Scientific method, measurement, units and data handling
What this domain tests
This domain covers the scientific method, variables, measurement, SI units, unit conversion, uncertainties, tables and graphs. Questions ask you to design a fair test, choose a sensible instrument, convert between prefixes, plot and read graphs, and judge whether a conclusion really follows from the data.
Core rules
- Method: research question → testable hypothesis → experiment → data → analysis → conclusion → evaluation of errors.
- Variables: the independent variable is changed, the dependent variable is measured, and all other variables are kept constant for a fair test.
- SI base units: metre, kilogram, second, ampere, kelvin, mole, candela. Derived units: N = kg·m/s², J = N·m, W = J/s, Pa = N/m², V = W/A, Ω = V/A.
- Prefixes: k = 10³, M = 10⁶, G = 10⁹, m = 10⁻³, µ = 10⁻⁶, n = 10⁻⁹. Useful conversions: 1 cm³ = 10⁻⁶ m³, 1 g/cm³ = 1000 kg/m³, 1 kWh = 3.6 MJ, 1 m/s = 3.6 km/h.
- Reading instruments: look at eye level to avoid parallax, note the smallest division, estimate the last digit, repeat and average to reduce random error.
- Errors: random errors scatter readings; systematic errors such as a zero error shift all readings the same way and are not removed by averaging.
- Graphs: independent variable on the x-axis, dependent on the y-axis, both axes labelled with quantity and unit, a sensible scale and a best-fit line. The gradient of a distance–time graph is speed; the area under a velocity–time graph is distance.
- Rounding: quote the answer to the precision of the least precise measurement.
Worked example
A metal block has a mass of 81.0 g and measures 3.0 cm × 3.0 cm × 2.0 cm. Find its density.
V = 3.0 × 3.0 × 2.0 = 18 cm³. ρ = m/V = 81.0/18 = 4.5 g/cm³. Convert: 4.5 g/cm³ = 4.5 × 1000 = 4500 kg/m³ = 4.5 × 10³ kg/m³. Comparing with a materials table identifies the metal as titanium.
Traps that cost marks
- Converting cm³ to m³ by multiplying by 10⁻² instead of 10⁻⁶.
- Plotting the measured variable on the x-axis out of habit.
- Leaving units off an axis label or off a gradient value.
- Averaging repeated readings without noticing an outlier or a drifting zero.
- Quoting more significant figures than the data support.
- Writing a conclusion that goes beyond the data, such as inferring a rule from two points.