JC Mathematics

Use plans such as drawing diagrams, making tables and working backwards to solve unfamiliar problems.

Use algebra to show that a pattern is always true, and counterexamples to show when it is not.

Add, subtract, multiply and divide positive and negative whole numbers.

Use the correct order (brackets, indices, multiplication and division, addition and subtraction) to evaluate calculations.

Find factors, multiples, prime factors, the HCF and the LCM of numbers.

Simplify, compare, add, subtract, multiply and divide fractions and find fractions of amounts.

Calculate with decimals and convert between fractions, decimals and percentages.

Round to decimal places and significant figures, estimate answers and find percentage error.

Find percentages of amounts, percentage changes and reverse percentages.

Share in a given ratio, use scales and solve direct and inverse proportion problems.

Use the rules of indices, including zero, negative and fractional indices (HL), and square roots.

Write very large and very small numbers in the form a × 10^n and calculate with them.

Use set notation, Venn diagrams, union, intersection, complement and set difference.

Use the relationship between speed, distance and time, including unit conversions.

Calculate VAT, discounts, profit, loss, mark-up and margin.

Calculate gross tax, tax credits, net tax and net pay using standard and higher rates.

Calculate simple and compound interest and depreciation over a few years.

Convert between currencies and calculate household bills such as electricity and phone bills.

Simplify and operate on square-root surds and tell rational from irrational numbers.

Describe linear and quadratic patterns, and find and use the general term Tn.

Use letters for numbers, simplify expressions and evaluate them for given values.

Multiply out brackets, including two binomials and squares of binomials.

Factorise using common factors, grouping, quadratic trinomials and the difference of two squares.

Add, subtract and simplify algebraic fractions and solve equations that contain them.

Form and solve equations in one unknown, including brackets and unknowns on both sides.

Solve a pair of linear equations in two unknowns by elimination, substitution or graphs.

Solve quadratic equations by factorising and, at Higher Level, using the formula.

Solve linear inequalities and show their solutions on a number line.

Rearrange formulae to make a different letter the subject.

Understand a function as a rule linking inputs to outputs and use function notation f(x).

Draw and interpret graphs of linear functions, including slope and intercepts.

Draw and interpret graphs of quadratic functions, including roots and turning points.

Interpret graphs that describe real situations, such as journeys and costs.

Divide quadratic and cubic expressions by a linear expression when there is no remainder.

Name angle types and use angles on a line, at a point, vertically opposite angles and parallel-line angles.

Use angle sums and properties of triangles, quadrilaterals and polygons, including congruence.

Apply the Junior Cycle theorems and corollaries, including similar triangles, and write simple proofs.

Carry out the standard constructions with ruler, compass and protractor.

Find the perimeter and area of rectangles, triangles, parallelograms, trapeziums and composite shapes.

Find the circumference and area of circles, semicircles and sectors using π.

Find the volume and surface area of cuboids, prisms and cylinders.

Find slope, midpoint, distance and the equation of a line.

Translate, reflect, rotate and (HL) enlarge shapes, and describe symmetry.

Use a² + b² = c² to find missing sides and to test for right angles.

Use sin, cos and tan to find sides and angles in right-angled triangles.

Convert between metric units of length, mass, capacity, area and time, and work with timetables and durations.

Draw and interpret nets of solids and use scales to read and draw diagrams.

Classify data, choose samples, avoid bias and plan a statistical investigation.

Find and compare the mean, median, mode and range of data sets.

Draw and interpret bar charts, pie charts, line graphs, stem-and-leaf plots and histograms.

List outcomes and use the fundamental principle of counting.

Find probabilities of equally likely outcomes and use relative frequency to estimate probability.