QUESTION 01 Algebra
If x + 1/x = 3, find x2 + 1/x2.
View worked answer
Answer: 7
Squaring both sides gives x2 + 2 + 1/x2 = 9. Subtract 2 to obtain 7.
STUDENT RESOURCES / PRACTICE SET 01
Start with the fundamentals.
9 original questions · Mathematics, Physics & Chemistry
Suggested time: 25 minutes · Foundation level
Try each question before opening its worked answer. This is a general starter set; follow your teacher’s assignments for batch-specific practice.
Mathematics
QUESTION 02 Number sense
Find the remainder when 7103 is divided by 10.
View worked answer
Answer: 3
The last digits of powers of 7 repeat in the cycle 7, 9, 3, 1. Since 103 leaves remainder 3 on division by 4, the required last digit is the third entry: 3.
QUESTION 03 Quadratic equations
The roots of x2 − 5x + k = 0 differ by 1. Find k.
View worked answer
Answer: 6
If the roots are α and β, then α + β = 5 and (α − β)2 = 1. Therefore 1 = (α + β)2 − 4αβ = 25 − 4k, giving k = 6. The roots are 2 and 3.
Physics
QUESTION 04 Motion
A car travels equal distances at 30 km/h and 60 km/h. Find its average speed over the whole journey.
View worked answer
Answer: 40 km/h
Let each distance be d km. Total time = d/30 + d/60 = d/20 hours. Average speed = total distance ÷ total time = 2d ÷ (d/20) = 40 km/h.
QUESTION 05 Force and acceleration
A net horizontal force of 6 N acts on a 2 kg body initially at rest. Find its speed after 4 s, assuming the net force stays constant.
View worked answer
Answer: 12 m/s
Acceleration a = F/m = 6/2 = 3 m/s². Using v = u + at, v = 0 + 3 × 4 = 12 m/s.
QUESTION 06 Electric circuits
Two resistors of 3 Ω and 6 Ω are connected in parallel across an ideal 6 V battery. Find the equivalent resistance and total current.
View worked answer
Answer: 2 Ω; 3 A
For parallel resistors, 1/R = 1/3 + 1/6 = 1/2, hence R = 2 Ω. Total current I = V/R = 6/2 = 3 A.
Chemistry
QUESTION 07 Mole concept
How many moles of water are present in 9 g of H₂O? Use H = 1 and O = 16 g/mol.
View worked answer
Answer: 0.5 mol
The molar mass of water is 2 × 1 + 16 = 18 g/mol. Amount of substance = mass ÷ molar mass = 9/18 = 0.5 mol.
QUESTION 08 Atomic structure
A neutral atom has atomic number 11 and mass number 23. State its numbers of protons, neutrons and electrons.
View worked answer
Answer: 11 protons; 12 neutrons; 11 electrons
Protons = atomic number = 11. A neutral atom has the same number of electrons, so electrons = 11. Neutrons = mass number − atomic number = 23 − 11 = 12.
QUESTION 09 Stoichiometry
Hydrogen reacts completely with sufficient oxygen: 2H₂ + O₂ → 2H₂O. How many grams of water form from 4 g of H₂? Use H = 1 and O = 16 g/mol.
View worked answer
Answer: 36 g
4 g of H₂ corresponds to 4/2 = 2 mol. The balanced equation gives 2 mol of water from 2 mol of H₂. The water mass is 2 × 18 = 36 g.
Finished? Reattempt any missed question tomorrow without looking at its solution.