IB Mathematics

Applications and interpretation,
Higher Level.

Everything in AI SL, then matrices, graph theory, advanced statistics and differential equations, with a third paper.

6 packs planned.

notion by notion

Exam papers.

Everything here is a PDF to download, notion by notion: the course, marked examples with an exercise under each, then more practice. Free opens a few marked examples; Premium opens the course, one marked example and its exercise in every sub-notion, and a practice sheet per notion; Excellence opens everything.

1Matrices and complex numbersplanned

Matrix algebra, eigenvalues and eigenvectors, complex numbers in every form.

1Course

The course of each sub-notion: definitions, results, methods, and the notation the markscheme expects.

  • Matrix algebraPremium
  • Eigenvalues and eigenvectorsPremium
  • Complex numbersPremium

2Marked examples

Each example comes with its full markscheme, mark by mark. Under it, a similar exercise to do on your own.

  • Matrix algebraExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Eigenvalues and eigenvectorsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Complex numbersExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence

3More practice

Further exercises in the style of Paper 1 and Paper 2, with their answers.

  • The whole notionPractice sheet, 12 questionsPremiumExam-style paper, with markschemeExcellence
  • Matrix algebraPractice set, 8 questionsExcellence
  • Eigenvalues and eigenvectorsPractice set, 8 questionsExcellence
  • Complex numbersPractice set, 8 questionsExcellence
2Advanced modellingplanned

Logistic models, linearising data with logarithms, piecewise models.

1Course

The course of each sub-notion: definitions, results, methods, and the notation the markscheme expects.

  • Logistic modelsPremium
  • Linearising dataPremium
  • Piecewise modelsPremium

2Marked examples

Each example comes with its full markscheme, mark by mark. Under it, a similar exercise to do on your own.

  • Logistic modelsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Linearising dataExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Piecewise modelsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence

3More practice

Further exercises in the style of Paper 1 and Paper 2, with their answers.

  • The whole notionPractice sheet, 12 questionsPremiumExam-style paper, with markschemeExcellence
  • Logistic modelsPractice set, 8 questionsExcellence
  • Linearising dataPractice set, 8 questionsExcellence
  • Piecewise modelsPractice set, 8 questionsExcellence
3Vectors and graph theoryplanned

Vectors in kinematics, adjacency matrices, minimum spanning trees, the Chinese postman and travelling salesman problems.

1Course

The course of each sub-notion: definitions, results, methods, and the notation the markscheme expects.

  • Vectors in kinematicsPremium
  • Adjacency matricesPremium
  • Spanning trees and routesPremium

2Marked examples

Each example comes with its full markscheme, mark by mark. Under it, a similar exercise to do on your own.

  • Vectors in kinematicsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Adjacency matricesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Spanning trees and routesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence

3More practice

Further exercises in the style of Paper 1 and Paper 2, with their answers.

  • The whole notionPractice sheet, 12 questionsPremiumExam-style paper, with markschemeExcellence
  • Vectors in kinematicsPractice set, 8 questionsExcellence
  • Adjacency matricesPractice set, 8 questionsExcellence
  • Spanning trees and routesPractice set, 8 questionsExcellence
4Hypothesis testing and Markov chainsplanned

Confidence intervals, the Poisson distribution, hypothesis tests, transition matrices and Markov chains.

1Course

The course of each sub-notion: definitions, results, methods, and the notation the markscheme expects.

  • Confidence intervalsPremium
  • The Poisson distributionPremium
  • Hypothesis testsPremium
  • Markov chainsPremium

2Marked examples

Each example comes with its full markscheme, mark by mark. Under it, a similar exercise to do on your own.

  • Confidence intervalsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • The Poisson distributionExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Hypothesis testsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Markov chainsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence

3More practice

Further exercises in the style of Paper 1 and Paper 2, with their answers.

  • The whole notionPractice sheet, 12 questionsPremiumExam-style paper, with markschemeExcellence
  • Confidence intervalsPractice set, 8 questionsExcellence
  • The Poisson distributionPractice set, 8 questionsExcellence
  • Hypothesis testsPractice set, 8 questionsExcellence
  • Markov chainsPractice set, 8 questionsExcellence
5Differential equationsplanned

Slope fields, Euler's method, coupled systems and phase portraits.

1Course

The course of each sub-notion: definitions, results, methods, and the notation the markscheme expects.

  • Slope fieldsPremium
  • Euler's methodPremium
  • Coupled systemsPremium

2Marked examples

Each example comes with its full markscheme, mark by mark. Under it, a similar exercise to do on your own.

  • Slope fieldsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Euler's methodExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Coupled systemsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence

3More practice

Further exercises in the style of Paper 1 and Paper 2, with their answers.

  • The whole notionPractice sheet, 12 questionsPremiumExam-style paper, with markschemeExcellence
  • Slope fieldsPractice set, 8 questionsExcellence
  • Euler's methodPractice set, 8 questionsExcellence
  • Coupled systemsPractice set, 8 questionsExcellence
P3Paper 3 problem-solvingplanned

Extended investigations of the kind set in the HL Paper 3: a context explored through several parts.

1Course

The course of each sub-notion: definitions, results, methods, and the notation the markscheme expects.

  • Investigation and conjecturePremium
  • Generalising and provingPremium

2Marked examples

Each example comes with its full markscheme, mark by mark. Under it, a similar exercise to do on your own.

  • Investigation and conjectureExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Generalising and provingExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence

3More practice

Further exercises in the style of Paper 1 and Paper 2, with their answers.

  • The whole notionPractice sheet, 12 questionsPremiumExam-style paper, with markschemeExcellence
  • Investigation and conjecturePractice set, 8 questionsExcellence
  • Generalising and provingPractice set, 8 questionsExcellence