Mathematics: Algebra, Geometry, Functions, and Problem Solving
Core content
The mathematics paper covers operations with rational numbers and algebraic expressions, linear equations and inequalities, systems of two linear equations, proportionality, percentages, powers and roots, polynomials and factoring, quadratic equations, linear functions and their graphs, and plane geometry (triangles, quadrilaterals, circles, the Pythagorean theorem, similarity, area and volume of solids). Basic statistics - mean, median, mode, range - also appears.
Traps that cost marks
Sign errors when removing brackets: -(2x - 5) becomes -2x + 5, not -2x - 5. Forgetting that dividing or multiplying an inequality by a negative number reverses the sign. Confusing the square of a sum with the sum of squares: (a + b)² = a² + 2ab + b². Mixing units, especially converting cm² to m² (divide by 10 000, not 100). Rounding too early in multi-step problems. And in geometry, using the diameter where the radius belongs - area of a circle is r²π, circumference is 2rπ.
Quadratic equations
Use factoring when the roots are obvious, otherwise the formula x = (-b ± √(b² - 4ac)) / 2a. The discriminant D = b² - 4ac tells you the number of real solutions: two if positive, one if zero, none if negative. Viete's rules, x₁ + x₂ = -b/a and x₁ · x₂ = c/a, are fast shortcuts for checking answers.
Worked example
Solve 2x + 3(x - 4) = 7. Expand: 2x + 3x - 12 = 7. Combine: 5x = 19, so x = 3.8. Check by substitution: 2(3.8) + 3(-0.2) = 7.6 - 0.6 = 7. Always substitute back; it catches nearly every arithmetic slip.
Geometry rule of thumb
Write the formula first, substitute known values second, solve last. Label every answer with its unit, and draw a sketch for any problem describing a figure - a correct diagram often reveals the intended theorem, usually Pythagoras or similarity.