Mathematics: notes and practice questions
- This topic covers advanced mathematical skills used in Higher Level Chemistry.
- Carry out calculations involving exponential functions.
- Propagate uncertainties in calculations involving exponents.
How it is examined
Paper 1B is built on it. May 2025 HL Paper 1B TZ1 asked candidates to compute 1/t as a rate proxy and state its unit (2 marks, one for the number and one for `s⁻¹`), to draw a best-fit smooth curve through plotted points (1 mark, with an explicit instruction not to accept point-to-point lines or a straight line), and to explain why a smaller quantity carries a larger relative uncertainty. Marking instruction 14 says examiners do not penalize errors in units or significant figures unless the Notes column says so, which matters: significant figures are usually free, and units are usually free, except where a marking point is specifically the unit.
Uncertainty and error formulas are in the booklet's mathematical section. Everything about how to apply them is recall. (The booklet's exact contents are researched, not on disk;
- Use basic arithmetic and algebraic calculations to solve problems.
- Carry out calculations involving decimals, fractions, percentages, ratios, reciprocals and exponents.
- Carry out calculations involving logarithmic functions.
- Determine rates of change from tabulated data.
Guiding questions
- None given.
Linking questions
- Structure 1.3, Reactivity 3.1 Why are log scales useful when discussing [H+] and ionization energies?
- Structure 1.5, Reactivity 2.2 Graphs can be presented as sketches or as accurately plotted data points. What are the advantages and limitations of each representation?
- Reactivity 2.2 How can graphs provide evidence of systematic and random error? What measurements are needed to deduce the order of reaction for a specific reactant?
- Reactivity 3.1 What is the shape of a sketch graph of pH against [H+]?
Practice questions
1 question · 1 mediumQuestion 1
MediumPaper 1A · calculator1 markA sealed reaction vessel of fixed volume contains a sample of nitrogen gas at an initial pressure of and a temperature of . During a process, of the nitrogen molecules are removed from the vessel, and the temperature is simultaneously increased to .
What is the new pressure of the gas in ?
A.
B.
C.
D.
Recall the ideal gas law, . For a fixed volume, how does pressure relate to the number of moles and temperature? Consider the ratio of final to initial conditions.
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Where marks are lost
- Reaching for "human error" or "only one trial." A source of error has to be a specific step in the method, not a general apology for the result.
- Joining the dots instead of drawing a curve.
- Naming a chemical instead of the property that distinguishes it, or vice versa. Answering with the nearest fact that comes to mind rather than the fact the command term and stem jointly ask for is a recurring way to answer a question that was not, quite, the one asked.
