Unit Overview

Number and algebra

IB Mathematics Applications and Interpretation HL· 5 min read 📊 15-20% of total IB AI HL examination

1. Unit at a glance

We start with core number skills including scientific notation and error estimation that underpin all quantitative work in this course. Next we move to sequences and series, with a focus on applied financial problems that are a key part of the AI syllabus. We then cover logarithms and exponential equations, which are critical for modeling exponential growth and decay in real-world contexts.

The unit concludes with logarithms, exponential equations, and an introduction to complex numbers, all of which support later topics in calculus, probability, and statistical modeling. Each concept builds on previous skills, so it is important to master sub-topics in order.

This unit includes the following sub-topics:

Operations with numbers in scientific notation

Perform addition, subtraction, multiplication and division with numbers in scientific notation.

★⏱ 10 min

Approximation, error and estimation

Calculate absolute error, percentage error, and apply rounding and significant figure rules.

★★⏱ 15 min

Arithmetic and geometric sequences and series

Find nth terms and sums of finite and infinite arithmetic and geometric sequences.

★★⏱ 20 min

Financial applications of geometric sequences and series

Calculate compound interest, depreciation, and the value of annuities using geometric sequences.

★★★⏱ 25 min

Laws of exponents

Combine, simplify and evaluate expressions using integer and rational exponents and radicals.

★★⏱ 15 min

Laws of logarithms

Simplify and rearrange logarithmic expressions using product, quotient and power laws.

★★★⏱ 15 min

Solving exponential equations with logarithms

Use logarithms to solve exponential equations from real-world modeling problems.

★★★⏱ 20 min

Complex numbers: definition, arithmetic and polar form

Perform arithmetic operations on complex numbers in both Cartesian and polar form.

★★★★⏱ 25 min

2. Common Pitfalls

Wrong move:

Forgetting to align powers of 10 when adding or subtracting scientific notation

Why:

This leads to incorrect order of magnitude and wrong final results

Correct move:

Always rewrite all terms to use the same exponent of 10 before adding or subtracting

3. Quick Reference Cheatsheet

Concept	Key Formula / Rule
nth term of arithmetic sequence	$u_{n} = u_{1} + (n - 1) d$
Sum of finite geometric series	$S_{n} = \frac{a ( 1 - r ^{n} )}{1 - r}, r \neq = 1$
Compound interest	$A = P (1 + \frac{r}{100})^{n}$
Product Law of Logarithms	$lo g_{b} (x y) = lo g_{b} x + lo g_{b} y$
Change of Base Formula	$lo g_{b} a = \frac{l n a}{l n b}$
Modulus of a complex number $x + i y$	$∣ x + i y ∣ = x^{2} + y^{2}$
Sum to infinity of geometric series	$S_{\infty} = \frac{a}{1 - r}, ∣ r ∣ < 1$

What's Next

Start this unit with the first sub-topic on operations with numbers in scientific notation to build your foundational number skills that will be used across all IB AI HL topics. After completing all sub-topics in this unit, you will be ready to move on to the next unit, which covers functions, the core tool for real-world mathematical modeling.