Scientific questions, evidence and quantitative reasoning
Measurement and uncertainty
What this domain tests
Instrument choice and reading, precision versus accuracy, random versus systematic error, combination of uncertainties, graph plotting and interpretation, and experimental design. Marks come from quoting a correct uncertainty with a sensible number of significant figures and from explaining why a procedure reduces error.
Measurement and uncertainty
- Read each instrument or supplied specification to determine resolution; familiar scale intervals are examples, not universal values for every device. Record calibration corrections and distinguish display resolution from total measurement uncertainty.
- State your uncertainty convention - commonly ± half the smallest division for a single reading, and the full division for a difference of two readings.
- Random errors scatter readings about a mean and are reduced by repeats; systematic errors shift every reading the same way (zero error, calibration) and are removed by correction, not averaging.
- For first-order worst-case bounds, add absolute contributions for sums and differences, and relative contributions for products, quotients and powers. Independent standard uncertainties are instead commonly propagated in quadrature; correlations require additional terms. State the convention.
Graphs and experimental design
- Plot the quantity that gives a straight line, label axes with quantity and unit, draw error bars where asked and a best-fit line with points balanced above and below.
- Gradient = Δy/Δx taken from two well-separated points on the line, with units.
- Reduce error by: repeating and averaging, timing many oscillations and dividing, using fiducial markers to avoid parallax, setting a micrometer to zero first, and controlling all variables except the one under test.
Worked example
A metal cylinder has mass 25.0 ± 0.1 g, diameter 10.00 ± 0.02 mm and height 40.0 ± 0.1 mm. Find its density with uncertainty.
V = πd²h/4 = π(10.00)²(40.0)/4 = 3142 mm³ = 3.142 cm³. Using first-order worst-case uncertainty bounds: mass 0.4%, diameter 0.2% (doubled to 0.4%), height 0.25%. Total = 0.4 + 0.4 + 0.25 ≈ 1.05%. ρ = 25.0/3.142 = 7.96 g cm⁻³; absolute uncertainty = 0.0105 × 7.96 ≈ 0.08. Result: ρ = (7.96 ± 0.08) g cm⁻³.
Traps that cost marks
- Quoting 7.95843 g cm⁻³ from data good to three significant figures.
- Adding absolute uncertainties for a multiplication instead of adding percentages.
- Forgetting the factor of 2 when a quantity is squared.
- Ignoring a vernier or micrometer zero error.
- Reading a meniscus or pointer without eye-level alignment.
- Extrapolating far beyond the measured range and presenting it as data.
Controlled biological models
Experimental Reasoning
Items here ask you to design, critique, and interpret investigations, and to tell scientific claims apart from pseudoscientific ones. The content is process and reasoning, not vocabulary recall.
Core rules and concepts
- A hypothesis is a testable, falsifiable statement about a relationship; a theory is a broad, repeatedly supported explanatory framework (cell theory, evolution by natural selection); a law states a consistent regularity, often mathematically. Science supports or fails to support claims - it does not "prove" them.
- The independent variable is manipulated by the researcher; the dependent variable is measured; controlled variables are held constant; the control group receives no treatment, a placebo, or a baseline condition.
- Random assignment can reduce systematic allocation bias and supports causal inference in a well-designed experiment. Observational association alone does not establish causation; additional design, assumptions and evidence are needed for causal interpretation.
- Accuracy is closeness to the true value; precision is reproducibility. Random error degrades precision; systematic error (miscalibrated instrument, biased thermometer) degrades accuracy.
- Replication and adequate sample size reduce the chance that a result reflects random variation; descriptive statistics (mean, standard deviation) summarize data, while inferential statistics (t-test, chi-square) test hypotheses.
- Deduction moves from a general principle to a specific prediction; induction builds general patterns from specific observations. In a school engineering-design comparison, criteria describe desired performance and constraints restrict choices, such as a supplied cost or mass limit. Compare alternatives using measured evidence, identify tradeoffs and revise a model. A design satisfying one criterion can still violate a constraint. This is introductory design reasoning rather than a complete teaching-performance assessment.
Worked example
A student counts oxygen bubbles released per minute by Elodea at five distances from a lamp and concludes that light intensity drives photosynthesis. Distance is the independent variable; bubble rate is the dependent variable. Controls that must be held constant include water temperature, dissolved CO₂ (bicarbonate concentration), plant mass, and counting interval. The design has a confound: an incandescent lamp also heats the water, so temperature, not light, could explain the trend. Fixing it requires a heat filter or water bath, plus independently replicated observations and a justified sample-size choice, reporting variation alongside means. Three replicates can illustrate a calculation but are not a universal guarantee of sufficient power. Even then the defensible conclusion is that light intensity is associated with increased photosynthetic rate in this system - a claim about a sample, not proof of a universal law.
Traps that cost marks
Calling a hypothesis a theory, or saying a result "proves" a hypothesis. Confusing the control group with controlled variables. Accepting causation from correlation. Ignoring a confound such as temperature, pH, or time of day. Treating a single trial as evidence. Forgetting that the sample must be representative before results are generalized.