IB Mathematics: Analysis and Approaches rewards algebraic fluency, proof discipline, and disciplined calculator and non-calculator work. Here is exactly what a 7-grade student does.
Velocity Tuition Academy · IB Maths AA · HL and SL
Updated May 2026·Written by Velocity Tuition Academy·Reviewed by experienced IB Maths AA HL and SL teachers
IB Mathematics: Analysis and Approaches (AA) is the most demanding IB Diploma subject for many students — particularly at HL — and the most heavily tutored. Strong content knowledge alone produces a 5 or 6. Reaching 7 requires disciplined algebraic fluency, comfortable proof technique, fluent calculator use on the calculator papers AND fluent non-calculator work on the non-calculator paper, a strong IA, and (HL only) substantial Paper 3 preparation. This guide covers exactly what a 7-grade AA student does at both HL and SL.
Paper 1 (SL and HL) — non-calculator. Short and extended response. SL: 90 minutes. HL: 120 minutes.
Paper 2 (SL and HL) — calculator allowed (graphing calculator). Short and extended response. SL: 90 minutes. HL: 120 minutes.
Paper 3 (HL only) — calculator allowed. Extended problem-solving questions, often investigation-style. 60 minutes.
Internal Assessment (IA) — Mathematical Exploration — 12-20 pages, individual mathematical investigation. Worth 20% of the SL and HL grade.
Paper 1 (Non-Calculator) Is Where 7s Are Won and Lost
Paper 1 — the non-calculator paper — separates the 7-grade students from the rest. The reason: many students rely heavily on graphing calculators in class and find Paper 1 exposes the gaps. The 7-grade habit:
Fluent algebraic manipulation — factorising, expanding, simplifying without slips. Drill this daily.
Exact-value trigonometry — know sin/cos/tan of standard angles (0, π/6, π/4, π/3, π/2) without thinking.
Logarithm rules — log(ab) = log a + log b, log(a/b) = log a - log b, log(a^n) = n log a, change of base.
Standard derivatives and integrals — d/dx of common functions, ∫ of common functions, all by heart.
Quadratic formula and completing the square — automatic, with sign discipline.
If your child can do calculus questions on Paper 2 but struggles on Paper 1, the gap is non-calculator fluency, not understanding. Daily drill closes it.
Proof Discipline (HL Especially)
HL Maths AA includes substantial proof content — proof by induction, proof by contradiction, direct proof. Mark schemes are unusually strict on proof structure:
Proof by induction: state the proposition P(n). Base case P(1) or P(k₀) — verify. Inductive step: assume P(k); prove P(k+1). Conclude: therefore P(n) holds for all n ≥ 1. State each step explicitly. Missing one of these standard steps loses marks even when the algebra is correct.
Proof by contradiction: assume the negation. Derive a contradiction. Conclude the original statement holds. State the structure clearly.
Direct proof: clear logical flow from premise to conclusion. Each implication justified.
Proof questions are 6-8 mark questions where a fluent student earns full marks and a confused student earns 2-3. Worth practising specifically.
Calculus Is Half The Course (HL)
At HL, calculus topics make up a substantial fraction of the syllabus. The 7-grade student is fluent in:
Maclaurin series (HL) — derive series for common functions, use them for approximations.
SL covers less depth — chain rule and standard derivatives/integrals, applications to areas and kinematics — but the same 7-grade fluency principle applies.
The Mathematical Exploration (IA)
The IA is a 12-20 page individual mathematical investigation worth 20% of the grade. Marked against five criteria: Presentation, Mathematical Communication, Personal Engagement, Reflection, Use of Mathematics.
7-grade IA characteristics:
Genuinely original topic. Not a textbook investigation. Personal Engagement marks come from genuine choice.
Appropriate level of mathematics. SL IAs should use SL-syllabus mathematics; HL IAs should reach HL-syllabus content. Beyond-syllabus mathematics is rewarded but must be correctly applied.
Mathematical Communication discipline — define every variable, state every theorem before using, label all graphs, use appropriate notation.
Reflection — honest assessment of limitations, alternative approaches considered, areas for further investigation.
Use of Mathematics — the mathematics actually drives insights, not just produces numbers.
Common IA mark losers: topic too narrow (not enough mathematics to explore) or too broad (no focused investigation); mathematics misapplied (e.g., quoting derivatives without justifying); presentation chaotic.
Start the IA in DP1, not DP2. Final draft by mid-DP2 at latest.
HL Paper 3 — The 7-Grade Differentiator
Paper 3 is HL-only and is the most distinctive part of IB Maths AA. It typically contains 2-3 extended problem-solving questions, each 25-30 marks, that require investigation-style mathematical thinking rather than recall.
What works for Paper 3:
Practice all the past Paper 3s available. Often 4-6 papers across recent years. They are unusually variable, so breadth of practice matters.
Get comfortable with longer-form mathematics. Show every step. Half-correct partial answers earn substantial method marks.
Use the calculator effectively. Graph functions, solve numerically, integrate numerically. Paper 3 explicitly rewards calculator-fluent students.
Manage the time. 60 minutes for 2-3 long questions. Don't get stuck on one question; come back if needed.
Past Paper Strategy
15-20 timed past papers across SL or HL papers in the final exam term. Maths AA is one of the highest past-paper-volume subjects.
Alternate Paper 1 (non-calc) and Paper 2 (calc) sittings to maintain both fluencies.
HL: 4-6 Paper 3 sittings minimum.
Mark with the official mark scheme. Track which topics consistently lose marks.
Daily mini-drills on weak topics — 20-30 minutes daily on identified gaps closes them faster than weekly long sessions.
Targeting a 7 in IB Maths AA?
Our 1-on-1 IB Maths AA tutors specialise in HL and SL — Paper 1 non-calculator fluency, proof discipline, calculus mastery, IA supervision, and HL Paper 3 preparation. Free diagnostic trial.
Five habits: (1) fluent algebraic manipulation drilled daily for Paper 1 non-calculator; (2) precise proof structure (induction, contradiction, direct) — state every step explicitly; (3) calculus fluency including differentiation rules and integration techniques; (4) strong IA with genuine topic, appropriate-level mathematics, and disciplined communication; (5) HL: substantial Paper 3 preparation across all available past papers.
It is widely considered the most demanding IB Diploma subject. The global average HL Maths AA score is lower than most other IB subjects. Content includes calculus, vectors, complex numbers, proof techniques, sequences and series, statistics, and more — at significant depth. Cambridge, Imperial, MIT and similar typically require Maths AA HL at grade 6 or 7 for Engineering and Mathematics applications.
Generally yes, particularly at HL. IB Maths AA HL covers more topics in greater depth than single A-Level Maths and includes proof, vectors, complex numbers and Paper 3's investigation style. A-Level Further Maths gets closer to AA HL in depth. The students who score 7 at AA HL typically have very strong mathematical fluency from earlier in school.
The Mathematical Exploration is a 12-20 page individual mathematical investigation. Students choose a mathematical topic of interest, develop it with original investigation, and write it up against five criteria (Presentation, Mathematical Communication, Personal Engagement, Reflection, Use of Mathematics). Worth 20% of the grade. Start in DP1.
Yes, for Paper 2 and Paper 3 (HL). Specifically a graphing calculator approved by the IB — typically Casio fx-9750GIII or fx-CG50, or TI-83/84 series. Paper 1 is non-calculator. Schools and exam centres confirm approved models. Buy the calculator early in DP1 and learn it thoroughly — graphing, equation solving, numerical integration and differentiation, statistics functions.
AA suits students aiming at Engineering, Physical Sciences, Maths, Computer Science and Economics at competitive universities. AI suits students aiming at Social Sciences, Business, and other less mathematically-demanding paths. The decision depends on university targets and the student's mathematical confidence. See our detailed guide on IB Maths AA vs AI.
