IB Math Tutor Online · Analysis & Approaches

IB Math AA Tutor - HL & SL

Struggling with proofs, calculus, or complex numbers? I help IB Math AA students at every level, from building foundations in SL to mastering the hardest HL topics, with personalised lessons designed around your specific gaps.

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What is IB Math AA?

IB Mathematics Analysis and Approaches (AA) is one of two IB Diploma Programme mathematics courses. It emphasises algebraic reasoning, mathematical proof, and calculus, making it the natural choice for students heading into STEM fields, economics, mathematics, or any subject that demands rigorous quantitative thinking.

AA is available at Higher Level (HL) and Standard Level (SL). HL goes considerably further: it includes proof by induction, complex numbers, harder integration techniques, Maclaurin series, differential equations, and vector geometry with lines and planes. Both levels share a common foundation but diverge sharply in depth and difficulty.

Which level is right for you? If you plan to study engineering, pure mathematics, physics, or economics at a selective university, AA HL gives you the strongest preparation. AA SL is appropriate for students who need mathematical reasoning but at a less intensive level, and it still counts as a serious academic qualification.

Full syllabus coverage

Every topic, every sub-topic. Nothing skipped.

Topic 1

Number & Algebra

  • Arithmetic & geometric sequences and series
  • Exponents, logarithms and their laws
  • Binomial theorem
  • Proof by induction (HL)
  • Complex numbers, modulus, argument, polar form (HL)
  • Partial fractions, systems of equations (HL)

Topic 2

Functions

  • Function notation, domain, range, inverse
  • Composite functions and transformations
  • Rational functions and asymptotes
  • Exponential and logarithmic functions
  • Solving equations graphically and algebraically
  • Odd/even functions, solving inequalities (HL)

Topic 3

Geometry & Trigonometry

  • Trigonometric ratios, exact values, radians
  • Sine rule, cosine rule, area of a triangle
  • Trig identities and equations
  • 3D geometry and surface area/volume
  • Vectors, dot product, angle between vectors (SL+HL)
  • Vector equations of lines and planes, cross product (HL)

Topic 4

Statistics & Probability

  • Descriptive statistics, box plots, outliers
  • Probability rules, tree diagrams, Venn diagrams
  • Binomial and normal distributions
  • Correlation and linear regression
  • Continuous random variables, CDF (HL)
  • Unbiased estimators, hypothesis testing (HL)

Topic 5

Calculus

  • Limits, continuity, derivatives from first principles
  • Chain, product and quotient rules
  • Applications: turning points, optimization, kinematics
  • Indefinite and definite integration, area between curves
  • Integration by substitution and by parts (HL)
  • Differential equations, Maclaurin series (HL)

How I approach HL vs SL

Same personalised method, different depth and focus.

AA HL

  • Deep algebraic reasoning and formal proof
  • Complex numbers: Cartesian, polar, Euler form
  • Integration techniques: by parts, substitution, partial fractions
  • Differential equations: separable, homogeneous, integrating factor
  • Maclaurin series and error estimation
  • Vector geometry: planes, intersections, distances
  • Paper 3 practice: extended problem-solving
  • Heavy emphasis on "show that" and proof questions

AA SL

  • Solid foundations in functions and algebra
  • Trig equations and identities without overcomplicating
  • Integration as area, intuitive understanding first
  • GDC use for SL-appropriate questions
  • Exam technique: reading command terms correctly
  • Identifying question types quickly in Paper 1 and 2
  • Focus on confidence and reducing exam anxiety

How lessons work

01

Diagnostic first

We start with a free diagnostic session to identify exactly where you're losing marks and what to prioritise.

02

Personalised plan

Every lesson is structured around your gaps, your exam timeline, and the specific AA topics you find hardest.

03

Live via Zoom

Sessions run on Zoom with GoodNotes and a shared screen. Notes are always accessible after the lesson.

04

Past paper practice

We work through real IB past papers. I show you how to comprehend the questions, IB math commands and most important, how to maximize marks.

Between lessons: Got a question mid-week? Send a message. Support doesn't stop when the session ends.

FAQs, IB Math AA

What is IB Math Analysis and Approaches (AA)?

IB Math AA is the IB Diploma mathematics course focused on algebraic reasoning, proof, and calculus. It's the standard choice for students planning STEM or economics degrees. Available at HL (harder) and SL.

What is the difference between AA HL and AA SL?

AA HL includes significantly more content: proof by induction, complex numbers, harder calculus (Maclaurin series, differential equations), vector planes, and a third exam paper. AA SL covers the same core topics but at a less advanced level and with two papers only.

How quickly can I improve my AA grade?

Most students see meaningful improvement within 4–8 weeks of consistent work. Students who start early in Year 11, or even Year 12, consistently reach their target grade. Even 6 weeks of focused preparation before exams makes a difference.

More resources

Free Guide

IB Math command terms

Show that, Hence, Justify, every term explained with exam tips.

Free Guide

How to maximise marks

M, A, R marks explained. Paper 1 vs Paper 2 strategy.

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About

About Patricia Akao

7+ years, hundreds of students, worldwide. The story behind the lessons.

Ready to improve your AA grade?

First lesson is free. No commitment. Just clear explanations and a plan built around your AA syllabus.

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