Unit Overview

Number & Algebra

IB Mathematics: Analysis and Approaches SL· 5 min read 📊 15-18% of overall examination

1. Unit at a Glance

This unit progresses from practical number skills to advanced algebraic manipulation and combinatorics, building the foundational tools you will use for functions, calculus, and statistics later in the course. We start with measurement and error handling, move to discrete sequence patterns, then explore exponential and logarithmic relationships, and finish with combinatorial counting needed for probability and binomials.

This unit is split into the following 8 sub-topics:

Approximation, significant figures and scientific notation

Learn to round correctly, write values in scientific notation, and identify significant figures for calculations.

★⏱ 10 min

Error bounds and absolute/relative error

Calculate upper and lower error bounds, and find absolute and relative error for measured values.

★★⏱ 8 min

Arithmetic sequences and series

Derive and use formulas for the nth term and sum of finite arithmetic sequences and series.

★★⏱ 10 min

Geometric sequences and infinite geometric series

Work with geometric sequences, and find sums of finite and infinite convergent geometric series.

★★★⏱ 12 min

Laws of exponents and logarithms

Simplify expressions using exponent rules and the core laws of logarithms.

★★★⏱ 12 min

Solving exponential and logarithmic equations

Solve exponential and logarithmic equations using algebraic and GDC methods.

★★★★⏱ 15 min

Permutations and combinations

Distinguish between permutations and combinations, and count arrangements of items.

★★★⏱ 10 min

Binomial expansion and binomial theorem

Apply the binomial theorem to expand binomials and find specific terms in expansions.

★★★⏱ 12 min

2. Common Pitfalls

Wrong move:

Mixing up permutations and combinations when counting arrangements

Why:

Permutations count ordered arrangements, while combinations count unordered groups

Correct move:

Always ask whether order matters before selecting the right counting formula

Wrong move:

Forgetting the convergence condition for infinite geometric series

Why:

Infinite sums only exist if the common ratio satisfies $∣ r ∣ < 1$

Correct move:

Check the value of $∣ r ∣$ before calculating an infinite geometric sum

Wrong move:

Premature rounding of intermediate results in multi-step calculations

Why:

Rounding early leads to accumulated error that shifts your final answer away from the correct value

Correct move:

Keep full precision on your calculator until the final step, then round to the required significant figures

3. Quick Reference Cheatsheet

Concept	Key Formula/Expression
nth term of arithmetic sequence	$u_{n} = u_{1} + (n - 1) d$
Sum of finite arithmetic series	$S_{n} = \frac{n}{2} (u_{1} + u_{n})$
nth term of geometric sequence	$u_{n} = u_{1} r^{n - 1}$
Sum of infinite convergent geometric series	$S_{\infty} = \frac{u _{1}}{1 - r}, ∣ r ∣ < 1$
Logarithm product rule	$lo g_{b} (x y) = lo g_{b} x + lo g_{b} y$
Logarithm power rule	$lo g_{b} (x^{n}) = n lo g_{b} x$
Permutation of n items taken k at a time	$^{n} P_{k} = \frac{n !}{( n - k )!}$
Binomial coefficient	$(k n) = \frac{n !}{k ! ( n - k )!}$

What's Next

Start your study of this unit with the first sub-topic on approximation, significant figures, and scientific notation to build core number skills you will use for all future calculations. Once you complete all 8 sub-topics in this unit, you will be ready to move on to the next unit on functions, which builds directly on the algebra skills you learn here.