Mathematics and Science
Mathematics and Science is a 60-mark composite section (30 Mathematics + 30 Science) for candidates opting for the Mathematics/Science stream, mixing content accuracy with pedagogy of the two subjects.
Mathematics core
- Divisibility: 3 and 9 by digit sum; 4 by the last two digits; 8 by the last three; 11 by the alternating digit sum.
- For any two numbers, HCF × LCM = product of the numbers.
- BODMAS order; percentage change; unitary method for ratio and proportion.
- Identities: (a + b)² = a² + 2ab + b², a² − b² = (a + b)(a − b).
- Pythagoras; angle sum of a triangle 180°; trapezium area ½(a + b)h; circle 2πr and πr²; cylinder volume πr²h.
Science core
- Newton's laws: inertia; F = ma; action–reaction. Speed = distance/time; velocity carries direction.
- Ohm's law V = IR; series resistances add, parallel add as reciprocals.
- Reflection: angle of incidence = angle of reflection, both measured from the normal.
- Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, needing chlorophyll and sunlight.
- Deficiency diseases: vitamin A night blindness, B1 beri-beri, C scurvy, D rickets, iron anaemia.
Worked example
Find the least number leaving remainder 3 when divided by 12 or 15. The number is a common multiple plus 3. LCM(12, 15) = 60, giving 63, 123, …; the least is 63. Check: 63 ÷ 12 = 5 remainder 3; 63 ÷ 15 = 4 remainder 3.
Traps
Swapping LCM and HCF in word problems; converting 1 m² into 100 cm² instead of 10,000 cm²; saying velocity when direction is irrelevant; measuring reflection angles from the mirror surface; forgetting that mass is constant while weight changes with g.