A Level Physics 9702 Calculations: Units, Graphs and Uncertainties

A correct formula can still produce a wrong answer if a length is entered in centimetres instead of metres, or a radius is mistaken for a diameter. Make your working a sequence you can inspect: quantities, assumptions, equation, conversion, substitution and final check. The original examples below focus on that process.

Start with the model, not the calculator

For every question, identify what is changing and which assumptions make the chosen relationship valid. Constant-acceleration equations need constant acceleration over the interval. A circuit calculation needs you to identify which components share a current or potential difference. Write the unknown symbol before searching for an equation, so you know what the calculation must produce.

Worked motion calculation

A trolley starts from rest and travels 1.80 m in 1.50 s with constant acceleration. From s = ut + ½at² and u = 0, rearrange to a = 2s/t². Substitute to get a = (2 × 1.80)/(1.50)² = 1.60 m s⁻². The final speed is v = u + at = 2.40 m s⁻¹.

Check the result using average speed: (0 + 2.40)/2 = 1.20 m s⁻¹, and 1.20 × 1.50 = 1.80 m. This agreement supports the arithmetic within the assumed model. It does not establish that a real trolley actually had constant acceleration; that would require evidence from the experiment.

Convert squared units carefully

Because 1 cm = 10⁻² m, an area of 1 cm² equals 10⁻⁴ m². Therefore 2.0 cm² = 2.0 × 10⁻⁴ m², not 0.020 m². Convert the length factor and square it. Use the same reasoning with volumes by cubing the conversion factor. Writing this step explicitly helps prevent errors in pressure, resistivity and density calculations.

Worked percentage uncertainty example

Suppose a rectangle has length 5.0 ± 0.1 cm and width 2.0 ± 0.1 cm. The percentage uncertainties are (0.1/5.0) × 100 = 2% and (0.1/2.0) × 100 = 5%. For area = length × width, the simple maximum percentage uncertainty is approximately 2% + 5% = 7%.

The calculated area is 10.0 cm², so its approximate absolute uncertainty is 0.07 × 10.0 = 0.7 cm². Report it as 10.0 ± 0.7 cm². This is the introductory uncertainty treatment used here, not a claim that every statistical uncertainty calculation uses the same combination rule.

The Cambridge 9702 syllabus for 2025–2027 includes units, dimensional checks and simple uncertainty combinations. Use your paper's instructions when presenting uncertainties, decimal places and significant figures.

Explain what the graph gradient represents

Match the equation to y = mx + c before calculating a gradient. If you plot potential difference V vertically against current I horizontally for an ohmic resistor at constant temperature, V = IR gives gradient R. Reversing the axes gives 1/R. The same plotted data can answer a different calculation depending on the axis choice.

Keep a calculation error log

Label errors as model choice, rearrangement, conversion, arithmetic or presentation. Practise a few targeted questions on the most frequent type, then return to a mixed set. Use our past-paper routine for marking and corrections, or explore Physics tutoring for feedback on your working and practical-data analysis.