Mathematics and Science: Content Anchors and Pedagogic Method
For the Mathematics–Science group, Paper 2 allots 60 marks: 30 Mathematics and 30 Science, drawn from NCERT Classes VI–VIII content plus the pedagogy of each subject. Numerical accuracy matters, but so does recognising the concept behind a classroom situation.
Mathematics content
Rational numbers and their operations; exponents and laws; squares, cubes and roots; percentage, profit–loss, discount; simple and compound interest; ratio and proportion; algebraic expressions, identities and linear equations; lines and angles, triangle congruence, quadrilateral properties; perimeter, area, surface area and volume of cube, cuboid and cylinder; mean, median, mode and simple probability.
Science content
Physics: motion and speed, force and pressure, laws of reflection, sound (frequency, amplitude), series and parallel circuits, magnetism. Chemistry: states of matter, separation techniques, acids–bases and indicators, metals and non-metals, combustion. Biology: cell organelles, photosynthesis, respiration, reproduction in plants, microorganisms and crop production.
Pedagogy
Polya's four steps (understand, plan, carry out, look back); Van Hiele levels of geometric thinking; inductive and deductive approaches; TLM such as Dienes blocks and geoboards; science process skills (observation, hypothesis, experiment, inference); inquiry and activity methods; diagnostic testing and error analysis.
Worked example
A shopkeeper marks an article 40% above cost and allows a 25% discount. Find the profit per cent. Take CP = 100, so MP = 140 and SP = 140 × 0.75 = 105. Profit = 5 on 100, i.e. 5%. Note the discount is calculated on the marked price, not on cost.
Traps
Computing discount on cost instead of marked price; mixing SI and CI (for two years the difference is P(r/100)²); measuring the angle of incidence from the mirror surface rather than the normal; claiming current is 'used up' in a series circuit; confusing mass with weight.