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Sample questions with worked solutions
Original foundation questions for concept practice. These are short learning exercises, not official previous-year papers or full mock tests.
Physics
1. A body starts from rest with constant acceleration 2 m/s². How far does it travel in 5 s?
Use s = ut + ½at². Here u = 0, a = 2 m/s² and t = 5 s. Therefore s = 0 + ½ × 2 × 25 = 25 m. This relation requires constant acceleration.
2. A 6 Ω resistor is connected across 12 V. Find the current and power.
For an ohmic resistor, I = V/R = 12/6 = 2 A. Power P = VI = 12 × 2 = 24 W. Check that voltage is across the resistor and resistance stays constant.
Mathematics
3. Solve x² − 7x + 10 = 0.
Factorise: (x − 5)(x − 2) = 0. Hence x = 5 or x = 2. Substituting either value into the original expression gives zero.
4. Find the derivative of f(x) = 3x² − 4x + 1.
Differentiate each term using the power rule: f′(x) = 6x − 4. The derivative of the constant 1 is zero. At x = 2, the slope is 8.
Chemistry
5. How many moles are present in 9 g of water? Use molar mass 18 g/mol.
Amount of substance n = mass / molar mass = 9/18 = 0.5 mol. Multiplying by the Avogadro constant gives approximately 3.01 × 10²³ water molecules.
6. Find the molarity of a solution containing 0.2 mol solute in 500 mL of solution.
Convert the final solution volume to litres: 500 mL = 0.500 L. Molarity = 0.2/0.500 = 0.4 mol/L. Use solution volume, not the volume of solvent added.
Biology
7. Which process produces haploid cells from a diploid precursor: mitosis or meiosis?
Meiosis reduces chromosome number from diploid to haploid through two divisions after one round of DNA replication. Mitosis normally preserves chromosome number.
8. In an Aa × Aa cross, what fraction of offspring is expected to be aa?
Each parent produces A and a gametes with equal probability. The four equally likely combinations are AA, Aa, aA and aa. Thus the expected aa fraction is ¼, assuming ordinary Mendelian segregation.
Review your attempt
Count correct answers out of eight and label errors as concept, calculation, units or recall. This short set checks foundations; it does not predict an exam score.