Most lost marks in calculation questions come from the maths, not the physics. Learn these, then try the 12 practice questions at the bottom.
1. Rearranging equations
- Golden rule: whatever you do to one side, do to the other.
- Undo in reverse order: to get v on its own in Eₖ = ½mv², first multiply by 2, then divide by m, then square root: v = √(2Eₖ ÷ m).
- Tip: it’s often easier to put the numbers in first, then rearrange. You get a mark for the correct substitution either way.
- Squared or square-rooted? If the unknown is squared (v², e², I²), square-root at the very end. Forgetting this is one of the most common errors.
2. Unit conversions
Always convert to standard units before you substitute.
| Quantity | Convert | How |
|---|---|---|
| Time | minutes → s; hours → s | × 60; × 3600 |
| Length | mm → m; cm → m; km → m | ÷ 1000; ÷ 100; × 1000 |
| Mass | g → kg; tonnes → kg | ÷ 1000; × 1000 |
| Area | cm² → m² | ÷ 10 000 |
| Volume | cm³ → m³; litres → m³ | ÷ 1 000 000; ÷ 1000 |
| Energy | kJ → J; MJ → J | × 1000; × 106 |
| Power | kW → W; MW → W | × 1000; × 106 |
| Current | mA → A | ÷ 1000 |
| Speed | km/h → m/s | ÷ 3.6 |
3. Standard form
- A number between 1 and 10, multiplied by a power of 10: 6 200 000 = 6.2 × 106; 0.00045 = 4.5 × 10−4.
- On a calculator use the ×10x (or EXP) key: type 3.0 ×10x 8 for 3.0 × 108. Don’t type “× 10” as well.
- Use brackets when dividing by a number in standard form.
4. Significant figures
- Give your answer to the same number of significant figures as the least precise data in the question (usually 2 or 3).
- Count from the first non-zero digit: 0.04672 to 2 s.f. is 0.047.
- Don’t round in the middle of a multi-step calculation – keep the full calculator value until the end.
5. Graphs
- Gradient = change in y ÷ change in x. Use a large triangle for accuracy.
- Curved line: draw a tangent (a straight line just touching the curve) and find its gradient.
- Area under a velocity–time graph = distance travelled (HT). Split into rectangles and triangles.
- Directly proportional: a straight line through the origin. Inversely proportional: doubling one quantity halves the other.
6. Percentages and efficiency
- Efficiency = useful ÷ total. Multiply by 100 for a percentage. It can never be more than 1 (100%).
- Percentage difference = (difference ÷ true value) × 100.
Practice questions
Q1 Rearrange V = IR to make I the subject.
Show answer
Divide both sides by R: I = V ÷ R
Q2 Rearrange Eₖ = ½mv² to make v the subject.
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× 2: 2Eₖ = mv²
÷ m: v² = 2Eₖ ÷ m
√: v = √(2Eₖ ÷ m)
Q3 Convert 2.5 km to metres and 45 minutes to seconds.
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2.5 × 1000 = 2500 m; 45 × 60 = 2700 s
Q4 Convert 350 g to kg and 25 cm to m.
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350 ÷ 1000 = 0.35 kg; 25 ÷ 100 = 0.25 m
Q5 Convert 1.2 kW to W and 3.5 MJ to J (in standard form).
Show answer
1.2 × 1000 = 1200 W; 3.5 × 106 J
Q6 A block’s base is 500 cm². What is this in m²?
Show answer
1 m² = 10 000 cm², so 500 ÷ 10 000 = 0.05 m². (Not ÷ 100 – that’s a common mistake.)
Q7 Write 0.00045 and 6 200 000 in standard form.
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4.5 × 10−4 and 6.2 × 106
Q8 Calculate (3.0 × 108) × (2.0 × 10−3).
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3.0 × 2.0 = 6.0; 108 × 10−3 = 105, so 6.0 × 105
Q9 Round 0.04672 to 2 s.f. and 23 856 to 3 s.f.
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0.047 and 23 900
Q10 A velocity–time graph is a straight line from (0 s, 0 m/s) to (8.0 s, 24 m/s). Find the acceleration.
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Gradient = 24 ÷ 8.0 = 3.0 m/s²
Q11 A motor gives 450 J of useful energy from 600 J supplied. Calculate its efficiency as a percentage.
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450 ÷ 600 = 0.75 → 75%
Q12 A student measures the specific heat capacity of water as 4410 J/kg °C. The true value is 4200 J/kg °C. Calculate the percentage difference.
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Difference = 4410 − 4200 = 210
(210 ÷ 4200) × 100 = 5%
