Course Specifications AI SL

Course Specifications for IB Math AI SL

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

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