Engineering and Applied Sciences - BS Admission Test
What the BS paper tests
The PIEAS BS admission test for Engineering and Applied Sciences is built on the HSSC/FSc pre-engineering core: Physics, Chemistry, Mathematics, and English. Questions are MCQ-style and reward fast, accurate recall plus one- or two-step numerical reasoning. The physics section stresses mechanics, electricity and magnetism, waves, and modern physics; chemistry covers stoichiometry, atomic structure, equilibrium, and organic functional groups; mathematics targets algebra, trigonometry, calculus, vectors, and matrices; English checks grammar, sentence correction, and comprehension.
Core rules and concepts
- Work in SI units and carry units through every calculation; many wrong options are unit mismatches.
- For projectile motion, use R = v² sin(2θ)/g and H = v² sin²θ/(2g); maximum range occurs at 45° in vacuum.
- In chemistry, balance equations before mole ratios; at STP, 1 mol gas occupies 22.4 L.
- For circuits, series resistances add; parallel conductances add; power P = VI = I²R = V²/R.
- In calculus, distinguish average vs instantaneous rate; check domain restrictions before simplifying.
Worked example
A ball is launched at 20 m/s at 30° above horizontal on level ground. Take g = 10 m/s². Find its range. Horizontal component: v_x = 20 cos30° = 17.32 m/s. Vertical: v_y = 20 sin30° = 10 m/s. Time of flight: t = 2v_y/g = 2 s. Range: R = v_x t = 34.6 m. Using the formula: R = 400 sin60°/10 = 34.6 m. The reasoning shows why the 45° formula cannot be used blindly: sin(2θ) = sin60° = 0.866, not 1.
Traps that cost marks
- Using degrees in a calculator set to radians.
- Forgetting that sin(2θ) is symmetric: 30° and 60° give the same range.
- Mixing molar mass and molecular mass in stoichiometry.
- Assuming series/parallel rules apply to mixed circuits without redrawing.
- Choosing a familiar formula without checking assumptions such as negligible air resistance.