Mathematical requirements

Apply the correct operation, estimate the scale, convert fractions and percentages, calculate arithmetic means and round the final answer to a precision supported by the data.

For addition/subtraction, decimal places control the final place; for multiplication/division, significant figures control it. Keep guard digits during working and attach units.

The mean of 2.10, 2.20 and 2.30 is 2.20. A 0.250 mol sample in 0.100 dm³ gives 2.50 mol dm⁻³, not 2.5×10⁶.

More digits are not more accuracy, and percentage change is not the same as percentage-point change.

Convert every quantity to the units required by the equation before calculating. Common traps include cm³↔dm³, kPa↔Pa, °C↔K, mg↔g and J↔kJ.

Use standard form for very large or small values, rearrange the formula symbolically, then substitute numbers with units. For pH, logarithms reverse powers of ten: [H⁺] = 10⁻pH.

250 cm³ = 0.250 dm³; 27 °C = 300 K approximately. A pressure of 101 kPa is 101 000 Pa.

Do not convert temperature by adding 273 to a temperature difference, and do not mix cm³ with dm³ in n = cV.

A direct proportion gives a straight line through the origin when the correct variables are plotted. For y = mx + c, m is the gradient and c is the y-intercept.

Choose axes from the model, use a scale that fills the grid, plot precise crosses and draw a justified best-fit line or curve. A non-zero intercept may reveal a background amount or systematic offset.

If gas volume is proportional to time, V/t stays constant and the V–t graph passes through the origin. If a line has points (2,5) and (6,13), m = 2 and c = 1.

A line that looks straight is not proof of direct proportionality unless the intercept and ratio support it.

A tangent gradient gives an instantaneous rate of change; an area under a curve represents an accumulated quantity only when the axes and units make that interpretation valid. Log transforms can linearise relationships, but every model has a range of validity.

Estimate orders of magnitude before calculating, use log₁₀ or ln consistently, and calculate core quantities such as n = m/Mr, c = n/V and ρ = m/V with compatible units.

The initial gradient of a concentration–time curve is an initial rate. If ln k is plotted against 1/T, a straight line can test an Arrhenius model within the measured range.

A tangent slope is not the same as the total change, and a straight transformed graph does not prove the underlying model is universally true.

Use the standard symbol and SI unit for each quantity: mass m (g or kg), volume V (dm³ or m³), amount n (mol), temperature T (K), pressure p (Pa), charge Q (C), potential difference E (V) and time t (s).

Constants and chemical quantities such as Nₐ, F, R, Kᵥ, Ar, Mr, E° and ΔH have fixed meanings; write units beside intermediate values so a mismatch is visible.

In Q = It, current is in amperes and time in seconds; in n = cV, convert V to dm³ when c is mol dm⁻³.

A symbol is not interchangeable with a similarly named quantity: E° is an electrode potential, while ΔH is an enthalpy change.