International Baccalaureate · IB Diploma Programme
IB Diploma Programme Mathematics: Applications and Interpretation
International Baccalaureate Diploma Programme Mathematics: Applications and Interpretation. What it covers, how it is assessed, a link to the official syllabus, and the free study material Marlbridge publishes for it.
- Syllabus
- DP Mathematics: Applications and Interpretation
- Qualification
- IB Diploma Programme
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Topics and resources
Each topic below is from the official International Baccalaureate document for International Baccalaureate Diploma Programme Mathematics: Applications and Interpretation, with its study guides, revision notes and practice questions together. Everything here is for IB Diploma Programme Mathematics: Applications and Interpretation only.
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- Revise with revision notes
- Practise with practice questions
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- Topic 1
Number and algebra
Covers Operations with numbers in the form a × 10^k, Arithmetic sequences and series, Geometric sequences and series, Financial applications of geometric sequences and series (compound interest, depreciation), Laws of exponents with integer exponents; introduction to logarithms, Approximation: decimal places, significant figures, upper/lower bounds, percentage error, estimation, Amortization and annuities using technology, Use technology to solve systems of linear equations and polynomial equations, Laws of logarithms (AHL only), Simplifying expressions involving rational exponents (AHL only), The sum of infinite geometric sequences (AHL only), Complex numbers: Cartesian form, the complex plane, quadratic equations with complex roots (AHL only), Complex numbers: modulus-argument (polar) and exponential (Euler) forms (AHL only), Matrices: definition, algebra, multiplication, determinants, inverses, solving linear systems (AHL only), Eigenvalues, eigenvectors, characteristic polynomial and diagonalization of 2×2 matrices (AHL only)
Study guides
- Applications and Interpretation – Laws of logarithms, rational exponents, infinite series and complex numbers (HL) Read guide
- Applications and Interpretation – Matrices, eigenvalues and eigenvectors (HL) Read guide
- Applications and Interpretation – Number, approximation, sequences and financial mathematics Read guide
Revision notes
- Applications and Interpretation – Laws of logarithms, rational exponents, infinite series and complex numbers (HL) Revise topic
- Applications and Interpretation – Matrices, eigenvalues and eigenvectors (HL) Revise topic
- Applications and Interpretation – Number, approximation, sequences and financial mathematics Revise topic
Practice questions
- Applications and Interpretation – Laws of logarithms, rational exponents, infinite series and complex numbers (HL) Try questions
- Applications and Interpretation – Matrices, eigenvalues and eigenvectors (HL) Try questions
- Applications and Interpretation – Number, approximation, sequences and financial mathematics Try questions
- Topic 2
Functions
Covers Different forms of the equation of a straight line; gradient, parallel and perpendicular lines, Concept of a function, domain, range and graph; inverse function, The graph of a function; sketching from information or a context, Determining key features of graphs; points of intersection of two curves using technology, Modelling with linear, quadratic, exponential, direct/inverse variation, cubic and sinusoidal functions, Modelling skills: developing, fitting, testing and using a model, Composite functions in context; inverse function including domain restriction (AHL only), Transformations of graphs: translations, reflections, stretches and composite transformations (AHL only), Further modelling: exponential (half-life), natural logarithmic, sinusoidal, logistic and piecewise models (AHL only), Scaling large or small numbers with logarithms; linearizing data; log-log and semi-log graphs (AHL only)
Study guides
Revision notes
- Topic 3
Geometry and trigonometry
Covers 3D distance and midpoint; volume and surface area of pyramids, cones, spheres and combinations; angles between lines/planes, Right-angled trigonometry; the sine rule, cosine rule and area of a triangle, Applications of right- and non-right-angled trigonometry, including Pythagoras’ theorem and bearings, The circle: length of an arc and area of a sector, Equations of perpendicular bisectors, Voronoi diagrams: sites, vertices, edges, cells; nearest-neighbour interpolation; the "toxic waste dump" problem, Radian measure; area of sector and arc length using radians (AHL only), Definitions of sinθ/cosθ via the unit circle; Pythagorean identity; ambiguous case of the sine rule (AHL only), Matrix transformations: reflections, stretches, enlargements, translations, rotations; determinant as area scale factor (AHL only), Vectors: concept, components, base vectors, magnitude, position vectors, normalization (AHL only), Vector equation of a line in two and three dimensions (AHL only), Vector applications to kinematics: linear motion with constant and variable velocity (AHL only), Scalar and vector product of two vectors; angle between vectors; components of vectors (AHL only), Graph theory: graphs, vertices, edges, degree, simple/complete/weighted/directed graphs, subgraphs and trees (AHL only), Adjacency matrices, walks, weighted adjacency tables, transition matrices for strongly-connected graphs (AHL only), Tree and cycle algorithms: Kruskal’s and Prim’s MST, Chinese postman and travelling salesman problems (AHL only)
Study guides
- Applications and Interpretation – 3D geometry, triangle trigonometry, bearings and sectors Read guide
- Applications and Interpretation – Geometry and Trigonometry Strand Read guide
- Applications and Interpretation – Graph theory, adjacency matrices and network algorithms (HL) Read guide
- Applications and Interpretation – Perpendicular bisectors and Voronoi diagrams Read guide
- Applications and Interpretation – Radians, the unit circle, matrix transformations and vectors (HL) Read guide
Revision notes
- Applications and Interpretation – 3D geometry, triangle trigonometry, bearings and sectors Revise topic
- Applications and Interpretation – Geometry and Trigonometry Strand Revise topic
- Applications and Interpretation – Graph theory, adjacency matrices and network algorithms (HL) Revise topic
- Applications and Interpretation – Perpendicular bisectors and Voronoi diagrams Revise topic
- Applications and Interpretation – Radians, the unit circle, matrix transformations and vectors (HL) Revise topic
Practice questions
- Applications and Interpretation – 3D geometry, triangle trigonometry, bearings and sectors Try questions
- Applications and Interpretation – Geometry and Trigonometry Strand Try questions
- Applications and Interpretation – Graph theory, adjacency matrices and network algorithms (HL) Try questions
- Applications and Interpretation – Perpendicular bisectors and Voronoi diagrams Try questions
- Applications and Interpretation – Radians, the unit circle, matrix transformations and vectors (HL) Try questions
- Topic 4
Statistics and probability
Covers Population, sample, sampling techniques, reliability and bias, interpretation of outliers, Presentation of data: frequency distributions, histograms, cumulative frequency graphs, box-and-whisker diagrams, Measures of central tendency and dispersion; effect of constant changes on data; quartiles, Linear correlation of bivariate data; Pearson’s product-moment correlation coefficient; regression line of y on x, Concepts of trial, outcome, sample space, event, probability and expected number of occurrences, Venn diagrams, tree diagrams; combined, mutually exclusive, conditional and independent events, Discrete random variables and their probability distributions; expected value, The binomial distribution; its mean and variance, The normal distribution and curve; normal probability and inverse normal calculations, Spearman’s rank correlation coefficient; limitations of Pearson’s and Spearman’s coefficients, Hypothesis testing: null/alternative hypotheses, significance levels, p-values, χ² tests, the t-test, Design of valid data collection methods; reliability and validity tests (AHL only), Non-linear regression; sum of square residuals; coefficient of determination R² (AHL only), Linear transformation and combination of random variables; unbiased estimators of μ and σ² (AHL only), Linear combinations of normal random variables; the central limit theorem (AHL only), Confidence intervals for the mean of a normal population (AHL only), The Poisson distribution, its mean and variance; sum of independent Poisson distributions (AHL only), Critical values/regions; hypothesis tests for mean, proportion and correlation; Type I and II errors (AHL only), Transition matrices, regular Markov chains, steady-state and long-term probabilities (AHL only)
Study guides
- Applications and Interpretation – Correlation, regression and hypothesis testing Read guide
- Applications and Interpretation – Data collection, non-linear regression, hypothesis tests and Markov chains (HL) Read guide
- Applications and Interpretation – Probability, discrete random variables, binomial and normal distributions Read guide
- Applications and Interpretation – Random variables, the central limit theorem, confidence intervals and the Poisson distribution (HL) Read guide
- Applications and Interpretation – Sampling, data presentation and summary statistics Read guide
- Applications and Interpretation – Statistics and Probability Read guide
Revision notes
- Applications and Interpretation – Correlation, regression and hypothesis testing Revise topic
- Applications and Interpretation – Data collection, non-linear regression, hypothesis tests and Markov chains (HL) Revise topic
- Applications and Interpretation – Probability, discrete random variables, binomial and normal distributions Revise topic
- Applications and Interpretation – Random variables, the central limit theorem, confidence intervals and the Poisson distribution (HL) Revise topic
- Applications and Interpretation – Sampling, data presentation and summary statistics Revise topic
- Applications and Interpretation – Statistics and Probability Revise topic
Practice questions
- Applications and Interpretation – Correlation, regression and hypothesis testing Try questions
- Applications and Interpretation – Data collection, non-linear regression, hypothesis tests and Markov chains (HL) Try questions
- Applications and Interpretation – Probability, discrete random variables, binomial and normal distributions Try questions
- Applications and Interpretation – Random variables, the central limit theorem, confidence intervals and the Poisson distribution (HL) Try questions
- Applications and Interpretation – Sampling, data presentation and summary statistics Try questions
- Applications and Interpretation – Statistics and Probability Try questions
- Topic 5
Calculus
Covers Introduction to the concept of a limit; derivative as gradient function and rate of change, Increasing and decreasing functions; graphical interpretation of f′(x), Derivative of f(x) = ax^n and sums of such terms, Tangents and normals at a given point, Introduction to integration as anti-differentiation; definite integrals and area using technology, Values where the gradient is zero; local maximum and minimum points, Optimisation problems in context, Approximating areas using the trapezoidal rule, Derivatives of sin x, cos x, tan x, e^x, ln x, x^n (n rational); chain, product and quotient rules; related rates of change (AHL only), The second derivative; concavity and points of inflexion (AHL only), Definite and indefinite integration of further functions; integration by inspection or substitution (AHL only), Area enclosed by a curve and an axis; volumes of revolution about the x- or y-axis (AHL only), Kinematic problems involving displacement, velocity and acceleration (AHL only), Setting up and solving first order differential equations by separation of variables (AHL only), Slope fields and their diagrams (AHL only), Euler’s method for numerical solutions of first order and coupled differential equations (AHL only), Phase portraits for coupled linear differential equations; qualitative analysis by eigenvalue type (AHL only), Second order differential equations by Euler’s method and via phase portraits (AHL only)
Study guides
- Applications and Interpretation – Differential equations, slope fields, Euler's method and phase portraits (HL) Read guide
- Applications and Interpretation – Differentiation, integration, optimisation and the trapezoidal rule Read guide
- Applications and Interpretation – Further differentiation and integration, volumes of revolution and kinematics (HL) Read guide
Revision notes
- Applications and Interpretation – Differential equations, slope fields, Euler's method and phase portraits (HL) Revise topic
- Applications and Interpretation – Differentiation, integration, optimisation and the trapezoidal rule Revise topic
- Applications and Interpretation – Further differentiation and integration, volumes of revolution and kinematics (HL) Revise topic
Practice questions
- Applications and Interpretation – Differential equations, slope fields, Euler's method and phase portraits (HL) Try questions
- Applications and Interpretation – Differentiation, integration, optimisation and the trapezoidal rule Try questions
- Applications and Interpretation – Further differentiation and integration, volumes of revolution and kinematics (HL) Try questions
Covering more than one topic
Course guides, exam preparation and pages that span several topics.
Source: International Baccalaureate Organization, Diploma Programme, Mathematics: applications and interpretation guide, first assessment 2021 (published February 2019, updated August 2019/May 2020/August 2020/November 2020) — First assessments for SL and HL—2021. Verified 2026-09-08. Subtopics are shown where Marlbridge has entered them; a topic may have more in the official document. This syllabus is tiered: see “About this course” below for the tier structure. A topic listed here is part of the syllabus; it does not mean Marlbridge has published material for it. Always check the current syllabus for your examination year.
About this course
- Qualification
- IB Diploma Programme Mathematics: Applications and Interpretation
- Spec code
- DP Mathematics: Applications and Interpretation
- Does Marlbridge teach it?
- Yes — request a free trial class
- Who teaches it?
- Muhammad Ghazali Siddiqui · Arslan Tanvir
- Are resources available?
- Yes — 61 published
- Is enrolment open?
- Enquire to join — no online enrolment yet
- Official syllabus
- International Baccalaureate syllabus
- Where was this verified?
- 2026-09-04, official International Baccalaureate specification
Compiled and maintained by the Marlbridge Academic Team, checked against the official International Baccalaureate specification on 2026-09-04.
Spotted something wrong on this page? Report an error — see the corrections policy.
The qualification
International Baccalaureate Diploma Programme Mathematics: Applications and Interpretation
Marlbridge's summary of the course
IB DP Mathematics: Applications and Interpretation recognizes the increasing role of mathematics and technology in a data-rich world, focusing on topics used in real-world modelling and interpretation, at Standard Level (SL) and Higher Level (HL).
The board's own description is on the official International Baccalaureate syllabus page.
First assessments 2021. Sourced from the freely public official subject brief plus the freely public official specimen exam papers, both read on 2026-09-04 – no licensed subject guide was needed. Five syllabus topics (Number and algebra; Functions; Geometry and trigonometry; Statistics and probability; Calculus), sharing 60 hours of common content with Mathematics: Analysis and Approaches, plus an internally assessed Mathematical Exploration; Higher Level sits an additional Paper 3. All external assessment in this course requires technology. See the matching assessment record for the sourced paper-by-paper breakdown, modeled at both tiers.
Specifications change between examination series. Always confirm the current syllabus and assessment structure on the International Baccalaureate syllabus page for your examination year.
Assessment structure
Component-based qualification
| Component | Duration | Marks | Weighting | Type |
|---|---|---|---|---|
| Paper 1: Paper 1 – Short-Response Questions, Technology Permitted (SL) | 1h 30m | 80 | 40% | Written exam |
| Paper 2: Paper 2 – Extended-Response Questions, Technology Permitted (SL) | 1h 30m | 80 | 40% | Written exam |
| Exploration: Internal Assessment – Mathematical Exploration (SL) | — | 20 | 20% | Coursework |
| Paper 1: Paper 1 – Short-Response Questions, Technology Permitted (HL) | 2h | 110 | 30% | Written exam |
| Paper 2: Paper 2 – Extended-Response Questions, Technology Permitted (HL) | 2h | 110 | 30% | Written exam |
| Paper 3: Paper 3 – Two Extended-Response Problem-Solving Questions (HL Only) (HL) | 1h 15m | 55 | 20% | Written exam |
| Exploration: Internal Assessment – Mathematical Exploration (HL) | — | 20 | 20% | Coursework |
Source: official International Baccalaureate specification, verified 2026-09-04. Both tiers modeled in full. Weighting and duration are read directly from the official public subject brief (first assessments 2021); all external papers require technology throughout this course. Paper 1 and Paper 2 Higher Level mark totals (110 marks each, 2 hours each) are read directly from the official freely public specimen papers, read on 2026-09-04; the same document could not be read in full far enough to confirm the Standard Level papers or Paper 3. Standard Level Paper 1/Paper 2 (80 marks each), Higher Level Paper 3 (55 marks, two compulsory extended-response problem-solving questions) and the Mathematical Exploration (20 marks at both tiers, the same five-criterion structure shared with Mathematics: Analysis and Approaches) were independently corroborated against a current, actively maintained third-party IB revision resource that publishes exact maximum-mark grade-boundary tables; those tables agree exactly with the primary specimen document everywhere the two overlap (Higher Level Paper 1 and Paper 2). HL Paper 3 duration: 1 hour 15 minutes, per the IB May 2026 examination schedule ("Mathematics: analysis and approaches HL paper 3 / Mathematics: applications and interpretation HL paper 3 1h 15m", read at ibo.org 2026-09-17); the subject guide (first assessment 2021, updated November 2020) and subject brief still say 1 hour and are superseded on this point for the current course.
Questions about this course
How is International Baccalaureate Mathematics: Applications and Interpretation (DP Mathematics: Applications and Interpretation) assessed?
International Baccalaureate Mathematics: Applications and Interpretation (DP Mathematics: Applications and Interpretation) is assessed through: SL candidates take: Paper 1 (Paper 1 – Short-Response Questions, Technology Permitted) — 1h 30m, 80 marks, 40% of the qualification; Paper 2 (Paper 2 – Extended-Response Questions, Technology Permitted) — 1h 30m, 80 marks, 40% of the qualification; Exploration (Internal Assessment – Mathematical Exploration) — no fixed duration, 20 marks, 20% of the qualification. HL candidates take: Paper 1 (Paper 1 – Short-Response Questions, Technology Permitted) — 2h, 110 marks, 30% of the qualification; Paper 2 (Paper 2 – Extended-Response Questions, Technology Permitted) — 2h, 110 marks, 30% of the qualification; Paper 3 (Paper 3 – Two Extended-Response Problem-Solving Questions (HL Only)) — 1h 15m, 55 marks, 20% of the qualification; Exploration (Internal Assessment – Mathematical Exploration) — no fixed duration, 20 marks, 20% of the qualification. It is a component based qualification. Source: official International Baccalaureate specification, verified 2026-09-04.
What topics does IB Diploma Programme Mathematics: Applications and Interpretation cover?
5 topics in the current syllabus: Number and algebra; Functions; Geometry and trigonometry; Statistics and probability; Calculus. The printable topic checklist lists every topic and subtopic on one page.
Can I get a tutor for IB Diploma Programme Mathematics: Applications and Interpretation?
Yes. Marlbridge teaches IB Diploma Programme Mathematics: Applications and Interpretation live online, one-to-one only, taught by a named subject teacher from its academy in Lahore, Pakistan. The first trial class is free.
Are there free IB Diploma Programme Mathematics: Applications and Interpretation revision notes and practice questions?
Yes. Marlbridge has published 61 free resources for this course (study guides, practice questions, revision notes, exam preparation guides, a subject guide), free to read with no sign-up.
The subject
IB Diploma Programme Mathematics: Applications and Interpretation teaching and study resources.
All Mathematics: Applications and Interpretation at Marlbridge
Mathematics: Applications and Interpretation at other qualifications
These are separate qualifications with different syllabuses and assessments — not different names for the same course. Check which one your school enters you for.
No other qualifications are published for this subject yet.
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