LGCSE Mathematics (0178) study guide
LGCSE Mathematics (0178) · Work through your exam, one topic at a time.
LGCSE Mathematics (0178) is a secondary-level mathematics qualification for candidates who need a solid, verifiable numeracy and algebra foundation - typically school leavers, candidates returning to study, and learners preparing for further academic or vocational routes that assume mathematical competence. The assessment is structured rather than purely factual: you are expected to select methods, show working, and communicate reasoning across Number, Algebra and Graphs, Geometry and Trigonometry, Mensuration, Coordinate Geometry, and Statistics and Probability. The LGCSE Mathematics (0178) study guide has 6 sections and about 1,732 words.
01Number
Number assesses exact and approximate calculation: fractions, decimals, percentages, ratio and proportion, standard form, indices, surds, bounds and rounding. Questions often combine two ideas, so choose a method before calculating.
294 words, about 1 min02Algebra and Graphs
Algebra and Graphs tests symbolic manipulation and the link between equations and their graphs: expanding and factorising, linear and quadratic equations, simultaneous equations, inequalities, sequences, functions and graph interpretation. Expand brackets by multiplying every term; factorise by taking out the highest common factor first.
313 words, about 2 min03Geometry and Trigonometry
Geometry and Trigonometry tests angle reasoning, polygons, circles, congruence and similarity, Pythagoras’ theorem, right-triangle trigonometry, the sine and cosine rules, and bearings. Angles on a straight line sum to 180°, angles at a point to 360°, and vertically opposite angles are equal.
302 words, about 2 min04Mensuration
Mensuration tests perimeter, area, surface area and volume of plane and solid shapes, including circles, sectors, prisms, cylinders, cones, spheres and composite figures. Circle: circumference = 2πr, area = πr².
277 words, about 1 min05Coordinate Geometry
Coordinate Geometry tests points in the Cartesian plane, distance, midpoint, gradient, straight-line equations, parallel and perpendicular lines, and simple intersections. Distance between (x₁, y₁) and (x₂, y₂) is √[(x₂ − x₁)² + (y₂ − y₁)²].
271 words, about 1 min06Statistics and Probability
Statistics and Probability tests data collection and representation, averages and spread, cumulative frequency and box plots, scatter graphs, probability rules, tree diagrams and conditional probability. Mean = total of values ÷ number of values.
275 words, about 1 min