England · AQASyllabus
Maths syllabus, dot point by dot point
Every dot point in the England 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 expand, factorise and simplify algebraic expressions?Collecting like terms, expanding single and double brackets, factorising into brackets, and simplifying algebraic fractions at Higher tier.9 min answer →
- How do you solve and represent linear and quadratic inequalities?Solving linear inequalities, representing solutions on a number line, solving quadratic inequalities at Higher tier, and graphing inequality regions.8 min answer →
- How do you recognise and sketch quadratic, cubic, reciprocal and exponential graphs?Recognising and sketching quadratic, cubic, reciprocal and exponential graphs, reading roots and turning points, and using function notation at Higher tier.9 min answer →
- How do you solve quadratic equations by factorising, the formula and completing the square?Solving quadratics by factorising, using the quadratic formula, completing the square at Higher tier, and interpreting the roots and turning point.10 min answer →
- How do you find the nth term of a sequence and recognise special sequences?Continuing sequences, finding the nth term of linear and quadratic sequences, and recognising geometric, triangular and Fibonacci sequences.9 min answer →
- How do you solve a pair of simultaneous equations by elimination and substitution?Solving linear simultaneous equations by elimination and substitution, and solving a linear and quadratic pair at Higher tier.9 min answer →
- How do you solve linear equations and rearrange formulae?Solving linear equations with the unknown on one or both sides, equations with brackets and fractions, and changing the subject of a formula.8 min answer →
- How do you find the gradient and equation of a straight line and use parallel and perpendicular rules?Plotting straight lines, finding gradient and intercept from the equation, writing equations of lines, and the conditions for parallel and perpendicular lines.9 min answer →
Geometry and measures
Module overview →- How do you use angle rules for lines, triangles and polygons?Angles on a line and around a point, angles in parallel lines, angles in triangles and quadrilaterals, and interior and exterior angles of polygons.9 min answer →
- How do you find the area of 2D shapes and the volume and surface area of solids?Areas of rectangles, triangles, parallelograms and trapezia, and the volume and surface area of prisms, cylinders, cones, spheres and pyramids.10 min answer →
- How do you find circumference, area, arc length and sector area, and use circle theorems?Circumference and area of a circle, arc length and sector area, and the circle theorems at Higher tier.9 min answer →
- How do you carry out standard constructions and find loci with a ruler and compasses?Constructing perpendicular and angle bisectors, perpendiculars from a point, and finding loci of points satisfying a given condition.8 min answer →
- How do you use Pythagoras theorem and trigonometry to find sides and angles?Using Pythagoras theorem, the sine, cosine and tangent ratios in right-angled triangles, and the sine and cosine rules at Higher tier.10 min answer →
- How do you describe and carry out reflections, rotations, translations and enlargements?Carrying out and describing reflections, rotations, translations and enlargements, including negative and fractional scale factors at Higher tier.9 min answer →
- How do you add, subtract and scale vectors and use them in geometry proofs?Writing and drawing column vectors, adding, subtracting and multiplying vectors by a scalar, and using vectors in geometric proofs at Higher tier.9 min answer →
Number
Module overview →- How do you find prime factors, highest common factors and lowest common multiples?Identifying factors, multiples and primes, writing a number as a product of prime factors, and finding the HCF and LCM.8 min answer →
- How do you calculate with fractions, decimals and percentages and convert freely between them?The four operations with fractions, converting between fractions, decimals and percentages, and finding percentages and percentage change of an amount.9 min answer →
- How do the laws of indices work and how do you simplify and rationalise surds?The laws of indices including negative and fractional powers, and simplifying, multiplying and rationalising surds at Higher tier.9 min answer →
- How do you read, order and calculate with place value, very large and very small numbers, and standard form?Place value, ordering integers and decimals, multiplying and dividing by powers of ten, and writing and calculating with numbers in standard form.9 min answer →
- How do you share quantities in a ratio and solve simple proportion problems?Writing and simplifying ratios, dividing a quantity in a given ratio, and solving direct proportion problems including the unitary method.8 min answer →
- How do you round numbers, estimate calculations and find upper and lower bounds?Rounding to decimal places and significant figures, estimating by rounding, and finding upper and lower bounds of rounded values at Higher tier.8 min answer →
Probability
Module overview →- How do you measure probability and combine the chances of events?The probability scale, equally likely outcomes, the fact that probabilities sum to one, and combining mutually exclusive and independent events.8 min answer →
- How do you estimate probability from experiments and predict expected outcomes?Estimating probability using relative frequency, the effect of more trials, comparing experimental and theoretical probability, and finding expected outcomes.8 min answer →
- How do you use tree diagrams and Venn diagrams to find combined probabilities?Drawing and using tree diagrams for combined events, conditional probability, and using Venn diagrams with set notation.9 min answer →
Ratio, proportion and rates of change
Module overview →- How do you recognise and solve direct and inverse proportion problems?Recognising direct and inverse proportion, setting up and using proportion equations with a constant, and interpreting their graphs.9 min answer →
- How do you work out percentage increase and decrease, reverse percentages and compound interest?Percentage increase and decrease using multipliers, reverse percentages, and simple and compound interest including depreciation.9 min answer →
- How do you read rates of change from graphs including distance-time and velocity-time graphs?Interpreting distance-time and velocity-time graphs, finding gradients as rates and areas as totals, and estimating gradients of curves at Higher tier.9 min answer →
- How do you use ratio with scale drawings, maps and combining ratios?Using ratio with scale factors, map scales and scale drawings, converting between ratio forms, and combining ratios that share a part.8 min answer →
Statistics
Module overview →- How do you calculate and compare averages and measures of spread?Finding the mean, median, mode and range, averages from frequency tables, and the median and interquartile range from grouped data at Higher tier.9 min answer →
- How do you draw and interpret statistical charts and graphs?Drawing and interpreting bar charts, pie charts, frequency tables, and cumulative frequency graphs, box plots and histograms at Higher tier.9 min answer →
- How do you collect reliable data and choose a fair sample?Types of data, populations and samples, random and stratified sampling, sources of bias, and designing good data collection.8 min answer →
- How do you use scatter graphs to describe correlation and make predictions?Plotting scatter graphs, describing correlation, drawing a line of best fit, using it to estimate values, and recognising the limits of extrapolation.8 min answer →