LGCSE Mathematics (0178) study plan

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

Convert fluently between fractions, decimals and percentages and order a mixed list of them by size

Compute with squares, cubes, square roots and cube roots, and apply index laws for multiplication and division of powers

Use standard form to write very large and very small quantities and to multiply or divide two numbers given in standard form

Round to a given number of decimal places or significant figures and estimate a calculation by rounding each value first

Solve ratio and proportion problems including direct and inverse proportion using the unitary method

Calculate percentage change, reverse percentages, simple and compound interest, and profit or loss in context

Apply upper and lower bounds to a rounded measurement and state the resulting range of a calculated value

Simplify algebraic expressions by collecting like terms, expanding single and double brackets, and factorising common factors

Solve linear equations including those with fractions and unknowns on both sides

Rearrange formulas to change the subject, including cases where the subject appears twice

Solve simultaneous linear equations by elimination and by substitution, and interpret the solution graphically

Factorise and solve quadratic equations by factorising and by using the quadratic formula

Complete the square and identify the turning point of a quadratic from completed-square form

Sketch the graphs of linear, quadratic, cubic and reciprocal functions, stating intercepts and key features

Construct and interpret tables of values and plot graphs from them, reading off values accurately

Recognise and use sequences including arithmetic and geometric progressions, finding the nth term of a linear sequence

Draw and interpret scatter diagrams, describe correlation and draw a line of best fit to estimate a value

Calculate and interpret the mean, median, mode and range for discrete and grouped data

Construct and read cumulative frequency curves and estimate the median and interquartile range from them

Compute probabilities using the basic probability scale and the complement rule for single events

Use tree diagrams and sample space diagrams to find probabilities of combined independent and dependent events

Apply the addition and multiplication rules correctly, distinguishing mutually exclusive from independent events

Calculate conditional probability from a two-way table and interpret the result in context

Compare experimental relative frequency with theoretical probability and explain the difference

Apply angle facts for lines, triangles, quadrilaterals and parallel lines to find unknown angles with reasons stated

Use circle theorems to find angles and justify each step with the theorem name

Apply Pythagoras' theorem and the trigonometric ratios to right-angled triangles in two and three dimensions

Calculate the perimeter and area of triangles, quadrilaterals, circles and compound shapes

Calculate the volume and surface area of prisms, cylinders, cones and spheres, and convert between units of area and volume

Use the sine rule, cosine rule and area formula for non-right-angled triangles

Solve problems involving bearings, scale drawings and three-figure bearing notation

Find the gradient, midpoint and length of a line segment between two coordinate points

Derive and use the equation of a straight line in the forms y = mx + c and general form, including parallel and perpendicular lines

Solve coordinate geometry problems involving intersections of lines and circles centred at the origin

Complete two full-length timed mock papers under exam conditions and record the score for each domain

Identify the three weakest domains from the mock results and re-teach each using the week sheets

Memorise and reproduce from memory all formulas required for mensuration, trigonometry and statistics

Practise exam technique: showing working, allocating time per mark and checking units and rounding

Build a personal error log of recurring mistakes and the correction for each