22.3 Mathematical and data-presentation skills
- Syllabus
- 0610–2026–2027
- Topic
- 22.3
- Level
- —
Learning objectives
22.3.1Numerical and algebraic calculations• Add, subtract, multiply and divide; use decimals, fractions, ratios, reciprocals, percentages, percentage change and standard form; round to appropriate decimal places or significant figures; use direct and inverse proportion; solve simple equations and substitute quantities into formulas.22.3.2Geometry, measurement and biological scales• Convert units including cm³ and dm³, mg, g and kg, and μm, mm, cm and m; use areas and volumes of common shapes, rulers, estimates, scale diagrams and surface-area-to-volume ratios; select appropriate units.22.3.3Graphs, charts and statistics• Draw and interpret line graphs, bar charts, pie charts and equal-interval histograms; interpolate and extrapolate; determine gradients and intercepts with units; select scales and axes; recognise proportionality; calculate means and ranges; use simple probability.22.3.4Record readings and tabulated data• Record readings to the precision of the instrument with correct units and significant figures; head table columns with quantity and unit separated by a solidus; omit units from table bodies.22.3.5Plot, analyse and present biological data• Plot independent and dependent variables on correctly labelled axes using sensible scales; mark points accurately; draw justified best-fit lines or curves; read by interpolation or extrapolation; produce clear biological drawings and appropriate pie or bar charts.
Calculate biological quantities accurately
Translate the required biological quantity into a mathematical relationship, substitute compatible values, calculate, then report with the requested unit and precision.
| Task | Relationship or check |
|---|---|
| percentage | part ÷ total × 100 |
| percentage change | (new − original) ÷ original × 100; retain a negative sign for a decrease when change is requested |
| rate or gradient | change in dependent variable ÷ change in independent variable; include compound units |
| mean and range | sum ÷ number; maximum − minimum |
| ratio/proportion | compare like units; scale every term consistently |
| formula | rearrange for the unknown, substitute values with units, then solve |
| standard form | write a × 10ⁿ where 1 ≤ a < 10 |
Keep unrounded calculator values during working and round only the final result to the stated decimal places or significant figures. Show selected values and substitution so the method is traceable.
Percentage change uses the original value as denominator. A percentage increase may exceed 100%, and ordinary percentage is not interchangeable with percentage change.
Convert units and work with biological scale
Convert all quantities to compatible units before applying area, volume, scale or surface-area-to-volume relationships.
| Conversion | Direction rule |
|---|---|
| 1 kg = 1000 g; 1 g = 1000 mg | larger mass unit → smaller: multiply by 1000 |
| 1 m = 100 cm = 1000 mm; 1 mm = 1000 μm | follow each length conversion explicitly |
| 1 dm³ = 1000 cm³ | dm³ → cm³: multiply by 1000 |
| area | square the length conversion factor |
| volume | cube the length conversion factor |
| Shape or scale | Relationship |
|---|---|
| rectangle | area = length × width |
| triangle | area = ½ × base × height |
| circle | area = πr²; circumference = 2πr |
| rectangular block | volume = length × width × height |
| cylinder | volume = πr²h |
| scale diagram | actual size = image size ÷ magnification |
| surface-area-to-volume ratio | calculate both in compatible units, then simplify SA:V |
Linear conversion factors cannot be used unchanged for area or volume. State an appropriate final unit such as cm², μm³ or stomata per cm².
Choose and interpret graphs, charts and statistics
Choose a representation that matches the data type, then read its scale, trend and numerical features without changing the underlying evidence.
| Data or purpose | Suitable representation |
|---|---|
| continuous change or relationship | line graph or scatter graph with justified best-fit line/curve |
| categorical or discrete groups | bar chart with equal-width separated bars |
| continuous frequency intervals | equal-interval histogram with touching bars |
| proportions of a whole | pie chart |
Read values to half a smallest square where possible. Interpolation estimates within the data range; extrapolation extends beyond it and is less certain. Gradient is Δy/Δx with units, and an intercept is where a line crosses an axis.
Calculate mean and range from the defined set. Recognise direct proportion as a straight line through the origin; inverse proportion falls as the other variable rises. Simple probability ranges from 0 to 1.
Bars touch only for continuous histograms. A line joining points is not automatically a best-fit line, and a straight trend not through the origin is not direct proportionality.
Record readings and tables to official conventions
Recorded data must reflect instrument precision and preserve quantity, unit and significant-figure conventions consistently.
| Feature | Required convention |
|---|---|
| instrument reading | record the smallest reliably detected scale difference; use consistent decimal places for the same instrument |
| calculated result | use appropriate or requested significant figures and include the unit |
| table heading | write quantity / unit, for example time / s |
| table body | enter numbers only; do not repeat units in cells |
| columns | put the independent variable first and keep raw repeats separate from a calculated mean |
| missing or anomalous value | preserve the raw record; do not invent or silently replace a value |
Significant figures describe meaningful digits; decimal places describe position after the decimal point. They are different instructions.
Plot and present biological data clearly
A valid presentation makes variables, values and biological structures readable without exaggerating precision or inventing detail.
| Graph feature | Official requirement |
|---|---|
| axes | independent variable on x and dependent on y unless instructed otherwise; label quantity / unit |
| scale | use more than half the grid in both directions with sensible 1, 2 or 5-based intervals; zero is not always required |
| points | mark clear × or encircled dots within half a smallest square |
| best fit | draw one thin smooth line or curve with points reasonably balanced around it; ignore a clear anomaly only for the fit |
| reading | show interpolation or extrapolation guides and read to half a smallest square |
Biological drawings use a sharp pencil, large clear unbroken lines, no shading or colour, all observed features, and ruled label lines that touch the labelled feature.
Use a pie chart for proportions, separated equal-width bars for categorical or discrete data, and touching bars for continuous histogram intervals.
Draw a best-fit line only when intermediate values can reasonably be predicted. Do not force it through every point or through the origin without evidence.