MathsQ&A by dot point

Simplify and manipulate algebraic expressions: collect like terms, expand single and double brackets, factorise (common factors, quadratics and the difference of two squares), and rearrange formulae to change the subject.

Solve linear inequalities and represent solutions on a number line; solve quadratic inequalities (Higher tier); and recognise and sketch the graphs of quadratic, cubic, reciprocal and exponential functions.

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

Generate sequences from a rule; find the nth term of a linear sequence and a quadratic sequence (Higher tier); and recognise arithmetic, geometric, square, cube, triangular and Fibonacci sequences.

Solve two simultaneous linear equations by elimination and substitution; solve a linear and a quadratic equation simultaneously (Higher tier); and interpret the solution as the point of intersection.

Solve linear equations in one unknown, including those with brackets, fractions and the unknown on both sides, and form linear equations from worded and geometric contexts.

Use the equation $y = mx + c$ to find the gradient and intercept; find the equation of a line through given points; and identify parallel and perpendicular lines (perpendicular at Higher tier).

Use angle facts at a point, on a straight line and in parallel lines (alternate, corresponding and co-interior); and calculate the interior and exterior angles of polygons.

Calculate the area and perimeter of rectangles, triangles, parallelograms, trapezia, circles and sectors; and the surface area and volume of prisms, cylinders, pyramids, cones and spheres.

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).

Carry out standard constructions (perpendicular bisector, angle bisector, perpendicular from a point) with ruler and compasses, and find loci of points satisfying a given condition, including in combination.

Use Pythagoras' theorem and the trigonometric ratios in right-angled triangles; and apply the sine rule, cosine rule and the area formula in any triangle (Higher tier).

Describe and perform the four transformations (translation, rotation, reflection and enlargement, including negative and fractional scale factors at Higher tier) and combine them.

Use vector notation; add, subtract and multiply vectors by a scalar; and use vectors to construct geometric arguments and proofs (proof at Higher tier).

Identify factors, multiples and primes; write a number as a product of its prime factors; and use prime factorisation to find the HCF and LCM of two or more numbers.

Add, subtract, multiply and divide fractions and mixed numbers; convert between fractions, decimals and percentages; and find a percentage of an amount and one number as a percentage of another.

Round to a given number of decimal places or significant figures; estimate calculations; and find and use upper and lower bounds, including in calculations (Higher tier).

Apply the laws of indices for integer, negative and fractional powers; and write, order and calculate with numbers in standard form $a \times 10^n$.

Order positive and negative integers, decimals and fractions; use the four operations and the correct order of operations (BIDMAS), including with negatives.

Simplify surds, carry out the four operations with surds, expand brackets containing surds, and rationalise the denominator of a fraction (Higher tier).

Use the probability scale from 0 to 1; calculate probabilities of single events from equally likely outcomes; use the fact that probabilities sum to 1; and list combined outcomes using sample space diagrams.

Use relative frequency (experimental probability) to estimate probabilities from data, understand how more trials improve the estimate, and calculate expected numbers of outcomes.

Draw and use tree diagrams to calculate probabilities of combined events, including independent events and conditional events without replacement (Higher tier).

Use Venn diagrams and set notation (union, intersection and complement) to represent and count outcomes and to calculate probabilities, including conditional probability (Higher tier).

Use compound measures including speed, density and pressure; rearrange the defining formulae; and convert between units such as m/s and km/h.

Solve problems involving direct and inverse proportion, including using the unitary method and forming proportion equations of the form $y = kx$ or $y = \dfrac{k}{x}$ with a constant of proportionality (Higher tier).

Model exponential growth and decay over repeated periods; and interpret the gradient of a graph as a rate of change and the area under a graph in real-life contexts (Higher tier).

Calculate percentage increase and decrease, find the percentage change between two values, solve reverse percentage problems, and apply repeated percentage change including compound interest using multipliers.

Use ratio notation; simplify ratios and express them in the form $1:n$; divide a quantity in a given ratio; and apply ratio to scale drawings, maps and similar shapes.

Calculate the mean, median, mode and range; find the mean from a frequency table and an estimated mean from grouped data; and compare distributions using an average and the range (and quartiles at Higher tier).

Identify types of data (qualitative and quantitative, discrete and continuous); understand populations and samples; use random and stratified sampling; and recognise sources of bias.

Plot and interpret scatter graphs; describe correlation; draw a line of best fit; use it to estimate values; and understand interpolation, extrapolation and the difference between correlation and causation.

Draw and interpret statistical charts including bar charts, pie charts, frequency polygons, stem-and-leaf diagrams, box plots and histograms with unequal class widths (histograms at Higher tier).