Numerical Solving Tips for Physics and Chemistry (Punjab Board)

Why numericals go wrong, and why it is fixable

Almost every Matric and FSc student finds numericals hard at the start. The good news is that most lost marks in numericals are not about intelligence. They come from a few habits: starting without writing the data, skipping units, mixing formulas and not checking the answer. These habits can be changed in a few weeks.

This guide gives you a five-line method for Physics and Chemistry numericals that works from 9th class to FSc, followed by worked examples with every calculation shown, and a list of common errors. It applies to students of all Punjab boards, whatever the paper style.

The five-line method

Use the same lines for every numerical. Do not skip any.

1. Given. Write every number from the question with its symbol and unit. Convert units now, not later.
2. Required. Write what you must find, with its symbol.
3. Equation. Write the formula in symbols first. If you need two formulas, write both.
4. Substitution. Put the numbers in, with units. Calculate step by step.
5. Answer. Write the answer with its unit, rounded sensibly. Then do a quick sense check.

This is not extra work. It is the structure that examiners look for when they give marks, and it protects you from silly errors.

Worked examples: Physics

Example 1: Motion with constant acceleration

A car starts from rest and accelerates uniformly at 2 m/s² for 8 s. Find its final velocity and the distance covered.

• Given: u = 0 m/s, a = 2 m/s², t = 8 s
• Required: v and s
• Equations: v = u + at and s = ut + ½at²
• Substitution: v = 0 + (2 × 8) = 16 m/s. s = 0 + ½ × 2 × 8² = ½ × 2 × 64 = 64 m
• Answer: v = 16 m/s and s = 64 m

Check. Use a third equation: v² = u² + 2as gives 16² = 256 and 2 × 2 × 64 = 256, so both sides match. Sense check: 16 m/s is about 58 km/h, which is reasonable for a car after 8 seconds.

Example 2: Unit conversion before using F = ma

A body of mass 500 g accelerates at 4 m/s². Find the force.

• Given: m = 500 g = 500 ÷ 1000 = 0.5 kg, a = 4 m/s²
• Equation: F = ma
• Substitution: F = 0.5 × 4 = 2 N
• Answer: F = 2 N

The common mistake. Multiplying 500 × 4 = 2000 and calling it newtons. That is wrong by a factor of 1000, because the newton needs mass in kilograms. The conversion line in “Given” prevents this.

Example 3: Current, resistance and power

A resistor carries a current of 0.5 A when connected to a 12 V supply. Find its resistance and the power it uses.

• Given: I = 0.5 A, V = 12 V
• Equations: R = V / I and P = VI
• Substitution: R = 12 ÷ 0.5 = 24 Ω. P = 12 × 0.5 = 6 W
• Answer: R = 24 Ω and P = 6 W

Check. Use the other power formula: P = I²R = (0.5)² × 24 = 0.25 × 24 = 6 W. It matches.

Worked examples: Chemistry

In Chemistry the key move is to go through moles. Convert to moles, use the equation, then convert back. Atomic masses used below are H = 1, O = 16, Na = 23.

Example 4: Moles and number of molecules

How many moles and how many molecules are in 9 g of water?

• Molar mass of H₂O: (2 × 1) + 16 = 18 g/mol
• Moles: n = mass ÷ molar mass = 9 ÷ 18 = 0.5 mol
• Molecules: 0.5 × 6.02 × 10²³ = 3.01 × 10²³

Check. 9 g is half of 18 g, so half a mole, so half of Avogadro’s number. That is 3.01 × 10²³.

Example 5: Mass of product from a balanced equation

How many grams of water are formed when 4 g of hydrogen burns completely in oxygen? Equation: 2H₂ + O₂ → 2H₂O.

• Moles of H₂: molar mass of H₂ = 2 g/mol, so n = 4 ÷ 2 = 2 mol
• Mole ratio: 2 mol H₂ gives 2 mol H₂O (ratio 2 : 2)
• Mass of water: 2 mol × 18 g/mol = 36 g

Check. Oxygen used is 1 mol = 32 g. Reactants 4 g + 32 g = 36 g, and product is 36 g. Mass is conserved.

Example 6: Molarity

4 g of sodium hydroxide (NaOH) is dissolved in water to make 500 cm³ of solution. Find its molarity.

• Molar mass of NaOH: 23 + 16 + 1 = 40 g/mol
• Moles: 4 ÷ 40 = 0.1 mol
• Volume in dm³: 500 cm³ = 500 ÷ 1000 = 0.5 dm³
• Molarity: 0.1 ÷ 0.5 = 0.2 mol/dm³

Check. A 0.2 M solution of volume 0.5 dm³ contains 0.2 × 0.5 = 0.1 mol, which is what we started with.

Unit handling: the habits that save marks

• Convert first. Grams to kilograms, centimetres to metres, cm³ to dm³, minutes to seconds, before any formula.
• Carry units through every line. If units on both sides of an equation do not match, something is wrong. For v = u + at, m/s = m/s + (m/s²)(s), and every term is in m/s.
• Use the right g. Use the value your textbook uses in solved examples, or the value given in the question, and write it down.
• Use standard form for very big and very small numbers, as in 3.01 × 10²³, instead of writing many zeros.
• Round only at the end. Keep extra digits in the middle steps, then round the final answer to the number of significant figures your textbook uses.

Common errors, and the one-line fix for each

• Starting with numbers and no formula. Fix: always write the formula in symbols first.
• Using a formula from the wrong chapter. Fix: ask “which quantities are given?” and match them to the formula’s symbols.
• Forgetting to balance the equation in Chemistry. Fix: balance first, then take mole ratios.
• Using grams where moles are needed. Fix: first line of every Chemistry numerical is “convert to moles”.
• Calculator slips. Fix: do the calculation twice, once in a different order, or estimate roughly beforehand.
• No unit in the final answer. Fix: draw a box around the answer and write the unit inside the box.
• Copying a solution without trying. Fix: cover the solution, solve alone, and compare only after you finish.

Record each error in an error log. If you practise with past papers, the log method in how to use past papers for science will show you which error is your most common one.

A practice routine that builds speed

1. Watch one solved example and pause it before the answer appears. Try the next step yourself.
2. Solve three similar questions using the five-line method, on paper.
3. Mark and fix. Redo any wrong one after two days, without looking.
4. Mix topics once a week so you learn to pick the right formula, not just repeat one.
5. Time yourself in the last month: a numerical of 4 to 5 marks should not take you more than a few minutes.

If a step is not clear, ask. A short doubt solved the same day saves an hour later. An AI tutor such as Ustad Gee can explain a step in Urdu or Roman Urdu, but always check it against your textbook, as explained in AI tutor for students in Pakistan.

For all Punjab boards and all levels

The method does not depend on the paper pattern of your board, only on the textbook. The same five lines work from 9th class Physics to FSc Part 2 Chemistry.

Creative Taleem’s lectures solve numericals step by step and the app has 2 lakh+ MCQs across Matric and FSc to practise afterwards. See the pricing page for open batches, or the guide to choosing an online academy for science.

Frequently asked questions