Mathematics
Core concepts
Angola's ISTM mathematics paper rewards fluency in algebra, functions, geometry and basic statistics. Prioritise: simplifying algebraic expressions and factorising (common factor, difference of squares, trinomials); solving linear and quadratic equations (factorisation, the quadratic formula, completing the square); systems of two linear equations; inequalities and their sign rules; indices and surds; direct and inverse proportion; straight-line graphs (gradient, intercepts); areas and volumes of triangles, circles, cylinders and cones; Pythagoras and basic trigonometry (sine, cosine, tangent); percentages, ratio and averages (mean, median, mode).
Traps to expect
- Sign errors when expanding brackets or moving terms across the equals sign.
- Dividing by a variable and losing a root: from x² = 5x, factor to x(x − 5) = 0, giving x = 0 or 5, not just 5.
- Units: converting cm to m before computing area or volume.
- Inequalities: multiplying or dividing by a negative number reverses the sign.
- Percentage change applied to the wrong base (increase then decrease does not return to the original).
Rule of thumb
For any quadratic ax² + bx + c = 0, first try factorising; if no integer factors appear quickly, use x = [−b ± √(b² − 4ac)] / 2a and check the discriminant b² − 4ac to see how many real roots exist (positive: two, zero: one, negative: none).
Worked example
Solve 2x² − 7x + 3 = 0. Discriminant = 49 − 24 = 25, so x = (7 ± 5)/4, giving x = 3 or x = 1/2. Verify by substitution.