LGCSE Mathematics (0178) case studies
LGCSE Mathematics (0178) · Put your knowledge to work in context.
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) case studies are 5 cases and about 2,673 words.
1Science-Fair Transport: Buses, Discounts and Budget
Grade 11 at Thuso High is planning a science-fair trip to Maseru, 240 km away. There are 186 learners and 12 teachers; every bus must carry at least one teacher.
539 words, about 3 min2Model Rocket: Quadratic Height and Safety Approval
A physics club launches a model rocket from a 1.5 m high platform on a flat field. The height h metres above the ground after t seconds is modelled by h = 1.5 + 18t − 4.9t² for 0 ≤ t ≤ 4.
557 words, about 3 min3Triangular Plot: Survey Check and Cost Estimate
A land surveyor measures a triangular plot ABC on a sloping site. Side AB = 38.5 m, side AC = 52.0 m, and the included angle BAC = 63°.
521 words, about 3 min4Village Water Tank: Capacity and Paint Cost
A village water committee is installing a new tank. The tank is a cylinder of radius 1.5 m and height 2.8 m, with a hemispherical roof on top.
473 words, about 2 min5Canteen Fruit Order: Survey Proportions and Discount
A school canteen manager surveys 180 learners about lunch habits. Of the 110 who buy lunch at the canteen, 45 also buy a fruit; of the 70 who bring a packed lunch, 28 buy a fruit.
583 words, about 3 min