BGCSE Mathematics 0563 study plan

Convert fluently among fractions, decimals and percentages, and order ten mixed values without a calculator.

Apply index laws, including zero and negative indices, to simplify fifteen expressions and evaluate square and cube roots.

Multiply and divide numbers written in standard form, then round results to a stated number of significant figures.

Find HCF and LCM by prime factorisation and carry out directed-number arithmetic in context.

Estimate answers before calculating and flag unreasonable calculator output across ten worked examples.

Expand and factorise brackets, including quadratics of the form x squared plus bx plus c, over twenty items.

Solve linear equations and inequalities, showing the solution set on a number line where required.

Solve pairs of simultaneous linear equations by elimination and by substitution, and check each answer by back-substitution.

Rearrange formulae to change the subject, including cases where the new subject appears twice.

Substitute values into expressions and simplify algebraic fractions with monomial denominators.

Apply angle facts for lines, triangles, parallel lines and polygons to find labelled unknowns with a stated reason for each step.

Calculate perimeter and area of circles, sectors, triangles and compound shapes, and volume of prisms and cylinders.

Use Pythagoras' theorem to find missing sides and decide when a triangle is right-angled.

Compute percentage increase and decrease, profit and loss, and simple and compound interest in shopping and savings contexts.

Share quantities in a given ratio and convert between currencies and units of measure using given rates.

Plot straight-line graphs from equations and read off gradient and intercepts to match an equation to its line.

Use function notation to evaluate and interpret inputs and outputs, and describe mappings as one-to-one or many-to-one.

Solve a pair of equations graphically and read the solution from the intersection point.

Interpret distance-time and conversion graphs, including average speed over a stated interval.

Work through wage, overtime, utility bill and hire-purchase calculations and identify the cheaper of two quoted options.

Select and apply sine, cosine and tangent ratios to find missing sides and angles in right-angled triangles.

Combine Pythagoras with trigonometry in two-step problems and round answers to one decimal place.

Solve angles of elevation and depression problems from a clearly labelled sketch.

Express three-figure bearings, convert them to back-bearings, and solve position problems involving two or more legs.

Use the sine rule, cosine rule and area formula in non-right-angled triangles where the given information permits.

Add, subtract and scale column vectors, and calculate a vector's magnitude and direction.

Perform and fully describe translations, reflections, rotations and enlargements, stating centre, angle, direction or scale factor.

Calculate mean, median, mode and range from raw data and estimate the mean from a grouped frequency table.

Read and construct cumulative frequency curves, frequency polygons and histograms with unequal class widths.

Compare two data sets by quoting a measure of average and a measure of spread in the same sentence.

List a sample space for one-stage and two-stage experiments and use it to count favourable outcomes.

Draw and use tree diagrams for independent and dependent events, multiplying along branches and adding across them.

Distinguish mutually exclusive from independent events and apply the complement rule correctly.

Estimate probability from relative frequency and predict expected outcomes over a stated number of trials.

Interpret statistical diagrams critically, spotting misleading scales or missing sample sizes in three given summaries.

Sit one full-length timed mock under exam conditions with no notes and record the time spent on each section.

Classify every lost mark by domain and by cause (concept, method, arithmetic slip, misread), then rank the top three leaks.

Redrill the three weakest topics with twenty targeted questions each and re-mark against the official mark scheme style.

Memorise and reproduce the formula sheet from memory, then check it against the source list.

Sit a second full-length mock and apply pacing rules so that no question is left blank at the end.