Basic Sciences: Mechanics, Equilibrium and Chemical Arithmetic
What this section tests
This section covers the physics, chemistry and mathematics all engineering disciplines draw on: kinematics and mechanics, electricity and magnetism, waves, atomic structure and bonding, stoichiometry, chemical equilibrium, and the algebra, trigonometry and calculus used to model them.
Core rules
- Projectile motion separates into independent horizontal (constant velocity) and vertical (constant acceleration g) components.
- Level-ground range R = v² sin2θ / g; maximum range at θ = 45°; maximum height H = v² sin²θ / (2g).
- pH = −log₁₀[H⁺]; a tenfold concentration change shifts pH by exactly one unit.
- Mole: n = m/M; Avogadro's number is 6.022 × 10²³ particles per mole.
- Le Chatelier: a system at equilibrium opposes the imposed change; raising pressure favours the side with fewer gas moles.
- d/dx(xⁿ) = nx^(n−1); integration accumulates area under a curve.
Worked example
A ball launches at 20 m/s, 30° above horizontal (g = 9.81 m/s²). v_x = 20cos30° = 17.3 m/s; v_y = 20sin30° = 10 m/s. Time of flight t = 2v_y/g = 20/9.81 = 2.04 s. Range R = v_x t = 17.3 × 2.04 = 35.3 m, matching v²sin60°/g = 400 × 0.866/9.81 = 35.3 m. Using g = 10 gives 34.6 m instead - a 2% gap that can decide a multiple-choice answer, so use the value the paper states.
Traps
Mixing degrees and radians on the calculator; forgetting pH falls as acidity rises; balancing equations by altering subscripts instead of coefficients; dropping the negative sign on an electron charge or an exothermic ΔH.