IB Math AA HL Unit 1: Number & Algebra

IB Maths AA HL Unit 1: Number and Algebra, topic by topic

Each topic in this unit has a free page with step-by-step worked examples and the key formulas, then exam-style questions with mark schemes.

• Complex Numbers questions46 questions · 3 worked examples
• Counting and Binomials questions22 questions · 3 worked examples
• Partial Fractions questions20 questions · 3 worked examples
• Proof questions38 questions · 3 worked examples
• Systems of Equations questions30 questions · 3 worked examples

Learn it first: AA HL Unit 1 notes

• Proof by induction
• Binomial theorem for rational and negative exponents
• Complex numbers
• De Moivre's theorem and roots of unity
• Systems of equations and partial fractions

Where marks go in AA HL Unit 1

From the IB subject reports we summarise on AA HL Examiner Insights, in our own words:

• Proof by induction: weak structure and "let n = k". Four parts, in words: show it is true for the first value; assume it is true for n = k; use that assumption to show it is true for n = k + 1; conclude (true for n = 1, and true for k implies true for k + 1, so true for all n ∈ ℤ⁺).
• Logs and exponentials: hidden quadratics and misapplied log laws. Look for aˣ and a²ˣ together: substitute u = aˣ. Logs of a sum do not split. log(xy)ⁿ = n log(xy) = n(log x + log y).
• Complex numbers and polynomials: conjugate roots, all the roots, general solutions. A real polynomial with root a + bi also has a − bi. Build the quadratic factor (z − (a + bi))(z − (a − bi)) = z² − 2az + a² + b² and divide, or use sum/product with every root.

The questions here are original, written in the style of IB papers with IB-style mark schemes; for real papers see the IB Maths AA HL past papers page.

FAQ

Also for AA HL: common exam mistakes · syllabus checklist