Revision guide
IB Math Analysis & Approaches
How to revise Math AA, what the papers actually test, and where students lose marks.
Math Analysis & Approaches is the more algebraic and proof-oriented of the two IB mathematics courses. It rewards fluency: the exams give you very little time per mark, so the difference between a 5 and a 7 is rarely about knowing more content — it's about how quickly and accurately you execute techniques you already know. Calculus carries the heaviest weight, especially at HL, and questions routinely chain several topics together (a trigonometry identity inside an integral inside a kinematics context).
The most reliable way to improve at AA is volume of past-paper-style questions done under time pressure, reviewed against the markscheme line by line. The markscheme shows exactly which intermediate steps earn method marks — students who write fluent but unstructured working leave easy marks on the table even when their final answer is right.
How you're assessed
Paper 1 (no calculator)
Short- and long-response questions with no calculator allowed. This paper punishes weak algebraic manipulation: exact values, surds, logarithm laws, and clean fraction work matter. Section A is shorter structured questions; Section B is multi-part problems that build on each other.
Paper 2 (calculator)
Same structure as Paper 1 but with a graphing calculator. The skill being tested is knowing when to switch to the GDC — solving equations graphically, evaluating definite integrals numerically, and using distributions directly instead of by hand.
Paper 3 (HL only)
Two extended problem-solving questions that walk you into unfamiliar territory step by step. You're not expected to know the result in advance — you're expected to follow the scaffolding, so never abandon a Paper 3 question early: later parts often become accessible again.
The IA (Exploration)
A written exploration on a topic you choose, worth 20% of the final grade. The highest-scoring explorations use mathematics at the level of the course on a question the student genuinely owns — personal engagement is assessed, and recycled topics (modelling a roller coaster, the golden ratio) make that criterion hard to earn.
How to revise
Drill by topic, then mix
Revise one unit at a time with topic-filtered questions until the method is automatic, then switch to mixed sets. AA exams interleave topics aggressively, and students who only ever practice by chapter freeze when a question doesn't announce which technique it wants.
Do no-calculator arithmetic daily
Paper 1 errors are overwhelmingly arithmetic, not conceptual. Ten minutes a day of fraction, surd, and log manipulation without a calculator rebuilds the fluency that GDC dependence erodes.
Learn the markscheme's language
Method marks are earned by visible steps: stating the derivative before setting it to zero, writing the integral before evaluating it. After every practice question, compare your working to the markscheme and note which lines carried marks.
Master your GDC before exam week
Know the fastest route to: solving any equation graphically, numerical derivatives and integrals, and the distribution menus. In Paper 2, a student fluent with the GDC banks 15–20 minutes over one who isn't.
Mistakes examiners see every year
Giving decimal answers where exact values are required on Paper 1.
Losing accuracy marks by rounding intermediate values instead of carrying full precision to the end.
Ignoring the three-significant-figure rule on final answers.
Spending ten minutes on a 4-mark question — marks-per-minute discipline wins papers.
Treating Paper 3 (HL) parts as independent instead of using earlier results in later parts.
What's in the syllabus
Number and Algebra
Indices and surds · Logarithms · Sequences and series · Binomial theorem · Complex numbers · Matrices · Proof by induction · Binomial theorem · Complex numbers
Functions
Function notation · Domain and range · Transformations · Inverse functions · Polynomial functions · Rational functions · Exponential and logarithmic functions
Geometry and Trigonometry
Trigonometric ratios · Unit circle · Trigonometric identities · Vectors · Vector equations of lines · Scalar product · Planes
Statistics and Probability
Descriptive statistics · Probability rules · Conditional probability · Discrete random variables · Binomial distribution · Normal distribution · Hypothesis testing
Calculus
Differentiation · Applications of derivatives · Integration · Area under curves · Kinematics · Differential equations · Maclaurin series
Frequently asked questions
Is Math AA HL the hardest IB subject?
It has one of the lowest 7 rates in the IB, but the curve is generous — grade boundaries for a 7 are often near 70%. Strong, consistent past-paper practice matters more than natural talent.
AA or AI — which should I take?
Take AA if your university course needs pure math (engineering, physics, math, some economics programs). AA emphasizes algebra, proof, and calculus by hand; AI emphasizes modelling, statistics, and technology.
How early should I start the IA?
Pick a topic by the end of the first year. The exploration takes longer than expected because finding mathematics that's the right difficulty level is itself the hard part.
Put this guide into practice
Everything above — topic-filtered practice questions, spaced-repetition flashcards, and a syllabus checklist for Math Analysis & Approaches — is free on Baccly.
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