GCSE Physics — Maths Skills 🧮

🔣 What Do the Symbols Mean?

Physics equations use letters and symbols that look mysterious until you know the code. Here's the whole dictionary.

💬 "Δ is not a mountain. λ is not a letter. ρ is not a pi. Once you know what each symbol means, the equations stop being scary and start being useful."

Click any symbol to see its full meaning and which equations it appears in:

Δ

Delta

λ

Lambda

ρ

Rho

η

Eta

∝

Proportional

≈

Approx.

²

Squared

√

Square root

α

Alpha

β

Beta

γ

Gamma

θ

Theta

Ω

Omega

μ

Mu / Micro

∑

Sigma / Sum

⊥

Perpendicular

👆 Click any symbol above — it'll show you exactly what it means and which equations use it.

📋 Letter Variables — Quick Reference

F — Force (N)

m — Mass (kg)

a — Acceleration (m/s²)

v — Velocity/speed (m/s)

t — Time (s)

d / s — Distance (m)

E — Energy (J)

P — Power (W)

W — Weight OR Work done (N or J)

g — Gravitational field (9.8 N/kg)

h — Height (m)

V — Voltage (V)

I — Current (A)

R — Resistance (Ω)

Q — Charge (C)

p — Momentum (kg m/s)

f — Frequency (Hz)

T — Period (s) OR Temperature (K/°C)

c — Specific heat capacity (J/kg°C)

L — Specific latent heat (J/kg)

n — Number of turns (transformer)

A — Area (m²) OR Mass number (atomic)

Z — Atomic / proton number

ρ — Density (kg/m³)

➗ The Four Operations — and the Others

Every equation is built from a small set of operations. Know what each one means and how to undo it.

💬 "Equations are just sentences with numbers. × means 'groups of', ÷ means 'shared between', = means 'the same as'. Once you see it that way, rearranging stops being magic."

+

Addition

Adds two quantities together

V_total = V₁ + V₂

−

Subtraction

Finds the difference

ΔT = T_final − T_initial

×

Multiplication

Also written as · or nothing: ma = m×a

F = m × a

÷

Division

Also written as a fraction: F/m

a = F ÷ m

x²

Squared

Multiply x by itself: x × x

v² = 20² = 400

√

Square root

Undoes squaring: √(x²) = x

v = √(2KE/m)

∝

Proportional to

As one goes up, the other goes up at the same rate

F ∝ a (if m fixed)

Δ

Delta = Change

Just means final − initial

ΔT = T_f − T_i

The inverse rule — undoing operations:

To undo × → use ÷
F=ma → a=F÷m

To undo ÷ → use ×
a=F/m → F=a×m

To undo + → use −
V=V₁+V₂ → V₁=V−V₂

To undo x² → use √
v²=2as → v=√(2as)

🔺 Formula Triangles — The Cover-Up Method

Cover the letter you want to find. What's left shows you the calculation. Works for any three-variable equation.

💬 "Formula triangles are not cheating. They're a memory tool. Physics teachers use them. Examiners use them. Use them."

How to use it: Put the three quantities in the triangle (one on top, two on bottom). To find any one of them, cover it with your thumb — what you can see is the formula you need. Side by side = multiply. One above the other = divide (top ÷ bottom).

Click a variable to find — it shows you the rearranged formula:

Click directly on any variable in the triangle

Select a formula above, then click a variable in the triangle to see the rearrangement.

↔️ Rearranging Equations — Step by Step

One rule governs everything: whatever you do to one side, you must do to the other. That's it.

💬 "An equation is a balance. Both sides weigh the same. If you add 5 to the left, add 5 to the right. If you divide the left by m, divide the right by m. The balance must stay balanced."

The Golden Rule: Whatever you do to one side of the = sign, you must do to the other side. Every time. No exceptions.

Pick a formula and the variable you want to solve for — see every algebraic step:

Solve for:

² Powers and √ Roots

Squaring and square-rooting trip up more students than almost anything else. Here's how to handle them confidently.

💬 "KE = ½mv². The v² is not optional. Forgetting to square the velocity is the single most common calculation error in GCSE Physics. Write it down. Square it. Then multiply."

x² — Squaring

x² = x × x

Multiply the number by itself

3² = 9 (3×3)

5² = 25 (5×5)

10² = 100

20² = 400 ← exam common

0.5² = 0.25 (less than 1!)

√ — Square Root

√x = the number that × itself gives x

Undoes squaring. Use the √ button on your calculator.

√9 = 3

√25 = 5

√100 = 10

√400 = 20

√900 = 30

Rearranging with v² — worked example (KE = ½mv²):

1

KE = ½ × m × v²

Start here

2

2 × KE = m × v²

Multiply both sides by 2 (to remove the ½)

3

2KE ÷ m = v²

Divide both sides by m

4

v = √(2KE ÷ m)

Square root both sides to find v

Try it — square root calculator:

→

√ = ?

×10 Standard Form

Big and small numbers written as a number between 1 and 10, multiplied by a power of 10.

💬 "The speed of light is 300,000,000 m/s. Or 3 × 10⁸ m/s. One of these fits on an exam paper without causing a crisis. Standard form is just a tidy way to write very large or very small numbers."

How to write in standard form

Write the digits with a decimal point after the first digit
Count how many places the decimal moved
That count is your power of 10
Moving left = positive power, moving right = negative

Common examples in physics

3×10⁸ m/s — speed of light

1.6×10⁻¹⁹ C — electron charge

6×10²⁴ kg — mass of Earth

1×10⁻¹⁰ m — size of atom

Standard form converter — type a number:

→

Type a number →

Multiplying in standard form:

      (3×10⁴) × (2×10³) = (3×2) × 10^(4+3) = 6×10⁷

      (6×10⁸) ÷ (2×10³) = (6÷2) × 10^(8-3) = 3×10⁵

Multiply/divide the front numbers normally. Add the powers when multiplying, subtract when dividing.

kMG Unit Prefixes

Prefixes are shortcuts for very large or very small numbers. kW means kilowatts — 1000 watts. They're everywhere in physics.

💬 "kilo = × 1000. So 2 kW = 2000 W. Milli = ÷ 1000. So 5 mA = 0.005 A. Get this wrong and every answer is off by a factor of 1000. Worth 30 seconds of your time."

Prefix	Symbol	Meaning	As a power	Example in physics
G	G	× 1,000,000,000	×10⁹	GHz (gigahertz, processor speed)
M	M	× 1,000,000	×10⁶	MHz (megahertz, radio frequency)
k	k	× 1,000	×10³	kW, kJ, km, kg
—	—	× 1 (base unit)	×10⁰	W, J, m, kg
c	c	÷ 100	×10⁻²	cm (centimetres)
m	m	÷ 1,000	×10⁻³	mA (milliamps), mm, mJ
μ	μ	÷ 1,000,000	×10⁻⁶	μA (microamps), μm
n	n	÷ 1,000,000,000	×10⁻⁹	nm (nanometres, wavelength of light)

Always convert to base units before putting into a formula.
Formula needs Watts? Convert kW → W first (×1000). Needs metres? Convert cm → m first (÷100). Do this BEFORE substituting, not after.

🔄 Unit Conversions — the Mark Dropper

Exam questions almost always give you values in non-standard units to catch you out. This is where marks are lost.

💬 "The question says '3 minutes'. The formula needs seconds. You use 3. You lose marks. Every year. Thousands of students. Don't be those students."

Live converter — type a value and select the conversion:

= ?

The Most Dropped Mark: Time Conversions

× 60

minutes → seconds

3 min = 180 s

× 3600

hours → seconds

2 hr = 7200 s

÷ 1000

g → kg

250 g = 0.25 kg

⚠️ The Most Common Maths Mistakes

These exact errors appear in mark schemes every year. Recognise them and you're already ahead.

💬 "Examiners release reports listing the most common mistakes. These are literally taken from those reports. They are not guesses."

❌ Not squaring v in KE = ½mv²
KE = ½ × 10 × 20 = 100 J → KE = ½ × 10 × 20² = ½ × 10 × 400 = 2000 J
Square the velocity FIRST, before doing anything else. Write v² = 20² = 400 on a separate line.

❌ Using minutes instead of seconds
E = 500 × 3 = 1500 J → E = 500 × 180 = 90,000 J (3 min = 180 s)
Every formula using time needs seconds. If the question says minutes or hours, convert BEFORE substituting.

❌ ΔT — using final temperature, not change
E = 2 × 4200 × 80 = 672,000 J → ΔT = 80 − 20 = 60°C → E = 2 × 4200 × 60 = 504,000 J
ΔT means CHANGE. Always final − initial. Write it out.

❌ Confusing weight (N) and mass (kg)
W = 70 N → W = mg = 70 × 9.8 = 686 N
Mass is in kg. Weight is in N. Use W = mg to find weight from mass. Never write "70 kg" as a weight.

❌ Efficiency over 100%
Eff = (800 ÷ 600) × 100 = 133% → Eff = (600 ÷ 800) × 100 = 75%
Efficiency = useful ÷ total. USEFUL is always less than total. If you get >100%, you divided the wrong way round.

❌ Forgetting to convert g to kg
ρ = 200 ÷ 0.4 = 500 kg/m³ → 200 g = 0.2 kg → ρ = 0.2 ÷ 0.4 = 0.5 kg/m³
Density formula ρ=m/V needs kg and m³. Always convert g→kg (÷1000) and cm³→m³ (÷10⁶) first.

❌ Rearranging incorrectly — only moving one term
F = ma → m = F + a → F = ma → m = F ÷ a
To isolate m, divide both sides by a — not add. Whatever operation connects letters, use its inverse to separate them.

The 30-second checklist before submitting any calculation:

Did I convert all units to base units (seconds, metres, kg, watts)?
Did I square any velocities in KE = ½mv²?
Is my ΔT a change, not a final value?
Is my answer a sensible size? (KE of a car shouldn't be 50 J)
Did I include the unit in my answer?

✅ Maths Skills Quiz

Five questions on the skills, not the physics — pure maths technique.

1. Rearrange V = I × R to make I the subject.

2. A question gives you time as 4 minutes. What value goes into your formula?

3. KE = ½mv². Mass = 5 kg, speed = 6 m/s. What is the first calculation to do?

4. Water is heated from 20°C to 80°C. What is ΔT for the formula E = mcΔT?

5. Rearrange KE = ½mv² to find v. What is the correct form?

Maths Skills for Physics 🧮