Many Physics students can state a law and still lose marks when a number is attached to it. The usual reasons are not mysterious: the wrong equation, a unit left unconverted, a rearrangement slip, an answer rounded too early or a result that was never checked for sense. Each of these can be reduced with a fixed method, which is what this guide sets out for Cambridge International A Level Physics (9702).
It focuses on solving calculations, not on timing or revision tools. Every step is shown in full across five worked examples, from a mechanics question to a decay calculation. The guide belongs to our wider series on A Level exam technique by subject, which explains why technique depends on the type of question, and it parallels our guides to common A Level Mathematics exam mistakes and A Level Biology practical and data questions.
The questions below are illustrations written for this guide, not questions from a past paper. Syllabuses and papers change, so check the current requirements on our A Level Physics page and in the official syllabus before relying on any detail.
What the 9702 Syllabus Says About Calculations
Several points that affect calculations are written into Cambridge's syllabus document for 9702, for examinations in 2025, 2026 and 2027, as checked on 27 October 2026. Always read the version that applies to your own exam year on Cambridge's 9702 syllabus page.
| Topic | What the syllabus says |
|---|---|
| Algebra and units | Candidates should be able to change the subject of an equation, substitute physical quantities into physical equations using consistent units and check the dimensional consistency of equations |
| Arithmetic | Candidates should use standard form, understand how to perform calculations so that significant figures are neither lost unnecessarily nor carried beyond what is justified, and use approximations to check the magnitude of results |
| Significant figures | If the least precise measured quantity has n significant figures, then n or n + 1 significant figures are appropriate for a calculated value (the syllabus gives this rule in its practical assessment section) |
| Data and formulae | A data sheet appears on page 2 of Papers 1, 2 and 4, with values such as g = 9.81 m s⁻². It lists only some formulae, such as s = ut + ½at² and v² = u² + 2as. Many others, including v = u + at and F = ma, are not on the sheet |
| Command words | Calculate means work out from given facts, figures or information. Determine means establish an answer using the information available. Show (that) means provide structured evidence that leads to a given result |
The data sheet row is the most useful for revision. Because the sheet is limited, you need a short list of equations you can recall without help, plus the habit of checking what is supplied. The list on the sheet may change between syllabuses, so look at the data sheet in a recent paper for your own year.
A Repeatable Method for Any Calculation
- 1
Read and list. Write each quantity with its symbol and unit, and mark the one you need to find. Convert to SI units now, not later.
- 2
Choose the equation. Match the equation to the quantities you have and want, and check whether it is given on the data sheet.
- 3
Rearrange in symbols. Make the unknown the subject before substituting. It reduces arithmetic slips and gives the method mark clearly.
- 4
Substitute with units. Write the numbers into the rearranged equation, with their units.
- 5
Calculate and round. Keep the unrounded value, then give the answer to a justified number of significant figures with its unit.
- 6
Check. Ask whether the size, sign and unit make sense. Substitute back if you can.
The method looks long, but written out it takes only a few lines. Its value is that you never have to wonder what to do next, which leaves your attention free for the physics.
Units and Conversions Before You Start
A large share of numerical errors are unit errors, so convert first. The table lists conversions that come up often. The area and volume rows are where most mistakes happen, because the conversion factor is squared or cubed.
| Quantity | Conversion to SI |
|---|---|
| Speed in km h⁻¹ | Divide by 3.6 to give m s⁻¹, since 1 km h⁻¹ = 1000 m ÷ 3600 s |
| Length in cm | Multiply by 10⁻² to give m |
| Area in cm² | Multiply by 10⁻⁴ to give m², because (10⁻²)² = 10⁻⁴ |
| Volume in cm³ | Multiply by 10⁻⁶ to give m³, because (10⁻²)³ = 10⁻⁶ |
| Mass in g | Multiply by 10⁻³ to give kg |
| Time in ms, µs | Multiply by 10⁻³ or 10⁻⁶ to give s |
Where the question supplies data, the syllabus says candidates should use units consistent with those supplied, and should not convert to other systems of units unless the question asks. That is a reason to be consistent, not to avoid conversion where the equation needs SI.
Worked Example 1: Choosing the Equation (Kinematics)
| Step | Working |
|---|---|
| List the data | u = 72 km h⁻¹ = 72 ÷ 3.6 = 20 m s⁻¹, v = 0, s = 40 m, a = ? |
| Choose the equation | No time is given, so use v² = u² + 2as, which is on the data sheet |
| Rearrange | a = (v² − u²) ÷ (2s) |
| Substitute | a = (0² − 20²) ÷ (2 × 40) = −400 ÷ 80 |
| Answer (a) | a = −5.0 m s⁻². The deceleration is 5.0 m s⁻², and the negative sign shows it acts against the motion |
| Part (b) | Use v = u + at, so t = (v − u) ÷ a = (0 − 20) ÷ (−5.0) = 4.0 s |
| Check | The average speed is (20 + 0) ÷ 2 = 10 m s⁻¹, and 10 × 4.0 = 40 m, which matches the stopping distance |
The common slip here is using 72 directly. That gives a deceleration of 72² ÷ 80, about 65 m s⁻², which is far larger than any car could produce. The magnitude check in the final row is worth making a habit. Notice also that part (b) uses the exact value of a, so no rounding error enters. The equation v = u + at is not on the data sheet, so it has to be recalled.
Worked Example 2: Unit Conversion and Standard Form (Density)
| Common mistake | Corrected method |
|---|---|
| Volume = 5.0 × 4.0 × 2.0 = 40, so density = 0.312 ÷ 40 = 0.0078 kg m⁻³. | Volume = 5.0 × 4.0 × 2.0 = 40 cm³ = 40 × 10⁻⁶ m³ = 4.0 × 10⁻⁵ m³. Density = m ÷ V = 0.312 ÷ (4.0 × 10⁻⁵) = 7800 kg m⁻³ = 7.8 × 10³ kg m⁻³ |
The mistake is to use a volume in cm³ with a mass in kg, so the units no longer match. A quick check shows the problem: a density of 0.0078 kg m⁻³ would be far lighter than air, and the block is clearly not. Writing the answer in standard form, 7.8 × 10³ kg m⁻³, also avoids implying more precision than the data support. The dimensions are given to two significant figures, so two significant figures is justified.
Worked Example 3: Keeping Unrounded Values (Electric Circuits)
| Step | Working |
|---|---|
| Parallel pair | 1 ÷ R = 1 ÷ 6.0 + 1 ÷ 12 = 0.25 Ω⁻¹, so R = 1 ÷ 0.25 = 4.0 Ω |
| Total resistance | R_total = 4.0 + 4.0 = 8.0 Ω |
| Part (a) | I = V ÷ R = 9.0 ÷ 8.0 = 1.125 A, so I = 1.1 A to two significant figures |
| Part (b) | V = IR = 1.125 × 4.0 = 4.5 V, using the unrounded current |
| Check | The p.d. across the 4.0 Ω resistor is also 1.125 × 4.0 = 4.5 V, and 4.5 + 4.5 = 9.0 V, which equals the cell p.d. |
Two mistakes are typical. One is to stop at 1 ÷ R = 0.25 and treat that as the resistance, forgetting to take the reciprocal. The other is to use the rounded 1.1 A in part (b), which gives 4.4 V, a small but avoidable discrepancy. The syllabus asks that significant figures are not lost unnecessarily, and carrying the unrounded value is the simplest way to follow that. The resistors in series and parallel formulae are on the data sheet.
Worked Example 4: Multi-Step Reasoning (Energy, Power and Efficiency)
| Step | Working |
|---|---|
| Plan | Efficiency = useful output power ÷ input power. Find the work done on the load first, then the power |
| Gain in gravitational potential energy | ΔE = mgΔh = 25 × 9.81 × 12 = 2943 J (using g = 9.81 m s⁻² from the data sheet) |
| Useful power | P = E ÷ t = 2943 ÷ 8.0 = 367.9 W (keep 367.875 in the calculator) |
| Efficiency | 367.875 ÷ 450 = 0.8175, which is 82% to two significant figures |
| Check | Efficiency must be below 100%, and 82% is plausible for a motor |
Multi-step questions are marked for the chain of reasoning as well as the answer. Writing the plan in one line shows the examiner your method even if an arithmetic slip follows. Efficiency has no unit, so give it as a percentage or a decimal fraction. A result above 100% would immediately tell you that something has gone wrong.
Worked Example 5: Show That, Then Use the Result (Radioactive Decay)
| Step | Working |
|---|---|
| Part (a) equation | λ = 0.693 ÷ t½ (this appears on the Paper 4 formulae page) |
| Substitute | λ = 0.693 ÷ 5.3 = 0.1308 year⁻¹, so λ = 0.13 year⁻¹ |
| Part (b) equation | x = x₀e^(−λt), so the fraction remaining is x ÷ x₀ = e^(−λt) |
| Substitute | e^(−0.1308 × 10) = e^(−1.308) = 0.270 |
| Answer | About 0.27, or 27%, of the original nuclei remain |
| Check | 10 years is almost two half-lives (10 ÷ 5.3 = 1.9), and two half-lives leave 25%, so 27% is sensible |
In a 'show that' question, the answer is given, so the marks are for the working. Show the substitution and give the value to at least one more significant figure than the quoted result (0.1308 before 0.13). The command word is defined in the syllabus as providing structured evidence that leads to a given result. In part (b), use the unrounded decay constant, and make sure the time and the half-life are in the same unit, years here. The magnitude check in the last row uses the idea of half-lives, which gives a quick independent estimate.
Significant Figures and the Final Answer
Significant figures are a source of avoidable doubt, so use a simple rule. Round the final answer, and only the final answer. Give it to the same number of significant figures as the least precise data, or one more, which matches the syllabus guidance that n or n + 1 significant figures are appropriate. In Example 1 the speed has two significant figures, so 5.0 m s⁻² is suitable.
| Situation | Sensible practice |
|---|---|
| Data given to 2 or 3 significant figures | Answer to 2 or 3 significant figures |
| Intermediate steps in a multi-part question | Keep extra figures in the calculator and write down 3 or 4 in your working |
| A very large or small answer | Use standard form, such as 7.8 × 10³ kg m⁻³ |
| A 'show that' result | Give one more figure than the quoted value before stating it |
Common Mistakes at a Glance
| Mistake | What to do instead |
|---|---|
| Using km h⁻¹, cm³ or g in an SI equation | Convert to m s⁻¹, m³ and kg before substituting |
| Squaring or cubing the numbers but not the conversion factor | Convert cm² with 10⁻⁴ and cm³ with 10⁻⁶ |
| Forgetting to take the reciprocal for parallel resistors | Find 1 ÷ R first, then invert it |
| Rounding early and using the rounded value later | Keep the unrounded value until the final step |
| Substituting numbers before rearranging | Rearrange in symbols first so the method is visible |
| Leaving out the unit or giving the wrong one | Write the unit with every substituted value and with the answer |
| Not checking size or sign | Estimate the answer and ask whether it is physically sensible |
| Calculator in the wrong angle mode | Check degrees or radians before any trigonometric calculation |
How to Practise Calculations
The way to improve is to solve real questions and mark them honestly. Choose calculation questions from our A Level past papers pages, write each solution in the format above and compare it with the official mark scheme line by line. Mark schemes award method marks and answer marks separately, so a correct method with a slip still earns credit, while a bare answer may not.
Keep a log of where marks were lost, in categories such as unit conversion, rearranging, rounding and equation choice. Then redo the questions you missed a week later without looking at the solution. If a question involves experimental data as well, our guide to A Level Biology practical and data questions covers the same habits of tables, units and evidence in a different subject, and our A Level practice pages offer extra questions. Returning to our guide to A Level exam technique by subject is a good way to see how calculation papers differ from other formats, and our guide to common A Level Mathematics exam mistakes deals with the algebra and rounding errors that Physics calculations share.
Practise the subjects you choose
Work through topic questions and past papers for your A Level subjects, and get your answers marked with the reasoning behind each mark.
