Scientific Reasoning and Quantitative Problem Solving
This section tests how you design, read and criticise experiments, and how you handle numbers: units, significant figures, error propagation, graph reading and the strength of a conclusion. It rewards disciplined bookkeeping rather than memorised facts.
Core rules
- Variables. Identify the independent variable (manipulated), the dependent variable (measured) and the controlled ones. A control group differs in exactly one factor; randomisation and blinding remove confounders and bias.
- Accuracy versus precision. Accuracy is closeness to the true value; precision is reproducibility. A systematic error shifts all readings the same way; random error scatters them.
- Units and dimensions. Convert to SI before calculating, and check that both sides of an equation carry the same dimensions. Write conversion factors as fractions so units cancel.
- Error propagation. When adding or subtracting, absolute uncertainties add; when multiplying or dividing, relative (percentage) uncertainties add.
- Graphs. The slope of a linear plot is a rate; the intercept is a baseline; a curve means the relationship is non-linear, so do not force a straight line.
Worked example
A 500 mL infusion is to run over 6 hours with a giving set of 20 drops/mL. Volume in drops = 500 × 20 = 10 000 drops; time = 6 × 60 = 360 min; rate = 10 000/360 ≈ 27.8, so 28 drops/min. For error: a mass of (25.0 ± 0.1) g in a volume of (10.0 ± 0.2) mL gives ρ = 2.50 g/mL with relative errors 0.4% and 2.0%, totalling 2.4%, i.e. ±0.06 g/mL.
Traps
Reporting more significant figures than the data support; quoting a percentage error as absolute; treating a correlation between two measured variables as proof of causation; reading a graph's axis labels after, not before, estimating the slope.