Course Specifications for IB Math AI SL
This page covers the full IB Math AI SL syllabus. Practise each topic with the AI SL question bank. Download the AI SL formula sheets and use past papers alongside this guide.
1. Number & Algebra
Number Toolkit
Standard Form
Laws of Indices
Introduction to Logarithms
Approximation
Upper & Lower Bounds
Percentage Error
Accuracy & Estimation
Solving Equations using a GDC
Sequences & Series
Language of Sequences & Series
Sigma Notation
Arithmetic Sequences & Series
Geometric Sequences & Series
Applications of Sequences & Series
Financial Applications
Compound Interest & Depreciation
Amortisation
Annuities
2. Functions
Linear Functions & Graphs
Equations of a Straight Line
Parallel & Perpendicular Lines
Further Functions & Graphs
Functions & Mappings
Inverse Functions
Graphing Functions & Their Key Features
Intersecting Graphs
Quadratic Functions & Graphs
Cubic Functions & Graphs
Exponential Functions & Graphs
Sinusoidal Functions & Graphs
Modelling with Functions
Linear & Piecewise Models
Quadratic Models
Cubic Models
Exponential Models
Direct & Inverse Variation
Sinusoidal Models
Strategy for Modelling Functions
3. Geometry & Trigonometry
Geometry Toolkit
Coordinate Geometry
Perpendicular Bisectors
Arcs & Sectors
Geometry of 3D Shapes
3D Coordinate Geometry
Volume & Surface Area
Trigonometry
Pythagoras & Right-Angled Trigonometry
Sine Rule, Cosine Rule & Area of a Triangle
Angles of Elevation & Depression
Bearings & Constructions
Voronoi Diagrams
Drawing Voronoi Diagrams
Interpreting Voronoi Diagrams
Toxic Waste Dump Problem
4. Statistics & Probability
Statistics Toolkit
Sampling & Data Collection
Measures of Central Tendency
Measures of Dispersion
Frequency Tables
Linear Transformations of Data
Outliers
Box & Whisker Diagrams
Cumulative Frequency Graphs
Histograms
Interpreting Data
Correlation & Regression
Scatter Diagrams & Correlation
Pearson’s Product-Moment Correlation Coefficient
Spearman’s Rank Correlation Coefficient
Comparison of Correlation Coefficients
Linear Regression
Probability
Probability & Types of Events
Independent & Mutually Exclusive Events
Conditional Probability
Venn Diagrams
Tree Diagrams
Probability Distributions
Discrete Probability Distributions
Expected Values
Binomial Distribution
The Binomial Distribution
Calculating Binomial Probabilities
Normal Distribution
The Normal Distribution
Calculations with Normal Distribution
Hypothesis Testing
Introduction to Hypothesis Testing
Chi-squared Test for Independence
Goodness of Fit Test
The t-test
5. Calculus
Differentiation
Introduction to Derivatives
Differentiating Powers of x
Gradients, Tangents & Normals
Increasing & Decreasing Functions
Local Minimum & Maximum Points
Modelling with Differentiation
Integration
Numerical Integration using the Trapezoidal Rule
Introduction to Integration
Integrating Powers of x
Finding the Constant of Integration
Finding Areas Using a GDC