IB Math AI HL Unit 1: Number & Algebra

IB Maths AI 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 and Argand Diagrams questions31 questions · 3 worked examples
• Eigenvalues, Eigenvectors and Markov Chains questions27 questions · 3 worked examples
• Logs and Infinite Geometric Series questions51 questions · 3 worked examples
• Matrices, Determinants and Inverses questions42 questions · 3 worked examples

Learn it first: AI HL Unit 1 notes

• Matrices
• Systems of linear equations and Gaussian elimination
• Complex numbers and Argand diagrams
• Sequences, series, and the sum to infinity
• Exponential models for real-world decay

Where marks go in AI HL Unit 1

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

• Finance on the GDC: signs, months vs years, P/Y and C/Y, and the rounding asked for. List every TVM entry (N, I%, PV, PMT, FV, P/Y, C/Y). Money out and money in have opposite signs. N = years × payments per year. Round the final answer as the question says.
• Markov chains: columns, the initial state, the right power of T. Label rows and columns (from → to) and check each column sums to 1. After n steps: Tⁿs₀. Count the steps from the starting day. Give the steady state as one vector whose entries sum to 1.
• Complex numbers and transformation matrices. Expand complex products fully (i² = −1), then collect real and imaginary parts. Work in radians. Learn the rotation and reflection matrices in the formula booklet and what their products represent.

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

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