BGCSE Mathematics 0563 study guide
BGCSE Mathematics 0563 · Work through your exam, one topic at a time.
BGCSE Mathematics (0563) is a senior-secondary mathematics qualification taken by candidates who need a formal school-leaving mathematics result for further study, employment, or vocational training. It suits students completing the final years of secondary schooling, as well as mature candidates returning to study or needing a mathematics grade for an application. The BGCSE Mathematics 0563 study guide has 9 sections and about 2,546 words.
01Number and Numeration
A candidate must move confidently between fractions, decimals, percentages and standard form, and must apply place value when ordering or rounding. Know the meanings of factor, multiple, prime, square, cube and reciprocal; be able to find HCF and LCM by listing or prime factorisation.
271 words, about 1 min02Ratio, Proportion, Percentage and Consumer Arithmetic
This domain links ratio notation, direct and inverse proportion, percentage change, and money calculations. You must simplify ratios, divide a quantity in a given ratio, use the unitary method, and recognise when two quantities increase together (direct proportion) or one falls as the other rises (inverse proportion).
271 words, about 1 min03Algebra
Algebra questions test manipulation and solving rather than memorised answers. You should simplify expressions by collecting like terms, expand single and double brackets, factorise by taking out a common factor, and recognise difference of two squares.
297 words, about 1 min04Relations, Functions and Graphs
Candidates must read and plot coordinates, understand relations as sets of ordered pairs, and use function notation. Know domain and range, identify whether a relation is a function, and interpret mappings.
294 words, about 1 min05Geometry and Mensuration
This domain covers angle facts, properties of triangles and quadrilaterals, parallel-line angles, polygons, congruence and similarity, Pythagoras theorem, circle vocabulary, and area, perimeter, surface area and volume. You must calculate angles in triangles, straight lines, at a point and in polygons; use the interior angle sum (n - 2) x 180 degrees; and apply similarity scale factors.
286 words, about 1 min06Trigonometry and Bearings
Right-angled trigonometry uses sine, cosine and tangent: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. You must choose the correct ratio, find missing sides and angles, and solve problems involving angles of elevation and depression.
282 words, about 1 min07Vectors and Transformations
Vector work includes column vectors, magnitude, addition, subtraction, scalar multiplication and position vectors. For points A and B, vector AB = b - a when a and b are position vectors.
287 words, about 1 min08Statistics
Statistics questions require collecting, organising and interpreting data. Know the difference between discrete and continuous data, construct frequency tables, and read bar charts, pie charts, line graphs and scatter diagrams.
293 words, about 1 min09Probability
Probability measures how likely an event is on a scale from 0 to 1. You must list sample spaces, count equally likely outcomes, use the complement rule, and combine probabilities for mutually exclusive and independent events.
265 words, about 1 min