Physics numericals for 10th class board exam Pakistan — learn the step-by-step method to solve numerical problems in electricity, optics, and mechanics.

How to Solve Physics Numericals in 10th Class — Step by Step Guide

Quick Answer: To solve physics numericals in 10th class, follow five steps: (1) write down all given values with units, (2) identify what you need to find, (3) choose the correct formula, (4) substitute values carefully, and (5) check units in your answer. Practice this method on 5 numericals daily for two weeks before the board exam.

Physics numericals are where many 10th class students drop marks unnecessarily. The problems look intimidating, but almost every numerical in the BISE board paper follows a predictable pattern. Once you understand the method — not just the formulas — you can solve them systematically and confidently.

This guide walks you through the step-by-step approach for every major topic in 10th class physics numericals.

The Universal Method for Any Physics Numerical

Before diving into specific chapters, you need to internalize a consistent method that works for every numerical, regardless of topic. Students who follow this method make far fewer errors in exams.

Step 1: List the Given Information

Read the problem once slowly. Then write down every piece of information the problem provides, with correct units and symbols. For example: V = 12 V, R = 4 Ω, I = ?

Do not skip this step even if it seems obvious. Writing given information forces your brain to process the problem clearly before you start calculating.

Step 2: Identify the Unknown

Write clearly what you are looking for. If the problem asks for current, write: Find: I = ?

Step 3: Select the Correct Formula

Identify which formula connects your given values to your unknown. For electricity: V = IR. For optics: 1/f = 1/v + 1/u. Write the formula before substituting anything.

Step 4: Rearrange the Formula

If needed, rearrange the formula to isolate the unknown. If you need R and you have V and I: R = V/I.

Step 5: Substitute and Calculate

Put the numbers in. Show every arithmetic step. Do not skip steps — in board exams, you get marks for working even if your final answer has a small error.

Step 6: Write the Answer with Units

A numerical answer without units is incomplete. Always write the unit — amperes, ohms, metres, joules, watts, etc.

This method takes 30 seconds longer per problem but eliminates the most common errors: using the wrong formula, substituting in the wrong place, and forgetting units.

Electricity Numericals — Chapter-wise Guide

Electricity is the most numerically heavy chapter in 10th class physics. Here are the key formulas and how to apply them.

Ohm's Law

Formula: V = IR

V = Voltage (volts, V)
I = Current (amperes, A)
R = Resistance (ohms, Ω)

Example: A bulb has resistance 60 Ω. It is connected to a 240 V supply. Find the current.

Given: R = 60 Ω, V = 240 V
Find: I = ?
Formula: I = V/R = 240/60 = 4 A

Series and Parallel Circuits

Series: R_total = R₁ + R₂ + R₃ (Current is same through all) Parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ (Voltage is same across all)

Electrical Power and Energy

Power: P = IV = I²R = V²/R (units: watts, W)
Energy: E = Pt (units: joules, J or kilowatt-hours, kWh)
1 kWh = 3.6 × 10⁶ J

Common exam question: An electric heater draws 5 A from a 230 V supply. How much energy does it use in 2 hours?

P = IV = 5 × 230 = 1150 W = 1.15 kW
E = Pt = 1.15 kW × 2 h = 2.3 kWh

Joule's Law of Heating

Heat = I²Rt (Heat produced in joules)

This appears frequently in questions about household appliances.

Optics Numericals — Lenses and Mirrors

Optics numericals follow very predictable patterns in BISE papers. The sign convention trips many students up — learn it properly once and you will not struggle again.

Mirror Formula

1/f = 1/v + 1/u

f = focal length
v = image distance
u = object distance

Sign Convention (New Cartesian):

Distances measured in direction of incident light: positive
Distances measured against incident light: negative
For concave mirror: f is negative, centre of curvature is negative
For convex mirror: f is positive

Lens Formula

1/f = 1/v − 1/u (same formula, different sign convention for lenses)

For lenses, the New Cartesian convention is:

Object on left: u is negative
Real image on right: v is positive
Virtual image on left: v is negative
Convex lens: f is positive
Concave lens: f is negative

Magnification

m = v/u (for mirrors)
m = v/u (for lenses)
If m is positive: image is upright
If m is negative: image is inverted
|m| > 1: image is magnified
|m| < 1: image is diminished

Example: An object is placed 30 cm in front of a convex lens of focal length 10 cm. Find image distance.

Given: u = −30 cm, f = +10 cm
Formula: 1/v = 1/f + 1/u = 1/10 + 1/(−30) = 3/30 − 1/30 = 2/30
v = 15 cm (positive, so real image on the other side)

Mechanics and Motion Numericals

Motion questions in 10th class physics are straightforward if you know the equations and can identify which one to use from the given information.

Equations of Motion

v = u + at
s = ut + ½at²
v² = u² + 2as

Where:

u = initial velocity (m/s)
v = final velocity (m/s)
a = acceleration (m/s²)
s = displacement (m)
t = time (s)

Key tip: If the problem says "starts from rest," then u = 0. If it says "comes to rest," then v = 0. These simplify calculations significantly.

Newton's Second Law

F = ma

F = force (newtons, N)
m = mass (kg)
a = acceleration (m/s²)

Gravitational Potential Energy and Kinetic Energy

PE = mgh (potential energy)
KE = ½mv² (kinetic energy)
W = Fs (work done)
P = W/t (power)

For board exam numericals involving energy, always check whether energy is conserved (no friction mentioned) or if work is done against friction.

Common Mistakes to Avoid in Physics Numericals

Understanding what goes wrong for other students helps you avoid the same traps in your exam.

Mistake 1: Not converting units before calculating If the problem gives time in minutes and you need seconds, convert before substituting. Always work in SI units (metres, kilograms, seconds) unless the question specifies otherwise.

Mistake 2: Forgetting the sign convention in optics This is the most common optics error. Make it a habit to write the sign convention at the top of every optics problem before you start.

Mistake 3: Using the wrong formula for series vs parallel Remember: resistance adds in series (simple addition), adds reciprocally in parallel (add the fractions, then take reciprocal).

Mistake 4: Stopping after the number, forgetting the unit Board examiners specifically mark units. "4" without "A" (amperes) gets partial marks at best.

Mistake 5: Rounding too early Keep 3-4 significant figures throughout your calculation and round only the final answer. Rounding intermediate steps introduces errors that compound.

Practice 5 numericals every day, from different chapters. Use past papers from the SSC Results era to find the most commonly repeated numerical types.

Frequently Asked Questions

Q: How many numericals appear in 10th class physics board paper? A: Typically 3-5 numericals appear in Section B (short questions) and 1-2 may appear in Section C (long questions). Electricity and optics are the most common sources.

Q: Do I need to memorize all physics formulas? A: Yes. The BISE board exam does not provide a formula sheet. Focus on 20-25 core formulas across electricity, optics, and motion, and make sure you can write them from memory.

Q: Can I score full marks in numericals without understanding theory? A: Partially, but not fully. Some numerical questions require you to explain the physics (e.g., why resistance increases with temperature). Theory and numericals support each other.

Q: What if I get the wrong answer in a numerical? A: Still show all your working. BISE examiners award method marks even if the final answer is wrong. A student who shows correct working but makes one arithmetic error will get more marks than one who just writes the final answer.

Q: Are 10th class physics numericals harder than 9th class? A: 10th class numericals are slightly more complex because they involve more formula combinations. But the method is identical — if you mastered the approach in 9th class, 10th class is a natural extension.

Q: How important are units in physics numericals? A: Extremely important. Every answer must include correct units. In some marking schemes, a correct numerical answer without units gets zero marks for that part of the question.

Q: Should I practice numericals from textbook or past papers? A: Both. Start with textbook exercise numericals to understand the method. Then move to past papers to practice under exam conditions. The 10th Class Result 2026 page has board information that can help you identify which board's papers to prioritize.