Mathematics
The Mathematics domain of CSEC Mathematics tests fluency across number, algebra, geometry, measurement, trigonometry, statistics, probability, vectors and matrices. Questions reward correct method, precise notation and sensible rounding, not only a final answer.
Core rules and concepts
- Number and consumer arithmetic: apply order of operations, indices, standard form, ratio and proportion; calculate percentage profit/loss, discount, sales tax, wages, simple and compound interest, and currency conversion. Use the original amount as the base for percentage change.
- Algebra: simplify and factorise expressions, solve linear and quadratic equations and simultaneous equations, rearrange formulae, solve inequalities, and interpret functions and graphs. Keep balance by applying the same operation to both sides.
- Geometry and measurement: use angle facts, circle theorems, Pythagoras’ theorem, congruence and similarity; convert units; calculate perimeter, area and volume. For similar figures, lengths scale by k, areas by k² and volumes by k³.
- Trigonometry and vectors: use sine, cosine and tangent ratios, the sine and cosine rules, and bearings measured clockwise from north. Add vectors by components or scale diagram; multiply matrices only when dimensions agree.
- Statistics and probability: construct and interpret frequency tables and graphs; calculate mean, median, mode and range; use probability values from 0 to 1 and the complement rule.
Worked example
A sum of $4,500 is invested at 6% per annum simple interest for 3 years. Find the interest and the total amount. Interest for one year = 6% of 4,500 = 0.06 × 4,500 = 270. For 3 years, interest = 270 × 3 = 810. Total amount = 4,500 + 810 = $5,310. The reasoning shows that simple interest is calculated on the original principal each year, not on accumulated interest.
Traps that cost marks
- Using the new price instead of the original price as the base for a percentage change.
- Rounding too early in multi-step calculations; keep full calculator values and round at the end.
- Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
- Mixing units or applying a length scale factor directly to area or volume.
- Using the wrong trigonometric mode or measuring a bearing anticlockwise.