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IB Math Applications & Interpretation Study Guide

Full IB Mathematics: Applications & Interpretation guide for HL and SL students. Covers number & algebra, functions, geometry, statistics, and the HL extension on calculus and graph theory.

The Prep Den IB Math Applications & Interpretation study guide is your complete companion for revising the course: full topic-by-topic coverage, spaced-repetition flashcards, practice quizzes with worked explanations, a key-terms bank, and exam-technique tips. Use it as your main study guide or as a supplement to your textbook and class notes.

Topics Covered

Number & Algebra

Functions & Modeling

Geometry & Trigonometry

Statistics & Probability

Calculus (HL)

What you get

Full topic-by-topic curriculum coverage

Spaced-repetition flashcards for every topic

Multiple-choice quizzes with explanations

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. AI Topic 1 emphasises applied algebra: scientific notation, sequences and series, financial mathematics, and basic exponents/logs. HL extends to complex numbers, matrix algebra (incl. eigenvalues), and transition matrices / Markov chains. The GDC is used heavily; AI rewards clear technology use and clear interpretation of numerical results.

Sample Flashcards

$5,000 is invested at $4%$ p.a. compound interest, compounded quarterly. Find value after 3 years.

Compound interest formula: $FV = PV (1 + \frac{r}{100 k})^{k n}$ with $PV = 5000$ , $r = 4$ , $k = 4$ , $n = 3$ .

$FV = 5000 (1 + \frac{4}{400})^{12} = 5000 (1.01)^{12} \approx 5, 634.13$ , i.e.

A car is worth $25,000 and depreciates at $15%$ per year. Find its value after 4 years.

Depreciation is compound interest with a negative rate.

$Value = 25000 (1 - 0.15)^{4} = 25000 (0.85)^{4} \approx 25000 \cdot 0.522 \approx 13, 050.16$ , i.e. $13,050.16.

The car retains about $52%$ of its value after 4 years.

Sample Key Terms

Scientific Notation

$a \times 1 0^{n}$ where $1 \leq ∣ a ∣ < 10$ and $n \in Z$ . Used to compactly express very large or very small numbers.

Percentage Error

$\frac{∣ v _{A} - v _{E} ∣}{v _{E}} \times 100%$ , where $v_{E}$ is the exact value and $v_{A}$ is the approximate. Always positive.

Arithmetic Sequence

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

What's Covered

Topic 1: Number and Algebra
Topic 2: Functions
Topic 3: Geometry and Trigonometry
Topic 4: Statistics and Probability
Topic 5: Calculus
Assessment & the Mathematical Exploration (IA)

6 topics · 78+ flashcards · quizzes included

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