OVERVIEW

What is IB Mathematics?

IB Mathematics offers two distinct pathways — Mathematics: Analysis and Approaches (AA) for students who enjoy algebraic rigour, proof, and calculus, and Mathematics: Applications and Interpretation (AI) for those who prefer statistics, modelling, and real-world application. Both are available at Higher Level (HL) and Standard Level (SL), giving four distinct courses with significantly different content and difficulty levels. Maths AA HL is widely regarded as the most demanding IB subject and is strongly preferred by top universities for Mathematics, Physics, Engineering, and Computer Science degrees. At Improve ME, our specialist IB Maths tutors cover all four pathways — AA HL, AA SL, AI HL, and AI SL — with dedicated Internal Assessment mentoring and timed past paper preparation aligned to the current IB syllabus.

IB

Qualification

Ages 16-18

Age range

SL & HL

Exam boards

COURSE CONTENT

IB Mathematics Course Content

SL & HL coverage plus Internal Assessment (IA) support and exam strategy.

Mathematics AA (Analysis and Approaches)

Number and Algebra — sequences and series (arithmetic and geometric), binomial theorem, proof by induction (HL), complex numbers (HL), systems of equations
Functions — domain and range, composite and inverse functions, transformations, rational functions, odd and even functions
Geometry and Trigonometry — triangle trigonometry, unit circle, trigonometric identities and equations, radians, arc length and sector area, vectors (HL: vector equations of lines and planes, cross product)
Statistics and Probability — descriptive statistics, probability rules, discrete distributions (binomial, Poisson HL), continuous distributions (normal), hypothesis testing, confidence intervals (HL)
Calculus — limits and continuity, differentiation (product, quotient, chain rules), integration (by substitution, by parts HL), differential equations (HL), Maclaurin series (HL), kinematics applications
HL Extensions — further proof techniques, complex number loci and De Moivre's theorem, further calculus techniques, solving systems of differential equations

Mathematics AI (Applications and Interpretation)

Number and Algebra — scientific notation, arithmetic and geometric sequences, financial mathematics (compound interest, annuities, amortisation), logarithmic functions
Functions — modelling with linear, quadratic, exponential, logarithmic, sinusoidal, and logistic functions; regression analysis; GDC-dependent graphing and analysis
Geometry and Trigonometry — volumes and surface areas of 3D shapes, right-angle and non-right-angle trigonometry, Voronoi diagrams (HL), graph theory (HL)
Statistics and Probability — sampling techniques, data presentation, measures of dispersion, regression, r and r² values, probability distributions (normal and binomial), hypothesis testing (chi-squared, t-test), Markov chains (HL)
Calculus — differentiation and integration for optimisation and area under curves, numerical methods, Euler's method (HL), coupled differential equations (HL)
HL Extensions — network graphs, transition matrices, further statistical analysis, calculus modelling with technology

Internal Assessment and eAssessment

Mathematics IA (Internal Assessment) — Mathematical Exploration worth 20% of final grade; student-chosen topic; assessed on five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection, Use of Mathematics
Topic selection guidance — choosing a topic with sufficient mathematical depth, personal engagement, and exploration potential
IA structure — introduction, mathematical content (the bulk of the IA), personal engagement, reflection, conclusion
Common IA pitfalls — insufficient mathematical complexity, lack of personal voice, poor reflection, over-reliance on GDC output without mathematical explanation
Paper 1 (no GDC) — tests algebraic fluency, manipulation, and recall without calculator assistance; heavily weighted toward pure mathematical reasoning
Paper 2 (GDC allowed) — tests application, modelling, and interpretation; GDC technique is a mark-earning skill in itself
Paper 3 (HL only) — problem-solving paper with two extended questions on unfamiliar scenarios; requires synthesis of multiple topic areas

ASSESSMENT

Assessment Structure

We support both Internal Assessment (IA) and final exams with a structured plan, feedback cycles, and timed practice. SL and HL requirements are clearly differentiated.

Paper 1

No GDC — Pure Mathematical Reasoning

AA SL / AI SL: 80 mins, 40% — short and extended response; no calculator; tests algebraic fluency and manipulation.
AA HL / AI HL: 120 mins, 30% — short and extended response; no GDC; heavily weighted toward pure mathematical reasoning and recall.
All papers externally marked by IB examiners; grade boundaries vary by session; 70%+ typically achieves a 7.

Paper 2

GDC Allowed — Application and Modelling

AA SL / AI SL: 90 mins, 40% — GDC permitted; tests application, modelling, and interpretation.
AA HL / AI HL: 120 mins, 30% — GDC permitted; GDC technique is a mark-earning skill in itself.
AI students use GDC in both papers; AA students only in Paper 2 (and Paper 3).

Paper 3 (HL only) + IA

Problem-Solving + Mathematical Exploration (20%)

HL only: Paper 3 — 60 mins, 20% — two extended questions on unfamiliar scenarios; requires synthesis of multiple topic areas.
IA (Internal Assessment): Mathematical Exploration — 20% of final grade; student-chosen topic; assessed on Presentation, Mathematical Communication, Personal Engagement, Reflection, Use of Mathematics.
IA is internally marked and externally moderated; topic selection and write-up mentoring are essential for high marks.

EXAM BOARDS

Assessment Framework

IB DP (SL)

IB DP (HL)

Internal Assessment (IA)

Not sure which board your child is on? We'll check at your free assessment.

TEACHING APPROACH

Our IB Mathematics Teaching Approach

01

Pathway-Specific Instruction

AA and AI require fundamentally different approaches — AA prioritises algebraic manipulation and proof while AI prioritises modelling, statistics, and GDC application. We never teach these interchangeably and ensure every session is precisely targeted at the student's specific pathway and level.

02

Paper 3 HL Problem-Solving Preparation

Paper 3 presents two extended unfamiliar problems that require students to synthesise knowledge across multiple topic areas under time pressure. We prepare students specifically for this paper with dedicated problem-solving sessions that build the flexible mathematical thinking it demands.

03

IA Topic Selection and Mentoring

The IA is worth 20% of the final grade and many students underperform because they choose topics with insufficient mathematical depth or fail to demonstrate personal engagement and reflection. We guide students through every stage — topic selection, mathematical development, write-up, and review — to maximise IA marks.

04

GDC Technique

For AI students especially, GDC technique is a mark-earning skill. We train students to use their calculator efficiently for regression, solving equations, and graphing — skills that directly earn marks in Paper 2.

WHY CHOOSE US