Tool 3 — Mathematics
The mathematical toolkit the course assumes — arithmetic, algebra, units, uncertainties and graphing.
Editorial framing The content below is transcribed from the IB Chemistry guide (first assessment 2025), section “Skills in the study of chemistry”. These skills are cross-cutting: they are integrated into the teaching of the syllabus rather than taught as stand-alone topics.
Applying general mathematics
- Arithmetic and algebra
- Decimals, fractions, percentages, ratios, reciprocals, exponents
- Logarithmic functions
- Exponential functionsHL
- Rates of change from tabulated data
- Mean and range
- Scientific notation
- Approximation and estimation; knowing when effects can be ignored
- Order-of-magnitude comparison
- Direct and inverse proportionality and positive/negative correlation
- Percentage change and percentage difference
- Percentage error and percentage uncertainty
- Continuous vs discrete variables
Using units, symbols and numerical values
- SI prefixes and units
- Symbols from the guide and data booklet
- Appropriate significant figures / decimal places
Processing uncertainties
- Significance of uncertainties in raw and processed data
- Record uncertainties as a range (±) to appropriate precision
- Propagate uncertainties through addition, subtraction, multiplication and division
- Propagate uncertainties through exponentsHL
- Propagate uncertainties through exponential functionsHL
- Express absolute, fractional (relative) and percentage uncertainties appropriately
- Apply the coefficient of determination R² to evaluate fit
Graphing
- Sketch graphs with labelled unscaled axes to describe trends qualitatively
- Construct and interpret tables, bar charts, histograms, scatter graphs, line and curve graphs
- Plot linear and non-linear graphs with appropriate scales
- Lines and curves of best fit
- Interpret gradient, changes in gradient, intercepts, maxima, minima and areas
- Draw and interpret uncertainty bars
- Extrapolate and interpolate
What is HL-only in the mathematics
Exponentials HL
Exponential functions are HL-only. The Arrhenius equation (k = Ae^(−Ea/RT)) and [H⁺] = 10⁻ᵖᴴ both require interpreting a negative exponent.
Logarithms SL
Logarithmic functions are SL — they appear in pH, pOH, pKa and pKb calculations throughout the course, not only at HL.
Common misconceptions & bridge items for Tool 3
Common misconceptions (6)
M-78 — Repeating a measurement improves accuracy.
Confidence: verified
Why it’s wrong: Repetition reduces random error and improves precision.
Correction: It does nothing about systematic error, which is what limits accuracy.
M-79 — 'Human error' is a valid source of error.
Confidence: verified
Why it’s wrong: It is a non-answer.
Correction: Name the specific measurement, its uncertainty, and whether the effect is random or systematic, and state the direction of the effect on the result.
M-80 — Write down all the digits the calculator gives.
Confidence: verified
Why it’s wrong: The number of significant figures is limited by the least precise measurement.
Correction: For multiplication/division, match the input with the fewest sig figs.
M-81 — A single burette reading has uncertainty ±0.05 cm³, so the titre does too.
Confidence: verified
Why it’s wrong: A titre is a difference of two readings, so the absolute uncertainties add.
Correction: The titre has uncertainty ±0.10 cm³.
M-82 — Percentage error and percentage uncertainty are the same.
Confidence: verified
Why it’s wrong: Percentage uncertainty comes from instrument precision (random); percentage error compares your result to an accepted literature value and reveals systematic error.
Correction: Compare the two: if percentage error ≫ total percentage uncertainty, there is a systematic problem.
M-83 — For a graph, just join the dots.
Confidence: verified
Why it’s wrong: A best-fit line or curve is required.
Correction: Draw a best-fit line/curve, and where the relationship is expected to be linear, use gradient and intercept quantitatively (with the linearised form of the equation where needed, e.g. ln k vs 1/T).