MathsQ&A by dot point

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.

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.

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).

Continue and describe sequences, find the nth term of a linear (arithmetic) sequence, and recognise quadratic, geometric, Fibonacci and other special sequences.

Solve simultaneous linear equations in two unknowns by elimination and by substitution, solve them graphically, and form simultaneous equations from worded contexts.

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

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).

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.

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.

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).

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.

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.

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).

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.

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).

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.

Calculate with fractions and mixed numbers, convert freely between fractions, decimals and percentages, and convert a recurring decimal to an exact fraction (Higher tier).

Apply the laws of indices including zero, negative and fractional powers (Higher tier), and write and calculate with numbers in standard form.

Calculate percentage increase and decrease, percentage change and reverse percentages, and solve financial problems involving simple interest, compound interest and repeated percentage change.

Use ratio notation, simplify ratios and share a quantity in a given ratio, and solve direct and inverse proportion problems including the unitary method.

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).

Understand place value, order integers, decimals and fractions, and calculate with the four operations and directed numbers using the correct order of operations (BIDMAS).

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 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.

Estimate probability from experimental data using relative frequency, understand how it stabilises with more trials, compare experimental with theoretical probability, and calculate expected frequencies.

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).

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).

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.

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).

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.

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.

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.