IB Math Analysis & Approaches HL/SL

Full IB Mathematics: Analysis & Approaches guide for HL and SL students. Covers algebra, functions, trigonometry, calculus, and statistics — plus HL-only complex numbers and further calculus topics.

Topics Covered

Algebra & Functions

Trigonometry

Calculus

Statistics & Probability

Complex Numbers (HL)

What you get

Full topic-by-topic curriculum coverage

Spaced-repetition flashcards for every topic

Multiple-choice quizzes with explanations

Term-matching vocabulary games

HL and SL content clearly labelled

Exam technique tips throughout

Key terms & definitions bank

12 months of access from purchase

Free Sample

Topic 1: Number and Algebra

THE BIG PICTURE. Topic 1 builds the algebraic foundation for everything that follows. SL focuses on sequences and series, exponents and logarithms, and the binomial theorem. HL extends to counting principles, complex numbers, proof, and partial fractions. Strong fluency here pays dividends across all five topics — every other topic uses these tools.

Sample Flashcards

Find the 20th term and sum of the first 20 terms of the arithmetic sequence $5, 9, 13, 17, \dots$

$u_{1} = 5$ , $d = 4$ . $u_{20} = u_{1} + (20 - 1) d = 5 + 19 \cdot 4 = 81$ . $S_{20} = \frac{20}{2} (u_{1} + u_{20}) = 10 \cdot 86 = 860$ . Alternatively, $S_{20} = \frac{20}{2} (2 \cdot 5 + 19 \cdot 4) = 10 \cdot 86 = 860$ .

A geometric series has first term $u_{1} = 8$ and common ratio $r = 0.75$ . Find $S_{\infty}$ .

$∣ r ∣ = 0.75 < 1$ , so an infinite sum exists. $S_{\infty} = \frac{u _{1}}{1 - r} = \frac{8}{1 - 0.75} = \frac{8}{0.25} = 32$ . Intuition: the terms $8, 6, 4.5, 3.375, \dots$ shrink fast enough that the total converges to $32$ .

Sample Key Terms

Arithmetic Sequence

Sequence with constant common difference $d$ . $u_{n} = u_{1} + (n - 1) d$ ; $S_{n} = \frac{n}{2} (u_{1} + u_{n})$ .

Geometric Sequence

Sequence with constant common ratio $r$ . $u_{n} = u_{1} r^{n - 1}$ ; $S_{n} = \frac{u _{1} ( 1 - r ^{n} )}{1 - r}$ . Infinite sum exists only when $∣ r ∣ < 1$ : $S_{\infty} = \frac{u _{1}}{1 - r}$ .

Sigma Notation

$\sum_{i = 1}^{n} u_{i}$ denotes $u_{1} + u_{2} + \dots + u_{n}$ . The index $i$ runs from the lower to upper bound.

What's Covered

Topic 1: Number and Algebra
Topic 2: Functions
Topic 3: Geometry and Trigonometry
Topic 4: Statistics and Probability
Topic 5: Calculus

5 topics · 76+ flashcards · quizzes & matching games included

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