Wales Β· WJECSyllabus
Maths syllabus, dot point by dot point
Every dot point in the Wales 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 β- How do you simplify expressions, expand brackets, factorise, substitute and rearrange formulae?Simplify expressions by collecting like terms, expand single and double brackets, factorise into brackets, substitute into expressions and formulae, and change the subject of a formula.12 min answer β
- How do you solve linear inequalities, show solutions on a number line, and list integer solutions?Solve linear inequalities in one variable, represent solutions on a number line and as integer lists, and solve double inequalities, including reversing the sign when dividing by a negative.11 min answer β
- How do you solve a quadratic equation by factorising, by the formula or by completing the square, and sketch its graph?Factorise and solve quadratic equations by factorisation, the quadratic formula and completing the square, and plot and interpret quadratic graphs and their roots and turning points (Higher tier).12 min answer β
- How do you continue a sequence, find the nth term of a linear sequence, and recognise special sequences?Continue and describe sequences, find the nth term of a linear (arithmetic) sequence, and recognise quadratic, geometric, Fibonacci and other special sequences.11 min answer β
- How do you solve a pair of simultaneous linear equations by elimination, substitution or graphically?Solve simultaneous linear equations in two unknowns by elimination and by substitution, solve them graphically, and form simultaneous equations from worded contexts.11 min answer β
- How do you solve linear equations, including ones with brackets, fractions and the unknown on both sides?Solve linear equations with one unknown, including those with brackets, fractions and the unknown on both sides, and form equations from worded contexts.11 min answer β
- How do you plot and interpret a straight line graph, find its gradient and intercept, and use y = mx + c?Plot and interpret straight line graphs, find the gradient and y-intercept, write the equation y = mx + c, and find equations of parallel and perpendicular lines (Higher tier).12 min answer β
Geometry and measures
Module overview β- How do you find unknown angles using angle facts, parallel line rules and the interior and exterior angles of polygons?Use angle facts at a point and on a line, in triangles and quadrilaterals, the corresponding, alternate and co-interior angles in parallel lines, and the interior and exterior angle properties of polygons, giving reasons.11 min answer β
- How do you find the perimeter, area, surface area and volume of 2-D shapes and 3-D solids, including circles, prisms, cylinders, cones and spheres?Calculate perimeter and area of 2-D shapes including circles, sectors and compound shapes, and the surface area and volume of prisms, cylinders, pyramids, cones and spheres, with appropriate units.12 min answer β
- What are the parts of a circle and the circle theorems, and how do you use them to find angles and write reasoned proofs?Recognise the parts of a circle, and know and use the circle theorems (angle at the centre, angle in a semicircle, angles in the same segment, cyclic quadrilateral, tangent properties and alternate segment) to find angles and construct reasoned proofs (Higher tier).12 min answer β
- How do you carry out ruler-and-compass constructions, draw loci and use bearings to solve geometric problems?Use ruler and compasses for standard constructions (perpendicular bisector, angle bisector, perpendicular from a point), draw loci of points satisfying given conditions, and use scale drawings and three-figure bearings.11 min answer β
- How do you use Pythagoras' theorem and trigonometry, including the sine and cosine rules, to find missing sides and angles in triangles?Use Pythagoras' theorem and the trigonometric ratios in right-angled triangles, and the sine rule, cosine rule and area formula in any triangle (Higher tier), to find missing lengths and angles.13 min answer β
- How do you recognise congruent and similar shapes, prove congruence and use scale factors for lengths, areas and volumes?Recognise and prove congruence (SSS, SAS, ASA, RHS) and similarity, use scale factors to find missing lengths in similar shapes, and apply area and volume scale factors (Higher tier).11 min answer β
- How do you describe and carry out translations, reflections, rotations and enlargements, and combine them?Carry out and describe the four transformations - translation, reflection, rotation and enlargement (including negative and fractional scale factors at Higher tier) - and identify the result of combined transformations.11 min answer β
- How do you use column vectors, add and subtract vectors, multiply by a scalar and use vectors in geometric proofs?Use column vector notation, add and subtract vectors and multiply by a scalar, and use vectors to find resultants and to prove that lines are parallel or points are collinear (Higher tier).12 min answer β
Number
Module overview β- How do you write a number as a product of its prime factors and use that to find the HCF and LCM?Identify factors, multiples and primes, write a number as a product of prime factors in index form, and use prime factorisation to find the highest common factor and lowest common multiple.11 min answer β
- How do you calculate with fractions, convert between fractions, decimals and percentages, and turn a recurring decimal into a fraction?Calculate with fractions and mixed numbers, convert freely between fractions, decimals and percentages, and convert a recurring decimal to an exact fraction (Higher tier).11 min answer β
- How do you use the laws of indices, including negative and fractional powers, and calculate with numbers in standard form?Apply the laws of indices including zero, negative and fractional powers (Higher tier), and write and calculate with numbers in standard form.11 min answer β
- How do you work out percentage change, reverse percentages, and simple and compound interest in real-life financial contexts?Calculate percentage increase and decrease, percentage change and reverse percentages, and solve financial problems involving simple interest, compound interest and repeated percentage change.12 min answer β
- How do you simplify and use ratios, share an amount in a ratio, and solve direct and inverse proportion problems?Use ratio notation, simplify ratios and share a quantity in a given ratio, and solve direct and inverse proportion problems including the unitary method.11 min answer β
- How do you round to decimal places and significant figures, estimate a calculation, and find the upper and lower bounds of a measurement?Round to decimal places and significant figures, estimate calculations by rounding to one significant figure, and find upper and lower bounds and use them in calculations (Higher tier).11 min answer β
- How do you order numbers and calculate accurately with integers, decimals and directed numbers using the correct order of operations?Understand place value, order integers, decimals and fractions, and calculate with the four operations and directed numbers using the correct order of operations (BIDMAS).11 min answer β
- How do you simplify surds, carry out the four operations 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).11 min answer β
Probability
Module overview β- How do you measure probability on the 0 to 1 scale, use sample spaces and handle mutually exclusive and combined events?Use the probability scale from 0 to 1, calculate probabilities of equally likely outcomes using sample spaces and listings, and apply the rules for mutually exclusive and exhaustive events including combined events in two-way tables.11 min answer β
- How do you estimate probability from experiments using relative frequency, and predict the expected number of outcomes?Estimate probability from experimental data using relative frequency, understand how it stabilises with more trials, compare experimental with theoretical probability, and calculate expected frequencies.11 min answer β
- How do you use a tree diagram to find the probability of combined events, with and without replacement?Draw and use probability tree diagrams for two or more events, multiplying along branches and adding across routes, including independent events and conditional events without replacement (Higher tier).12 min answer β
- How do you use Venn diagrams and set notation to organise events and calculate probabilities?Construct and interpret Venn diagrams for two or three sets, use set notation for union, intersection and complement, and calculate probabilities from a Venn diagram (Higher tier).11 min answer β
Statistics
Module overview β- How do you calculate and interpret the mean, median, mode and range, including from frequency and grouped frequency tables?Calculate and interpret the mean, median, mode and range for lists and frequency tables, estimate the mean and identify the modal class from grouped data, and compare distributions using an average and a measure of spread.12 min answer β
- How do you draw and read a cumulative frequency curve, find the quartiles and interquartile range, and use box plots to compare distributions?Construct and interpret a cumulative frequency curve to estimate the median, quartiles and interquartile range, and draw and compare box plots from five-number summaries (Higher tier).12 min answer β
- How do you choose a sample, design data collection and classify data so that conclusions are reliable?Understand populations and samples, use random and other sampling methods and recognise bias, design data collection including questionnaires, and classify data as qualitative or quantitative and discrete or continuous.11 min answer β
- How do you plot a scatter graph, describe correlation and use a line of best fit to make predictions?Plot and interpret scatter graphs, describe the type and strength of correlation, draw a line of best fit and use it to estimate values, and understand that correlation does not imply causation.11 min answer β
- How do you construct and interpret bar charts, pictograms, pie charts, frequency diagrams and histograms?Construct and interpret bar charts, pictograms, vertical line graphs, pie charts and frequency diagrams, and at Higher tier draw and interpret histograms using frequency density for unequal class widths.12 min answer β