Won by Mfantsipim School

NSMQ 2025 past questions with answers

10 questions from the 2025 contests, across the rounds and all four subjects. Try each one before you open the answer. The full set of 640 2025 questions is in the Fomla app and the 2025 book.

Round 1: Fundamentals

Q1 · Physics · Regional Qualifiers

A uniform bar of length 2.0 m is pivoted at one end. A 25 N force is applied 48 cm from the pivot. Calculate the force that must be applied at the far end of the bar (2.0 m from the pivot) to balance it.

Show answer

Answer

6 N

1.Convert the distance 48 cm to meters: $d_{1} = 0.48$ m.
2.Calculate the moment produced by the 25 N force: $τ_{1} = F_{1} \times d_{1} = 25 \times 0.48 = 12$ Nm.
3.For equilibrium, set the clockwise moment equal to the anticlockwise moment: $F_{2} \times 2.0 = 12$ , so $F_{2} = \frac{12}{2.0} = 6$ N.

Q2 · Mathematics · Regional Qualifiers

Find a quadratic inequality with integer coefficients whose solution set is - $\frac{1}{2}$ < x < $\frac{1}{3}$ .

Show answer

Answer

6x² + x - 1 < 0

1.Identify the boundary roots as $r_{1} = - \frac{1}{2}$ and $r_{2} = \frac{1}{3}$ .
2.Write the inequality in factor form: $(x - r_{1}) (x - r_{2}) < 0$ , i.e. $(x + \frac{1}{2}) (x - \frac{1}{3}) < 0$ .
3.Clear denominators by multiplying both sides by $6$ (a positive integer to preserve the inequality): $6 (x + \frac{1}{2}) (x - \frac{1}{3}) < 0$ , which gives $(2 x + 1) (3 x - 1) < 0$ . Expand to get $6 x^{2} + x - 1 < 0$ .
4.Conclude that the solution set of $6 x^{2} + x - 1 < 0$ is exactly $- \frac{1}{2} < x < \frac{1}{3}$ .

Q3 · Chemistry · Regional Qualifiers

Give the IUPAC name of the straight-chain compound with molecular formula C4H10.

Show answer

Answer

Butane

1.Recall that alkanes follow the formula CnH2n+2, so C4H10 is an alkane.
2.Identify the prefix 'but-' for 4 carbon atoms in IUPAC nomenclature.
3.Add the suffix '-ane' for alkanes to get 'butane'.

Round 2: Speed Race

Q4 · Physics · Semi-final

A diffraction grating with 400 lines per mm is illuminated with white light at 60°. Find the wavelength of light diffracted at 30° in second order.

Show answer

Answer

$458 nm$ and $1.71 \times 1 0^{- 6}$ m

1.Calculate the grating spacing d. Given 400 lines/mm = 400×10³ lines/m, so d = 1/(400×10³) m = 2.5×10⁻⁶ m.
2.Use the grating equation in second order (m = 2) with i = 60° and θ = 30°. There are two cases: $sin i + sin θ$ and $sin i - sin θ$ .
3.For the plus case: $λ = \frac{d}{m} (sin 60° + sin 30°) = \frac{2.5 \times 1 0 ^{- 6}}{2} (0.8660 + 0.5) = 1.71 \times 1 0^{- 6}$ m. For the minus case: $λ = \frac{2.5 \times 1 0 ^{- 6}}{2} (0.8660 - 0.5) = 4.58 \times 1 0^{- 7}$ m = 458 nm.

Q5 · Mathematics · One-Eighth

Two fair dice thrown; probability total is 5.

Show answer

Answer

$\frac{1}{9}$

1.Determine the size of the sample space when two fair dice are thrown: $6 \times 6 = 36$ possible outcomes.
2.List the outcomes that sum to 5: (1,4), (2,3), (3,2), (4,1), giving 4 favourable outcomes.
3.Apply the probability formula: $P (sum = 5) = \frac{4}{36} = \frac{1}{9}$ .

Q6 · Chemistry · Regional Qualifiers

What volume of ammonia gas at STP is produced from 10.7 g of ammonium chloride (Cl = 35.5)?

Show answer

Answer

4.48 dm³

1.Calculate the molar mass of NH4Cl: M = 14 + (4×1) + 35.5 = 53.5 g/mol.
2.Determine the moles of NH4Cl: n = m/M = 10.7 g / 53.5 g/mol = 0.2 mol.
3.Use the reaction NH4Cl → NH3 + HCl to find moles of NH3: n(NH3) = n(NH4Cl) = 0.2 mol.
4.Calculate the volume of NH3 at STP: V = n × 22.4 L/mol = 0.2 × 22.4 L = 4.48 L (or dm³).

Round 4: True/False

Q7 · Biology · Grand Finale

True or false?Growing alkali-tolerant crops is more advisable than growing acid-tolerant crops in soil that turns methyl orange red.

Show answer

Answer

False

Red = acidic; choose acid-tolerant crops.

Q8 · Mathematics · Grand Finale

True or false?The number of ordered pairs (X, Y) such that XY = 14 is 2.

Show answer

Answer

False

14 has two positive factor pairs and considering order gives 4 ordered pairs, not 2.

Round 5: Riddles

Q9 · Physics · One-Eighth

1.I am a type of material.
2.I am usually non‑magnetic.
3.I am usually electrically insulating.
4.I have a high electrical polarizability.
5.I am the type of material that fills the space between capacitor plates. What am I?

Show answer

Answer

Dielectric

Q10 · Mathematics · One-Eighth

1.I am a type of polygon.
2.For any polygon, I fit my outline in the most symmetric way possible.
3.For any polygon, I have the largest number of axes of symmetry. What am I?

Show answer

Answer

A regular polygon

All 640 questions from 2025

Every 2025 contest on paper, with answers and worked solutions, plus practice papers.

Buy on Selar

Practise them timed

Speed Races, the True or False round and riddles, marked as you go.

Get it onGoogle Play