IB Mathematics: Applications and Interpretation (first assessment 2021) is about using mathematics to model real situations, with technology at its centre. It is offered at Standard Level (SL) and Higher Level (HL). This guide explains the content, the papers and the exploration, and how to plan revision week by week.
What the course covers
- Number and algebra: standard form, finance, sequences and series, exponents and logarithms, and solving equations with technology.
- Functions: linear, quadratic, exponential, trigonometric and other models, and how to fit and interpret them.
- Geometry and trigonometry: lengths, areas and volumes in two and three dimensions, triangle rules, arc length and sector area, and at HL radians, vectors, matrices and graph theory.
- Probability and statistics: summarising data, regression, correlation, probability, distributions, hypothesis tests and, at HL, further inference.
- Calculus: rates of change, differentiation, integration and their applications, with differential equations and modelling at HL.
How you are assessed
| Level | Component | Duration | Marks | Weighting | Content and rules |
|---|---|---|---|---|---|
| SL | Paper 1 | 1 h 30 min | 80 | 40% | Short questions. A GDC is required and a formula booklet is provided. |
| SL | Paper 2 | 1 h 30 min | 80 | 40% | Longer questions. A GDC is required and a formula booklet is provided. |
| SL | Exploration | Set by your school | Internal | 20% | A piece of independent mathematical writing on a topic you choose. |
| HL | Paper 1 | 2 h | 110 | 30% | A GDC is required and a formula booklet is provided. |
| HL | Paper 2 | 2 h | 110 | 30% | A GDC is required and a formula booklet is provided. |
| HL | Paper 3 | 1 h | 55 | 20% | Extended problems with a GDC and a formula booklet. |
| HL | Exploration | Set by your school | Internal | 20% | A piece of independent mathematical writing on a topic you choose. |
What each paper asks of you
Paper 1 has short questions that test a wide range of topics quickly. Move fast on the opening questions, since they are usually direct, and keep time for the later ones that need several steps.
Paper 2 uses longer questions, often built around one context with several connected parts. Read the whole context, define any variable you use, and carry forward answers from earlier parts when asked.
Paper 3 (HL) gives extended problems where you model, explore and generalise. Expect a sequence of linked steps that build towards a conclusion, so keep your work clear and your notation consistent.
Exploration rewards a topic you care about, clear aims, correct mathematics and honest reflection. Start early, and keep your own voice.
Because a GDC is required throughout, learn its menus well before the papers. Write down the setup you used, such as the regression type or the distribution and its parameters, so your reasoning is visible.
Command words and how to answer them
| Command word | What it asks you to do |
|---|---|
| Write down | Give an answer with little or no working. |
| Calculate | Find a numerical answer, showing relevant steps or GDC setup. |
| Find | Obtain an answer, showing the method used. |
| Determine | Reach a definite answer from the information, with justification. |
| Show that | Reach a stated result by clear steps; the final result must be shown. |
| Interpret | Say what a number or graph means in the context of the problem. |
| Comment | Give a short judgement, usually about how reasonable or reliable a result is. |
| Sketch | Draw a graph showing the shape and key features, with axes labelled. |
| Justify | Give valid reasons or evidence for an answer or conclusion. |
Calculators
A graphic display calculator (GDC) is required in all papers. Know how to enter lists, fit models, find roots and intersections, compute integrals and use probability distributions. Practise on the exact model you will take into the room, and keep its batteries and software in good order.
How to revise this course
- Day 1: read the topic note and rework its examples without looking at the solutions.
- Day 2: go through the flashcards, then practise the matching GDC routine until it is automatic.
- Day 3: work question bank questions on the topic, writing full solutions, and mark them honestly against the worked answers.
- Day 4: tackle a mixed set from earlier topics to keep older material fresh.
- Weekend: sit a timed test, alternating between a Paper 1 style and a Paper 2 style test. HL students add a Paper 3 style problem every second week. Record every lost mark by cause.
Keep a log of the GDC routines you use most. For each, write the menu path, the inputs and a short example with its result. Reviewing this log weekly makes the routines fast and reliable under time pressure. Alongside it, keep a short list of the formulas that the booklet does not simply hand you in usable form, such as how to choose between triangle rules or which test fits a given situation, so you can decide quickly what to do.
After each timed test, sort your lost marks into causes: a method you did not know, an arithmetic or entry slip, a misread question, or a missing interpretation. Aim your next week of practice at the largest group. For the exploration, set small deadlines: choose a topic, draft the aim, collect or generate the data, do the analysis, and then write and reflect. Short, regular sessions beat last-minute writing, and they leave time for your teacher's feedback.
In the final weeks, move from learning towards retrieval. Do full papers under timed conditions, check your solutions carefully, and revisit any topic where the same type of mistake appears twice.
Common errors
- Writing only a final answer from the GDC with no method or setup, so there is nothing to credit if the number is wrong.
- Rounding too early, which shifts later results; keep full values and round only at the end, normally to three significant figures.
- Leaving the calculator in the wrong mode, such as degrees when radians are needed.
- Failing to interpret an answer in context, or giving it without units.
- Picking a model without checking whether it suits the data, for example a linear fit for clearly curved data.
Exam tip: when a question says to interpret or comment, finish with a sentence that uses the context's own words and units. A number alone is rarely the whole answer.