IB Math AI SL Unit 2: Functions

IB Maths AI SL Unit 2: Functions, 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.

• Applications of Functions questions40 questions · 5 worked examples
• Direct/Inverse Variation and Cubic Models questions14 questions · 3 worked examples
• Exponential Modelling questions16 questions · 3 worked examples
• Functions: Domain, Range & Inverses questions28 questions · 5 worked examples
• Graphing Linear, Quadratic, Exponential and Logarithmic Functions questions85 questions · 3 worked examples
• Linear Modelling questions19 questions · 3 worked examples
• Quadratic Modelling questions27 questions · 3 worked examples
• Sinusoidal Modelling questions13 questions · 3 worked examples
• Solving Equations questions12 questions · 3 worked examples

Learn it first: AI SL Unit 2 notes

• Linear functions and modelling
• Quadratic functions
• Sinusoidal models for periodic data
• Piecewise functions and modelling

Where marks go in AI SL Unit 2

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

• Exponential and log models: e⁰ = 1, the equation vs the inequality, reading the model. At t = 0 any bᵗ or e^(kt) equals 1. For "after how many complete years…", solve the inequality and round in the direction the context needs. Use the model's equation in any comment on it.
• Function notation and answer form: f⁻¹(a), ranges and inequalities. f⁻¹(a) means solve f(x) = a. For a range, sketch the graph on the GDC and read the y-values it actually takes. If the answer is a set of values, write it as an inequality.
• Interpreting in context: parameters, derivatives and justifications. Name the quantity and its units: "0.35 is the cost in dollars per extra kilometre". Base every justification on a calculated value from the question.

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 SL past papers page.

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Also for AI SL: common exam mistakes · syllabus checklist