MathsQ&A by dot point

Algebraic manipulation: simplifying expressions, expanding single and double brackets, factorising (common factors, quadratics and the difference of two squares), and rearranging (changing the subject of) formulae.

Solving linear and quadratic inequalities and representing solutions on number lines and graphs, and recognising and sketching the graphs of quadratic, cubic, reciprocal and exponential functions.

Solving quadratic equations by factorising, by the quadratic formula and by completing the square (Higher tier), and interpreting the roots and the turning point of the curve.

Sequences: generating terms, finding the nth term of a linear (arithmetic) sequence and a quadratic sequence (Higher tier), and recognising geometric, triangular, square, cube and Fibonacci sequences.

Solving simultaneous equations: two linear equations by elimination and by substitution, finding the solution graphically, and solving one linear and one quadratic equation (Higher tier).

Solving linear equations in one unknown, including equations with brackets, equations with the unknown on both sides, and equations involving fractions, and forming equations from worded contexts.

Straight line graphs: plotting lines, finding the gradient and y-intercept, using the equation y = mx + c, finding the equation of a line through two points, and parallel and perpendicular lines (Higher tier).

Angle facts: angles on a line and around a point, vertically opposite angles, angles in parallel lines (alternate, corresponding and co-interior), angles in triangles and quadrilaterals, and the interior and exterior angles of polygons.

Area of triangles, parallelograms and trapeziums; circumference and area of circles; volume and surface area of prisms and cylinders; and the volume and surface area of cones, spheres and pyramids (Higher tier).

Parts of a circle, arc length and sector area, and the circle theorems including the angle at the centre, angles in a semicircle, angles in the same segment, cyclic quadrilaterals, the tangent-radius angle and the alternate segment theorem (Higher tier).

Standard constructions with ruler and compasses (perpendicular bisector of a line, perpendicular from a point, angle bisector), constructing triangles, and finding loci and regions satisfying given conditions.

Pythagoras' theorem in right-angled triangles, the trigonometric ratios sine, cosine and tangent, exact trig values, and the sine rule, cosine rule and area formula for any triangle (Higher tier).

The four transformations: translation by a vector, reflection in a line, rotation about a point, and enlargement by a scale factor including fractional and negative scale factors (Higher tier), and describing a single transformation fully.

Vectors: column vectors, adding, subtracting and multiplying vectors by a scalar, the magnitude of a vector, and using vectors in geometric proofs including parallel lines and points lying on a straight line (Higher tier).

Factors, multiples and primes: prime factor decomposition (product of prime factors), the highest common factor (HCF) and lowest common multiple (LCM), and using Venn diagrams to find them.

Calculating with fractions (the four operations, including mixed numbers), converting between fractions, decimals and percentages including recurring decimals, and working with percentages of amounts.

Rounding to decimal places and significant figures, estimating calculations using rounding, and finding the upper and lower bounds of measurements, including error intervals and bounds in calculations (Higher tier).

The laws of indices including zero, negative and fractional powers, and standard form: writing very large and very small numbers and calculating with them.

The structure of the number system: ordering integers and decimals, the four operations with positive and negative numbers, place value, the priority of operations (BIDMAS), and inverse operations.

Surds: simplifying surds, the four operations with surds, expanding brackets containing surds, and rationalising the denominator (Higher tier).

The probability scale and notation, probabilities of single events, mutually exclusive and exhaustive events, the AND and OR rules for combined events, and listing outcomes using sample space diagrams.

Estimating probability from experimental data using relative frequency, comparing experimental and theoretical probability, and calculating the expected number of outcomes from a probability.

Tree diagrams for two or more events, multiplying along branches and adding between paths, and conditional probability where the second event depends on the first (without replacement) at Higher tier.

Venn diagrams for two or three sets, set notation (union, intersection and complement), and using a completed Venn diagram to find probabilities including conditional probability (Higher tier).

Compound measures: speed, distance and time; density, mass and volume; pressure, force and area; and converting between compound units such as metres per second and kilometres per hour.

Direct and inverse proportion: the unitary method, recognising and using proportion relationships, and forming and using proportion equations with a constant of proportionality (Higher tier).

Growth and decay problems (including compound growth and depreciation), interpreting the gradient of a graph as a rate of change, and estimating the gradient of a curve and the area under a graph (Higher tier).

Percentage change: percentage increase and decrease using multipliers, percentage profit and loss, reverse percentages (finding the original amount), and simple and compound interest.

Ratio: simplifying ratios, dividing a quantity in a given ratio, expressing ratios as fractions and unit ratios, combining ratios, and using scale factors, maps and scale drawings.

The mean, median, mode and range; finding averages from frequency tables and from grouped data using the midpoint and an estimated mean; and comparing distributions using an average and the range.

Populations and samples, representative and biased sampling, random sampling, types of data (qualitative and quantitative, discrete and continuous), and designing questionnaires and data collection.

Scatter graphs and bivariate data, describing correlation (positive, negative or none), drawing and using a line of best fit to estimate values, and recognising the dangers of extrapolation and correlation versus causation.

Drawing and interpreting statistical diagrams: bar charts, pictograms, pie charts, frequency polygons, cumulative frequency graphs and box plots, and finding the median, quartiles and interquartile range (Higher tier).