Unit Overview

Number and Algebra

IB Mathematics: Applications and Interpretation SL· 5 min read 📊 18-20% of overall IB AI SL exam

1. Unit at a Glance

This unit moves from basic number skills through to algebraic tools that you will use for modeling and problem solving throughout the course. We start with working with numbers in scientific notation, before moving to arithmetic sequences, then geometric sequences and their real-world financial applications.

We then build exponent and logarithm rules, learn how to solve exponential equations, and finish with core skills for approximation and error calculation that are required for all practical problem-solving in IB AI SL.

This unit is split into the following sub-topics:

Operations with numbers in scientific notation

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

★★⏱ 8 min

Arithmetic sequences and series

Find nth terms, common differences, and sums of finite arithmetic sequences and series.

★★⏱ 10 min

Geometric sequences and series

Calculate common ratios, nth terms, and sums of finite and infinite geometric series.

★★★⏱ 10 min

Financial applications of geometric sequences and series

Apply geometric sequences to solve compound interest, depreciation, and other common financial problems.

★★★⏱ 12 min

Laws of exponents with rational exponents

Simplify and manipulate expressions involving rational exponents using core exponent rules.

★★⏱ 9 min

Simplification of logarithmic expressions

Apply logarithm laws to simplify and rewrite logarithmic expressions of any base.

★★★⏱ 10 min

Solving exponential equations using logarithms

Use logarithms to solve exponential equations with any base for unknown exponents.

★★★⏱ 11 min

Approximation, absolute and percentage error

Calculate absolute error and percentage error for approximate measurements and calculations.

★★⏱ 9 min

Standard form of numbers

Convert between ordinary numbers and standard (scientific) form for large and small values.

★⏱ 8 min

2. Common Pitfalls

Wrong move:

Forgetting to re-normalize results after adding/subtracting numbers in scientific notation

Why:

Many students add the coefficients but leave the result with a coefficient outside the required 1-10 range for standard form

Correct move:

After any operation, adjust the coefficient and exponent to meet the standard form definition

Wrong move:

Confusing nth term formulas with sum formulas for sequences

Why:

Arithmetic and geometric formulas are similar enough to mix up under exam pressure

Correct move:

Always confirm if the question asks for a specific term or the total sum of a set of terms before selecting a formula

Wrong move:

Treating regular percentage growth/decay as an arithmetic (linear) pattern

Why:

Students often assume repeated percentage changes follow a linear sequence

Correct move:

Recognize percentage changes are multiplicative, so they always follow a geometric sequence pattern

3. Quick Reference Cheatsheet

Concept / Formula	Key Use
Standard form: $a \times 1 0^{k}$ , $1 \leq a < 10$ , $k \in Z$	Represent very large or very small numbers
Arithmetic nth term: $u_{n} = u_{1} + (n - 1) d$	Find any term in an arithmetic sequence
Arithmetic sum: $S_{n} = \frac{n}{2} (u_{1} + u_{n})$	Sum the first n terms of an arithmetic sequence
Geometric nth term: $u_{n} = u_{1} r^{n - 1}$	Find any term in a geometric sequence
Geometric finite sum: $S_{n} = \frac{u _{1} ( 1 - r ^{n} )}{1 - r}, r \neq = 1$	Sum the first n terms of a geometric sequence
Compound interest: $F V = P V (1 + \frac{r}{100 k})^{k n}$	Calculate future value of compound interest investments
Exponent rule: $a^{m} \times a^{n} = a^{m + n}$ , $(a^{m})^{n} = a^{mn}$	Simplify expressions with rational exponents
Logarithm rule: $lo g (ab) = lo g a + lo g b$ , $lo g a^{b} = b lo g a$	Simplify logarithmic expressions
Percentage error: $\frac{∣ v _{a pp r o x} - v _{e x a c t} ∣}{∣ v _{e x a c t} ∣} \times 100%$	Calculate percentage error for approximations

What's Next

Begin your study of this unit with the first sub-topic, Operations with numbers in scientific notation, to start building core number skills. After completing all sub-topics in this Number and Algebra unit, you will progress to the next unit on Functions, starting with an introduction to core function concepts that build on your new algebra skills.