LC Foundation Maths study plan

Apply the four operations to fractions, decimals and mixed numbers, including negative values, without a calculator

Convert fluently between fractions, decimals and percentages, then order a mixed list of ten values from smallest to largest

Apply the order of operations, including brackets, indices and roots, to multi-step calculations

Calculate with numbers in standard form and round answers to a given number of decimal places or significant figures

Estimate answers by rounding to one significant figure and use the estimate to check a calculator result

Calculate percentage change, simple interest, compound interest and depreciation over up to three years

Work backwards from a final value to an original amount using reverse percentages, including a price that includes tax

Divide a quantity into a given ratio, including three-part ratios, and scale a recipe or mixture up and down

Solve direct and inverse proportion problems using the unitary method, stating the multiplier each time

Apply the compound measures for speed, density and pressure, and convert between the units involved

Simplify algebraic expressions and expand single and double brackets, including where a negative sign sits outside the bracket

Factorise expressions into a single bracket and factorise quadratics of the form x squared plus bx plus c

Solve linear equations containing brackets or fractions, and solve linear inequalities showing the solution set on a number line

Solve a pair of simultaneous linear equations by elimination and by substitution

Generate terms of a sequence from a term-to-term rule and find the nth term of a linear sequence

Substitute values into formulae, including negative values, and rearrange a formula to change the subject

Plot and interpret straight-line graphs, reading off the gradient and the y-intercept and using them to compare two relationships

Recognise and use graphs of direct proportion and conversion graphs to read values off both axes

Form an equation from a written context, solve it, and check that the answer is sensible in the original context

Apply angle facts for straight lines, points, triangles and parallel lines, and calculate interior and exterior angles of polygons

Calculate the area and perimeter of rectangles, triangles, parallelograms, trapezia and compound shapes made from them

Calculate the circumference and area of a circle, and the perimeter and area of a simple sector

Calculate the volume and surface area of cuboids, prisms and cylinders

Convert between metric units of length, area and volume, including between cubic centimetres and litres

Apply Pythagoras' theorem to find a missing side of a right-angled triangle, including in a real-world context

Use sine, cosine and tangent to find a missing side or angle, choosing the correct ratio and rounding as instructed

Use scale factors on similar shapes, map scales and scale drawings to find missing lengths and real distances

Measure and calculate bearings, and use a scale drawing to locate a point from two given bearings

Calculate the mean, median, mode and range from a list and from a frequency table, and compare two data sets using an average and the range

Interpret bar charts, pie charts, line graphs and scatter graphs, describe the correlation and draw a line of best fit

Use the probability scale and the fact that probabilities sum to 1 to find a missing probability

Calculate theoretical probability from equally likely outcomes and estimate probability from relative frequency

Use sample space diagrams, two-way tables and tree diagrams to find the probability of two combined events

Complete two full papers under exam conditions with strict timing and no notes

Re-drill the three weakest skills identified in the gap analysis until each is answered correctly five times in a row

Reproduce every formula and key fact from memory in 10 minutes and check against the formula sheet

Apply exam technique: show working for method marks, allocate time by marks available, and check units and rounding before finishing