Mathematics: clean steps in algebra and mensuration
Mathematics in PECE rewards clean, stepwise work in arithmetic, algebra, geometry, mensuration, trigonometry and statistics. Most questions are Class 10 standard; the difficulty comes from time pressure and from careless unit or sign mistakes.
Core rules
- Arithmetic: percentage change = (change/original) × 100; simple interest = PRT/100; compound interest = P(1 + R/100)ⁿ − P.
- Algebra: quadratic formula x = [−b ± √(b² − 4ac)]/2a; check the discriminant b² − 4ac before promising real roots.
- Geometry: angle sum of a triangle = 180°; Pythagoras; circle: tangent ⟂ radius at the point of contact.
- Mensuration: area of circle = πr²; volume of cylinder = πr²h; volume of sphere = (4/3)πr³; use the same unit throughout.
- Trigonometry: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; standard values for 0°, 30°, 45°, 60°, 90°.
- Statistics: mean = sum/observations; median = middle value after sorting; mode = most frequent.
Worked example
Solve 2x² − 5x + 2 = 0. Reasoning: a = 2, b = −5, c = 2. Discriminant = (−5)² − 4(2)(2) = 25 − 16 = 9. Roots = [5 ± √9]/(2 × 2) = [5 ± 3]/4. So x = 8/4 = 2 or x = 2/4 = 0.5. Both roots are real and distinct.
Traps
Losing the negative sign in −b; using diameter as radius; mixing cm and m in mensuration; forgetting to sort data before finding the median; and cancelling terms across a plus sign, which is invalid.