Mathematics and Science: Content plus Pedagogy
Mathematics and Science is a 60-mark section for Paper II candidates opting for the maths–science stream. Content is drawn from Classes V–VIII, with a pedagogy component on how children learn mathematics and science.
Arithmetic and algebra
Number system and place value; HCF × LCM = product of the two numbers (true only for two numbers); ratio, proportion, percentage; profit and loss with SP = CP(100 + P)/100; discount on marked price; simple interest PRT/100; average; speed–time–distance; unitary method. Algebra: identities (a² − b², (a ± b)²), linear equations in one variable, exponents and their laws.
Geometry and mensuration
Angle sum of a polygon = (n − 2) × 180°; congruence criteria (SSS, SAS, ASA, RHS); Pythagoras' theorem; circle - chord, tangent, cyclic quadrilateral. Areas: triangle ½ × base × height, Heron's formula, circle πr²; circumference 2πr; volume of cylinder πr²h, cone ⅓πr²h, sphere 4/3 πr³.
Science anchors
States of matter and separation techniques; motion equations v = u + at and s = ut + ½at²; Newton's laws, friction, pressure, Archimedes' principle; rectilinear reflection, refraction, lenses; sound - frequency, pitch, loudness; Ohm's law V = IR, series and parallel circuits, magnetic effect of current; cell and tissues, photosynthesis, respiration, digestion, circulation; food chains, ecosystems, natural resources and pollution.
Pedagogy
Polya's four steps for problem solving (understand, plan, carry out, look back); inductive and deductive routes; laboratory and activity method; scientific method - observation, hypothesis, controlled experiment, conclusion; error analysis and remedial teaching.
Worked example
A trader marks goods 25% above cost and allows a 10% discount. Take CP = ₹100, so MP = ₹125; SP = 125 × 0.90 = ₹112.50; profit = ₹12.50, i.e. 12.5%. The trap is adding 25% and subtracting 10% to claim 15% profit - discount applies to the marked price, not the cost.
Traps that cost marks
Using HCF × LCM = product for three numbers; interchanging mass and weight; treating speed and velocity as identical; ignoring sign conventions in mirrors and lenses; writing πr² for circumference.