Mathematics
Core ideas
BGCSE Mathematics rewards secure arithmetic and clear algebra. You must handle fractions, percentages, ratio, indices, standard form, and directed numbers without a calculator error. In algebra, expand and factorise confidently, solve linear and simultaneous equations, rearrange formulae, and sketch linear and quadratic graphs. Geometry requires angle facts, circle theorems, Pythagoras, trigonometry (SOHCAHTOA and the sine and cosine rules), area and volume, and accurate constructions. Statistics covers averages, cumulative frequency, probability, and interpreting charts.
Traps
Common traps include mixing units (cm with m, minutes with hours), ignoring the order of operations, losing a negative sign when expanding brackets, and rounding too early. In trigonometry, check whether your calculator is in degrees or radians. In probability, remember that mutually exclusive events add but independent events multiply. Read the final sentence of the question twice: it often asks for a reason, a unit, or a rounded value.
Worked example
Solve 3(2x − 5) = 4x + 7. Expand: 6x − 15 = 4x + 7. Subtract 4x: 2x − 15 = 7. Add 15: 2x = 22. Divide by 2: x = 11. Check: left side 3(22 − 5) = 51; right side 44 + 7 = 51.
Rule of thumb
Always show working, keep units, and substitute your answer back into the original equation. If a question says 'hence' or 'show that', the previous part is a required stepping stone.