7 rearranging mistakes that cost GCSE physics marks

By Mehmood Kakar · Updated 14 November 2026

These are the rearranging slips that come up again and again in GCSE physics answers. Each one is easy to fix once you know to look for it. If you are new to rearranging, start with how to rearrange physics equations, then come back to this list.

1. Flipping a division the wrong way

Density is ρ = m ÷ V. To find mass, students sometimes write m = ρ ÷ V or m = V ÷ ρ. The mass was being divided by V, so the fix is to multiply both sides by V.

2. Dividing by only one term

In E_p = mgh, the height is multiplied by both m and g. To get h on its own, you must divide by both.

The same applies to ΔE = mcΔθ: to find c, divide by m and by Δθ.

3. Losing the 2 from ½

Kinetic energy and elastic potential energy both have a ½. When you rearrange, the ½ becomes a 2 on the other side. Leave it out and your answer is wrong by a factor of 2.

4. Missing the square root

This is the big one. When the letter you want is squared, the last step is always a square root. Students work through to v² = 900, then write v = 900 m/s.

A quick sense check catches it: a tennis ball at 900 m/s would be faster than a bullet. The kinetic energy calculator flags the square root as its own step.

5. Square-rooting too early

The opposite problem: taking the square root before everything else is cleared from that side. In E_e = ½ke², you must get e² completely on its own before you square-root.

Put the whole fraction inside the square root sign, and use brackets on your calculator.

6. Moving a term without changing its sign

This shows up in v² − u² = 2as (Higher). To find v², add u² to both sides. Students sometimes carry it across as a minus.

Remember the rule: you never "move" a term, you do the same operation to both sides. The u² was subtracted, so you add it.

7. Typing it into the calculator wrongly

Sometimes the rearrangement on paper is perfect and the calculator still gives the wrong answer. For h = E_p ÷ (m × g), typing E_p ÷ m × g divides by m and then multiplies by g.

Work out the bottom line first and write it down, or use brackets. Both make the step visible to the examiner too.

One check that catches them all

Put your answer back into the original equation along with the values you were given. If both sides match, your rearrangement was right. If they don't, look at the seven mistakes above; it will almost always be one of them.

Then ask whether the answer is sensible. A runner's mass of 0.7 kg, a spring stretched by 50 m, or a kettle with a power of 0.0003 W all point to a rearranging slip.

Spot the mistake

Each rearrangement below has one error. Click to see which it is.