Mathematics (Algebra and Geometry)
Mathematics tests algebra and geometry: quadratic equations and functions, progressions, trigonometry, probability, triangle similarity, circle theorems, and areas. Marks are lost when a formula is recalled but substitution, units, or the geometric ratio is mishandled.
Algebra core
- Quadratic: ax²+bx+c=0; D=b²−4ac; roots (−b±√D)/2a; Vieta: x₁+x₂=−b/a, x₁x₂=c/a.
- Arithmetic progression: aₙ=a₁+(n−1)d; Sₙ=(a₁+aₙ)n/2.
- Geometry: similarity ratio k gives area ratio k²; an inscribed angle is half the central angle on the same arc; sector area = πr²·α/360.
Worked example
In triangle ABC, D lies on AB and E on BC with DE ∥ AC. AD:DB=1:2 and the area of triangle BDE is 8 cm². Find the area of ABC. Since DE ∥ AC, triangles BDE and BAC are similar. DB:AB=2:3, so k=2/3 and the area ratio is k²=4/9. Thus area ABC = 8 ÷ 4/9 = 18 cm². Reasoning: similarity gives side ratio, then square it for areas.
Traps
- A negative discriminant means no real roots; do not invent roots.
- Squaring both sides can introduce extraneous solutions; check in the original.
- Using k instead of k² for areas.
- Confusing central and inscribed angles.