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NSMQ 2023 past questions with answers

10 questions from the 2023 contests, across the rounds and all four subjects. Try each one before you open the answer. The full set of 582 2023 questions is in the Fomla app and the 2023 book.

Round 1: Fundamentals

Q1 · Physics · Regional Qualifiers

Find the wavelength of an electromagnetic wave of frequency $24.0$ THz in a medium of refractive index $1.25.$

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Answer

10 micrometers

1.Convert the frequency from terahertz to hertz: $f = 24.0 THz = 24.0 \times 1 0^{12} Hz$ .
2.Calculate the wave speed in the medium using $v = \frac{c}{n}$ : $v = \frac{3.00 \times 1 0 ^{8} m/s}{1.25} = 2.40 \times 1 0^{8} m/s$ .
3.Find the wavelength with $λ = \frac{v}{f}$ : $λ = \frac{2.40 \times 1 0 ^{8} m/s}{24.0 \times 1 0 ^{12} Hz} = 1.00 \times 1 0^{- 5} m = 10 μ m$ .

Q2 · Chemistry · Regional Qualifiers

Give the formula of the major product formed from radium metal and oxygen.

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Answer

RaO

1.Recall that radium (a Group 2 element) forms a Ra2+ cation.
2.Recall that oxygen forms an O2− anion (oxide ion).
3.Combine one Ra2+ ion with one O2− ion in a 1:1 ratio to achieve charge neutrality, giving RaO.

Q3 · Mathematics · Prelims

Express $\frac{3 x - 3}{( x + 1 ) ( x - 2 )}$ as partial fractions.

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Answer

$\frac{2}{x + 1} + \frac{1}{x - 2}$

1.Write the partial fraction ansatz: $\frac{3 x - 3}{( x + 1 ) ( x - 2 )} = \frac{A}{x + 1} + \frac{B}{x - 2}$ .
2.Multiply both sides by $(x + 1) (x - 2)$ to get $3 x - 3 = A (x - 2) + B (x + 1)$ .
3.Substitute $x = 2$ : $3 (2) - 3 = B \cdot 3 ⟹ 6 - 3 = 3 B ⟹ B = 1$ .
4.Substitute $x = - 1$ : $3 (- 1) - 3 = A (- 3) ⟹ - 3 - 3 = - 3 A ⟹ A = 2$ .
5.Therefore $\frac{3 x - 3}{( x + 1 ) ( x - 2 )} = \frac{2}{x + 1} + \frac{1}{x - 2}$ .

Round 2: Speed Race

Q4 · Mathematics · Regional Qualifiers

If α and β are roots of x² + 5x + 3 = 0, evaluate (1/α + 1/β)².

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Answer

$\frac{25}{9}$

1.Identify from Vieta's formulas that α+β=-b/a=-5 and αβ=c/a=3.
2.Compute 1/α+1/β using (α+β)/(αβ)=(-5)/3=-5/3.
3.Square the result: (−5/3)²=25/9.

Q5 · Chemistry · Quarter-final

Determine the mass of nitrogen dioxide formed when 0.5 mol of zinc nitrate undergoes thermal decomposition.

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Answer

46 g

1.Write and balance the thermal decomposition reaction: $Z n (N O_{3})_{2} \to Z n O + 2 N O_{2} + \frac{1}{2} O_{2}$ , showing a 1:2 mole ratio between Zn(NO $_{3}$ ) $_{2}$ and NO $_{2}$ .
2.Calculate moles of NO $_{2}$ produced: 0.5 mol Zn(NO $_{3}$ ) $_{2}$ × (2 mol NO $_{2}$ / 1 mol Zn(NO $_{3}$ ) $_{2}$ ) = 1.0 mol NO $_{2}$ .
3.Determine the mass of NO $_{2}$ using $m = n \times M$ , with molar mass $M (N O_{2}) = 46.0$ g/mol: $m = 1.0$ mol × 46.0 g/mol = 46 g.

Q6 · Physics · Quarter-final

Find the torque about the origin of force (2i − j + 2k) N acting at position 4k m.

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Answer

4i + 8j N·m

1.Identify the vectors. Position vector $r = 4 k = (0, 0, 4)$ and force vector $F = 2 i - j + 2 k = (2, - 1, 2)$ .
2.Set up the cross product determinant: $τ = r \times F = i 02 j 0 - 1 k 42$ .
3.Compute each component: $τ_{i} = 0 \cdot 2 - 4 \cdot (- 1) = 4$ , $τ_{j} = - (0 \cdot 2 - 4 \cdot 2) = 8$ , $τ_{k} = 0 \cdot (- 1) - 0 \cdot 2 = 0$ . Hence $τ = 4 i + 8 j$ .

Round 4: True/False

Q7 · Biology · Regional Qualifiers

True or false?Algae are always red, brown, or green.

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Answer

False

Many microscopic algae have varied pigments.

Q8 · Physics · Semi-final

True or false?The particle is subject to a periodic net force with period 0.2 s and initial horizontal direction.

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Answer

False

Round 5: Riddles

Q9 · Chemistry · Regional Qualifiers

1.I increase across a period.
2.I decrease down a group.
3.I depend on electronic configuration.
4.I am the energy required to remove an electron. Who am I?

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Answer

Ionization energy

Q10 · Mathematics · Semi-final

1.I am a type of relation associated with consecutive terms of a sequence.
2.I express the nth term as a function of one or more previous terms.
3.I have an order: the number of earlier terms needed to compute a new term.
4.A famous example of me defines each term as the sum of the two preceding ones, producing the Fibonacci numbers. Who am I?

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Answer

Recurrence relation

All 582 questions from 2023

Every 2023 contest on paper, with answers and worked solutions, plus practice papers.

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Practise them timed

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

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