Basic Sciences and Mathematics
Scope of the paper
This section rewards precision rather than memory. Applied physics covers units and dimensions, Newton's laws, work-energy-power, simple machines, heat and specific heat, reflection and refraction, and basic electricity. Applied chemistry covers atomic structure, the periodic table, acids and bases with pH, oxidation-reduction, water hardness, alloys and corrosion. Mathematics covers algebra, simultaneous and quadratic equations, logarithms, trigonometry with sine and cosine rules, coordinate geometry, mensuration and elementary statistics.
Traps that recur
Dimensional analysis questions often hide a non-dimensional constant, so a formula can be dimensionally correct yet physically wrong. In trigonometry, the calculator mode (degree versus radian) causes silent errors. In mensuration, candidates use diameter where radius belongs, or forget the curved surface area excludes the base. In chemistry, molarity and molality are confused, and the mole ratio in a balanced equation is skipped before mass calculation. In statistics, the mean of grouped data needs class midpoints, not class limits.
Worked example
Find the pH of a 0.01 M hydrochloric acid solution. HCl is a strong monobasic acid, so [H⁺] = 0.01 = 10⁻² M, and pH = −log(10⁻²) = 2. Rule of thumb: for a strong monobasic acid, pH equals the negative logarithm of molarity directly; for weak acids you must use the dissociation constant.
Practice habit
Maintain a single formula sheet organised by topic, and re-derive each entry once so you can reconstruct it under pressure.