International Baccalaureate · IB Diploma Programme
IB Diploma Programme Mathematics: Analysis and Approaches
International Baccalaureate Diploma Programme Mathematics: Analysis and Approaches. 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: Analysis and Approaches
- 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: Analysis and Approaches, with its study guides, revision notes and practice questions together. Everything here is for IB Diploma Programme Mathematics: Analysis and Approaches 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, Laws of exponents and introduction to logarithms, Simple deductive proof, Laws of exponents and laws of logarithms, Sum of infinite convergent geometric sequences, The binomial theorem, Counting principles and extension of the binomial theorem (AHL only), Partial fractions (AHL only), Complex numbers: Cartesian form and the complex plane (AHL only), Complex numbers: modulus-argument (polar) and Euler form (AHL only), Complex conjugate roots and De Moivre’s theorem (AHL only), Proof by mathematical induction, contradiction and counterexample (AHL only), Solutions of systems of linear equations (AHL only)
Study guides
- Analysis and Approaches – Complex numbers (HL) Read guide
- Analysis and Approaches – Counting principles, partial fractions, proof and linear systems (HL) Read guide
- Analysis and Approaches – Exponents, logarithms, the binomial theorem and simple proof Read guide
- Analysis and Approaches – Sequences, series and financial applications Read guide
Revision notes
- Analysis and Approaches – Complex numbers (HL) Revise topic
- Analysis and Approaches – Counting principles, partial fractions, proof and linear systems (HL) Revise topic
- Analysis and Approaches – Exponents, logarithms, the binomial theorem and simple proof Revise topic
- Analysis and Approaches – Sequences, series and financial applications Revise topic
Practice questions
- Analysis and Approaches – Complex numbers (HL) Try questions
- Analysis and Approaches – Counting principles, partial fractions, proof and linear systems (HL) Try questions
- Analysis and Approaches – Exponents, logarithms, the binomial theorem and simple proof Try questions
- Analysis and Approaches – Sequences, series and financial applications Try questions
- Topic 2
Functions
Covers Equations of a straight line, Concept of a function, domain, range and inverse, The graph of a function, Key features of graphs and points of intersection, Composite functions and inverse functions, The quadratic function, Solving quadratic equations and inequalities; the discriminant, The reciprocal function and rational functions, Exponential and logarithmic functions, Solving equations graphically and analytically, Transformations of graphs, Polynomial functions, zeros, roots and factors (AHL only), Rational functions of higher degree (AHL only), Odd and even functions; self-inverse functions (AHL only), Solutions of inequalities g(x) ≥ f(x) (AHL only), Graphs of |f(x)|, f(|x|) and related functions; modulus equations (AHL only)
Study guides
- Analysis and Approaches – Functions Strand Read guide
- Analysis and Approaches – Polynomials, rational functions, odd/even functions and modulus graphs (HL) Read guide
- Analysis and Approaches – Rational, exponential and logarithmic functions, solving equations and transformations Read guide
- Analysis and Approaches – Straight lines, functions, inverses and quadratics Read guide
Revision notes
- Analysis and Approaches – Functions Strand Revise topic
- Analysis and Approaches – Polynomials, rational functions, odd/even functions and modulus graphs (HL) Revise topic
- Analysis and Approaches – Rational, exponential and logarithmic functions, solving equations and transformations Revise topic
- Analysis and Approaches – Straight lines, functions, inverses and quadratics Revise topic
Practice questions
- Analysis and Approaches – Functions Strand Try questions
- Analysis and Approaches – Polynomials, rational functions, odd/even functions and modulus graphs (HL) Try questions
- Analysis and Approaches – Rational, exponential and logarithmic functions, solving equations and transformations Try questions
- Analysis and Approaches – Straight lines, functions, inverses and quadratics Try questions
- Topic 3
Geometry and trigonometry
Covers 3D geometry: distance, midpoint, volume and surface area, The sine rule, cosine rule and area of a triangle, Applications of right and non-right-angled trigonometry, The circle: radian measure, arc length and area of a sector, Definitions of cosθ, sinθ and tanθ using the unit circle, The Pythagorean identity and double angle identities, The circular functions sin x, cos x and tan x, Solving trigonometric equations, Reciprocal trigonometric ratios and inverse circular functions (AHL only), Compound angle identities (AHL only), Relationships between trigonometric functions and symmetry of their graphs (AHL only), Vectors: concept, components and algebraic/geometric operations (AHL only), The scalar product of two vectors (AHL only), Vector equation of a line in two and three dimensions (AHL only), Coincident, parallel, intersecting and skew lines (AHL only), The vector product of two vectors (AHL only), Vector equations of a plane (AHL only), Intersections of lines and planes (AHL only)
Study guides
Revision notes
- Topic 4
Statistics and probability
Covers Concepts of population, sample, sampling techniques and outliers, Presentation of data: frequency distributions, histograms and box-and-whisker diagrams, Measures of central tendency and measures of dispersion, Linear correlation of bivariate data and the regression line of y on x, Concepts of trial, outcome, sample space, event and probability, Combined, mutually exclusive, conditional and independent events, Discrete random variables and their probability distributions, The binomial distribution, The normal distribution, The regression line of x on y, Formal definition of conditional probability and independence, Standardization of normal variables (z-values), Bayes’ theorem (AHL only), Variance of discrete and continuous random variables (AHL only)
Study guides
Revision notes
- Topic 5
Calculus
Covers Introduction to the concept of a limit; derivative as gradient function, Increasing and decreasing functions, Derivative of f(x) = ax^n, Tangents and normals at a given point, Introduction to integration as anti-differentiation, Derivatives of x^n, sin x, cos x, e^x and ln x; chain, product and quotient rules, The second derivative and graphical behaviour of functions, Local maximum and minimum points, optimization and points of inflexion, Kinematic problems: displacement, velocity, acceleration and distance, Indefinite integration by inspection or substitution, Definite integrals and areas between curves, Continuity, differentiability and derivative from first principles (AHL only), Evaluation of limits using l’Hôpital’s rule or Maclaurin series (AHL only), Implicit differentiation, related rates of change and optimisation (AHL only), Derivatives and indefinite integrals of further functions (AHL only), Integration by substitution and by parts (AHL only), Areas enclosed with the y-axis and volumes of revolution (AHL only), First order differential equations (AHL only), The Maclaurin series (AHL only)
Study guides
- Analysis and Approaches – Calculus Strand Read guide
- Analysis and Approaches – Integration, areas and kinematics Read guide
- Analysis and Approaches – Limits, derivatives, tangents, rules of differentiation and graph behaviour Read guide
- Analysis and Approaches – Limits, further differentiation and integration, differential equations and Maclaurin series (HL) Read guide
Revision notes
- Analysis and Approaches – Calculus Strand Revise topic
- Analysis and Approaches – Integration, areas and kinematics Revise topic
- Analysis and Approaches – Limits, derivatives, tangents, rules of differentiation and graph behaviour Revise topic
- Analysis and Approaches – Limits, further differentiation and integration, differential equations and Maclaurin series (HL) Revise topic
Practice questions
- Analysis and Approaches – Calculus Strand Try questions
- Analysis and Approaches – Integration, areas and kinematics Try questions
- Analysis and Approaches – Limits, derivatives, tangents, rules of differentiation and graph behaviour Try questions
- Analysis and Approaches – Limits, further differentiation and integration, differential equations and Maclaurin series (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: analysis and approaches guide, first assessment 2021 (published February 2019, updated August 2019/May 2020/August 2020/November 2020) — First assessment 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: Analysis and Approaches
- Spec code
- DP Mathematics: Analysis and Approaches
- Does Marlbridge teach it?
- Yes — request a free trial class
- Who teaches it?
- Muhammad Ghazali Siddiqui · Arslan Tanvir
- Are resources available?
- Yes — 55 published
- Is enrolment open?
- Enquire to join — no online enrolment yet
- Official syllabus
- International Baccalaureate syllabus
- Topic checklist
- Printable DP Mathematics: Analysis and Approaches checklist
- 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: Analysis and Approaches
Marlbridge's summary of the course
IB DP Mathematics: Analysis and Approaches recognizes the need for analytical expertise, developing important mathematical concepts in a comprehensible, coherent and rigorous way with a strong emphasis on constructing, communicating and justifying correct mathematical arguments, 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) plus an internally assessed Mathematical Exploration; Higher Level sits an additional Paper 3. 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 – No Technology Permitted (SL) | 1h 30m | 80 | 40% | Written exam |
| Paper 2: Paper 2 – Technology Permitted (SL) | 1h 30m | 80 | 40% | Written exam |
| Exploration: Internal Assessment – Mathematical Exploration (SL) | — | 20 | 20% | Coursework |
| Paper 1: Paper 1 – No Technology Permitted (HL) | 2h | 110 | 30% | Written exam |
| Paper 2: Paper 2 – 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). 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, technology required) and the Mathematical Exploration (20 marks at both tiers, marked against five criteria – Presentation (4), Mathematical Communication (4), Personal Engagement (3), Reflection (3), Use of Mathematics (6) – an internally assessed written investigation, compulsory at both tiers) 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: Analysis and Approaches (DP Mathematics: Analysis and Approaches) assessed?
International Baccalaureate Mathematics: Analysis and Approaches (DP Mathematics: Analysis and Approaches) is assessed through: SL candidates take: Paper 1 (Paper 1 – No Technology Permitted) — 1h 30m, 80 marks, 40% of the qualification; Paper 2 (Paper 2 – 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 – No Technology Permitted) — 2h, 110 marks, 30% of the qualification; Paper 2 (Paper 2 – 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: Analysis and Approaches 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: Analysis and Approaches?
Yes. Marlbridge teaches IB Diploma Programme Mathematics: Analysis and Approaches 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: Analysis and Approaches revision notes and practice questions?
Yes. Marlbridge has published 55 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: Analysis and Approaches teaching and study resources.
Mathematics: Analysis and Approaches 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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