimates improve with more trials, identify bias, and calculate expected frequencies.10 min answer →
- How do you use tree diagrams to find probabilities of combined events, with and without replacement?Draw tree diagrams for two or more events, multiply along branches and add between branches, and handle independent events and conditional probability without replacement (Higher tier).11 min answer →
- How do you use Venn diagrams and set notation to find probabilities of combined events?Use Venn diagrams to organise data into sets, apply set notation for union, intersection and complement, and find probabilities from a Venn diagram (Higher tier).10 min answer →
Statistics
Module overview →- How do you find and compare the mean, median, mode and range, including from grouped data?Find the mean, median, mode and range of a data set, estimate the mean from grouped data, find the modal class, and use averages and range to compare two distributions.10 min answer →
- How do you collect data and represent it in tables, charts and diagrams?Understand the data-handling cycle, distinguish types of data and sampling, use frequency and two-way tables, and draw and interpret bar charts, pie charts, pictograms, frequency polygons and histograms.10 min answer →
- How do you use cumulative frequency curves and box plots to find and compare the median, quartiles and spread?Construct and read cumulative frequency curves, find the median and quartiles, calculate the interquartile range, and draw and compare box plots (Higher tier).11 min answer →
- How do you plot a scatter graph, describe correlation, and use a line of best fit?Plot scatter graphs, describe the type and strength of correlation, draw a line of best fit, use it to estimate values, and understand interpolation, extrapolation and the difference between correlation and causation.10 min answer →