Master modelling, technology and interpretation with purpose.

A full AI HL course that makes the technology-heavy syllabus feel coherent, with emphasis on modelling, interpretation and communication.

What you’ll learn

Understand the method and know when to use it.

The goal is not simply to watch more videos. It is to make unfamiliar IB questions feel more manageable because the underlying mathematics is clear.

01Choose and apply appropriate mathematical models
02Interpret calculator output accurately
03Communicate conclusions in IB-ready language
04Connect topics across extended questions

Full curriculum

See exactly what is covered.

The curriculum is structured directly from the complete course syllabus. Open any topic to see its lesson sequence.

01Number and algebra37 lessons

1.1Scientific notation
1.2.1Arithmetic sequences and series
1.2.2Sigma notation
1.3Geometric sequences and series
1.4.1Compound interest
1.4.2Depreciation
1.4.3Inflation
1.5.1Laws of exponents
1.5.2Introduction to logs
1.5.3The number e
1.6.1Rounding
1.6.2Upper and lower bounds
1.6.3Percentage error
1.7.1Loans
1.7.2Annuities
1.8.1System of linear equations
1.8.2Polynomial equations
1.9.1Laws of logarithms
1.9.2. Change of Base
1.10More Exponents
1.11Sum of an infinite geometric series
1.12.1Complex numbers introduction
1.12.2Operations with complex numbers
1.12.3Complex solutions to polynomial equations
1.13.1Modulus-argument form
1.13.2Euler form
1.13.3Frequency and phase
1.13.4Geometric interpretation
1.14.1Introduction to matrices
1.14.2Algebra of matrices
1.14.3Multiplication of matrices
1.14.4Identity and zero matrices
1.14.5Properties of matrices
1.14.6Determinant and Inverse
1.14.7System of linear equations
1.15.1Eigenvalues and eigenvectors
1.15.2Powers of matrices

02Functions29 lessons

2.1.1Gradient of a line
2.1.2Equation of a straight line
2.1.3Parallel and perpendicular lines
2.2.1Functions introduction
2.2.2Evaluating functions
2.2.3Inverse functions
2.3Sketching functions
2.4.1Features of graphs
2.4.2Asymptotes
2.5.1Linear modelling
2.5.2Quadratic functions
2.5.3Quadratic modelling
2.5.4Exponential modelling
2.5.5Direct and inverse variation
2.5.6Cubic modelling
2.5.7Sinusoidal graphs
2.5.8Creating a sinusoidal model
2.6Finding parameters of a model
2.7.1Composite functions
2.7.2Finding the inverse functions
2.8.1Transformations
2.8.2Composite transformations
2.9.1Half life
2.9.2Natural logarithmic modelling
2.9.3Sinusoidal modelling extension
2.9.4Logistic modelling
2.9.5Piecewise models
2.10.1Scaling using logs
2.10.2log log graphs

03Geometry and trigonometry57 lessons

3.1.1Midpoint of a line segment
3.1.2Distance between 2 points
3.1.3Volume and surface area
3.1.4Trigonometry in 3d
3.2.1Pythagoras’ theorem
3.2.2Soh cah toa
3.2.3Sine rule
3.2.4Cosine rule
3.2.5Area of a triangle
3.3.1Bearings
3.3.2Angles of elevation and depression
3.4Arcs and sectors
3.5Perpendicular bisectors
3.6.1Voronoi diagram intro
3.6.2Voronoi examples
3.7.1Introduction ro radians
3.7.2Arcs and sectors
3.8.1Mr. Flynn's exact triangles
3.8.2Unit circle
3.8.3The CAST diagram
3.8.4Graphs of sin, cos and tan
3.8.5Sine ule ambiguous case
3.8.6Trig identities
3.8.7Solving trig equations
3.9.1Matrix transformations (intro and stretches)
3.9.2Translations
3.9.3Enlargements
3.9.4Rotations
3.9.5Reflections
3.9.6Composite transformations
3.9.7Geometric interpretation of determinant
3.10.1Introduction to vectors
3.10.2Operations with vectors
3.10.3Magnitude and unit vectrs
3.11Vector equation of a line
3.12.1Vectors and kinematics
3.12.2Motion with variable velocity
3.13.1Scalar product and angle between vectors
3.13.2Angle between two lines
3.13.3Vector product
3.13.4Areas using the vector product
3.13.5Components of vectors
3.14.1Graph theory introduction
3.15.1Adjaceny matrices
3.15.2Weighted adjacency tables
3.15.3Walks
3.16.1. Graph routes
3.16.2Kruskal's algorithm
3.16.3Prim's algorithm
3.16.4Prim's algorithm with adjacency table
3.16.5Eulerian graphs
3.16.6Chinese postman problem
3.16.7Hamiltonian graphs
3.16.8Travelling salesman problem
3.16.9TSP practical problems
3.16.10Nearest neighbour algorithm
3.16.11Deleted vertex algorithm

04Statistics and probability53 lessons

4.1.1. Discrete v continuous data
4.1.2Sampling techniques
4.2.1. Histograms and cumulative frequency curves
4.2.2box and whisker diagrams
4.2.3interpreting box plots
4.2.4Outliers
4.3.1Averages and spread
4.3.2Frequency tables
4.3.3Constant changes in data
4.3.4Variance and standard deviation by hand
4.4Linear regression and correlation
4.5Probability formulae
4.6.1Venn diagrams
4.6.2Tree diagrams
4.7Discrete random variables
4.8Binomial distribution
4.9Normal distribution
4.10Spearman’s rank correlation coefficient
4.11.1Chi squared intro
4.11.2Chi squared test for independence
4.11.3Chi squared goodness of fit
4.11.4T-test
4.12.1Surveys and questionnaires
4.12.2Reliability v validility
4.12.3Chi squared (categorising data)
4.12.4Chi squared (degrees of freedom)
4.13.1Regression with non-linear functions
4.13.2Sum of square residuals
4.13.3R squared
4.14.1Linear transformations of X
4.14.2Linear combinations of n random variables.
4.14.3Unbiased estimates for mean and variance
4.14.4Unbiased estimates example questions
4.15.1Linear combination of n independent normal random variables
4.15.2Normal distribution sampling
4.15.3Central limit theorem
4.16.1Confidence intervals (known variance)
4.16.2Confidence intervals (unknown variance)
4.17Poisson distribution
4.18.1Z-test one tailed
4.18.2Z-test two tailed
4.18.3T-test
4.18.4Matched pairs
4.18.5Testing for populations proportion
4.18.6Test for mean using Poisson distribution
4.18.7Testing for correllation
4.18.8Type 1 and 2 errors
4.18.9Normal errors
4.18.10Poisson errors
4.18.11Binomial errors
4.19.1Markov chains
4.19.2Transition matrices
4.19.3Steady state and long term probabilities

05Calculus50 lessons

5.1.1Introduction to differentiation
5.1.2Introduction to limits
5.2Increasing and decreasing functions
5.3.1Differentiation power rule
5.3.2Derivative at a point
5.4Tangents and normals
5.5.1Integration (power rule)
5.5.2Finding $f (x)$
5.5.3Area under the curve
5.6Stationary (max/min) points
5.7Optimization
5.8Trapezoidal rule
5.9.1Differentiating trigonometric functions, $e^{x} and ln x$
5.9.2Differentiating $x^{n}$ where n is rational
5.9.3Chain Rule
5.9.4Product Rule
5.9.5Quotient rule
5.9.6Related rates of change
5.10.1Second derivative
5.10.2Relationship between graphs and derivatives
5.10.3Classifying stationary points
5.10.4Points of inflexion
5.11.1Integration of $x^{n}$ where n is rational
5.11.2Integrating trig
5.11.3Integrating $e^{x}$
5.11.4Inverse chain rule
5.11.5Integration by substitution
5.12.1Area between curve and x axis
5.12.2Area between curve and y axis
5.12.3Volume of revolution about x axis
5.12.4Volume of revolution about y axis
5.13.1Kinematics
5.13.2Kinematics 2
5.14.1Setting up differential equation
5.14.2Solving by separation of variables
5.15Slope field and their diagrams
5.16.1Euler's method
5.16.2Euler's method example
5.16.3Euler's method for coupled systems
5.17.1Phase portraits intro
5.17.2Solutions of coupled differential equations (p1)
5.17.3Solutions of coupled differential equations (p2 and saddle)
5.17.4Sketching phase portraits introduction
5.17.5Sketching phase portraits (source)
5.17.6Sketching phase portraits (sink)
5.17.7Sketching phase portraits (spiral sink)
5.17.8Sketching phase portraits (spiral source)
5.17.9Sketching phase portraits (centre)
5.18.1Second order differential equations (Euler's method)
5.18.2Second order differetnial equations (exact solutions)

Also included

Support beyond the topic lessons.

Internal Assessment guidance

Clear guidance for understanding the IA process, developing an idea and improving the finished exploration.

Past-paper solutions

Worked solutions that show how to approach IB Mathematics questions and communicate the method clearly.