Every reading you take is a best estimate wrapped in a band of doubt. The skill is not pretending the doubt away but quantifying it: knowing which errors a repeat will cure, which it will not, and how the uncertainty grows when you combine measurements into a result.
A systematic error shifts every reading the same way and is not reduced by repeating; a random error scatters readings and is reduced by averaging. Accuracy is closeness of the mean to the true value; precision is closeness of repeats to each other. When measurements combine, absolute uncertainties add for a sum or difference, and percentage uncertainties add for a product or quotient, multiplied by the power.
The bullseye is the true value. A systematic offset slides the whole cluster off-centre; a random spread blows the cluster outward. Set each, take a run, then decide whether the result is accurate, precise, both or neither.
Pick the rule by the operation, not the quantity. These four cover almost every AS calculation.
| Operation | Rule for the uncertainty |
|---|---|
| y = a + b or y = a − b | Δy = Δa + Δb (add absolute) |
| y = ab or y = a / b | %Δy = %Δa + %Δb (add percentage) |
| y = an | %Δy = |n| × %Δa |
| y = k a (k exact) | %Δy = %Δa (constants carry no uncertainty) |
Percentage uncertainty is (Δa / a) × 100%. Notice that a difference of two close numbers is dangerous: the absolute uncertainties still add, but the result is small, so the percentage uncertainty can become very large.
Four quick checks on error types, accuracy versus precision, and combining uncertainties. Each correct answer earns XP and lights this skill on your star map.
A balance reads 0.3 g when nothing is on its pan. Every mass measured with it is therefore too high by 0.3 g. This is an example of:
In the simulator, a run is tightly clustered but well off the bullseye. The readings are:
Two lengths are measured as (40.0 ± 0.5) cm and (25.0 ± 0.5) cm. What is the uncertainty in their difference?
A current has a 2% uncertainty and a resistance has a 3% uncertainty. The percentage uncertainty in the power dissipated, P = I²R, is:
Do not claim that "taking more readings improves accuracy". More repeats reduce the effect of random error and so improve precision, but they do nothing to a systematic error, which is exactly what limits accuracy. The other classic slip is mixing the rules: add absolute uncertainties for a sum or difference, but add percentage uncertainties for a product or quotient. And for a power such as r², multiply the percentage uncertainty by the power before adding.
Unlocks once the four checks above are done. Worth more XP, written to AS Paper 1 and 2 standard.
The diameter of a wire is measured as (0.80 ± 0.02) mm. The percentage uncertainty in the cross-sectional area, A = πd²/4, is:
A density is found from a mass with 1% uncertainty and a volume with 4% uncertainty, using ρ = m / V. The best statement of the result's uncertainty is:
A student times 20 oscillations rather than one, then divides by 20 to find the period. The main benefit of this method is to:
A resistance is calculated as 12.4 Ω with a percentage uncertainty of 5%. Which is the correct way to quote the result?
This skill is now lit gold on your star map. Keep the chain going.