IB Mathematics

Applications and interpretation,
Standard Level.

The course for students who model the world: data, statistics, finance, and technology used at every step.

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.

1Financial mathematics and approximationplanned

Standard form, percentage error, compound interest, loans and annuities, sequences in context.

1Course

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

  • Standard form and errorsPremium
  • Compound interest and depreciationPremium
  • Loans and annuitiesPremium

2Marked examples

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

  • Standard form and errorsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Compound interest and depreciationExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Loans and annuitiesExample 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
  • Standard form and errorsPractice set, 8 questionsExcellence
  • Compound interest and depreciationPractice set, 8 questionsExcellence
  • Loans and annuitiesPractice set, 8 questionsExcellence
2Modelling with functionsplanned

Linear, quadratic, exponential, cubic and sinusoidal models, and what their parameters mean.

1Course

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

  • Linear and quadratic modelsPremium
  • Exponential modelsPremium
  • Cubic and sinusoidal modelsPremium

2Marked examples

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

  • Linear and quadratic modelsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Exponential modelsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Cubic and sinusoidal 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
  • Linear and quadratic modelsPractice set, 8 questionsExcellence
  • Exponential modelsPractice set, 8 questionsExcellence
  • Cubic and sinusoidal modelsPractice set, 8 questionsExcellence
3Geometry, trigonometry and Voronoi diagramsplanned

Volumes and surface areas, right-angled and non-right-angled triangles, perpendicular bisectors, Voronoi diagrams.

1Course

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

  • Volumes and surface areasPremium
  • Triangles and bearingsPremium
  • Perpendicular bisectors and Voronoi diagramsPremium

2Marked examples

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

  • Volumes and surface areasExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Triangles and bearingsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Perpendicular bisectors and Voronoi diagramsExample 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
  • Volumes and surface areasPractice set, 8 questionsExcellence
  • Triangles and bearingsPractice set, 8 questionsExcellence
  • Perpendicular bisectors and Voronoi diagramsPractice set, 8 questionsExcellence
4Correlation and statistical testsplanned

Regression, Spearman's rank correlation, chi-squared tests and the t-test.

1Course

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

  • Regression and rPremium
  • Spearman's rank correlationPremium
  • Chi-squared testsPremium
  • The t-testPremium

2Marked examples

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

  • Regression and rExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Spearman's rank correlationExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Chi-squared testsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • The t-testExample 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
  • Regression and rPractice set, 8 questionsExcellence
  • Spearman's rank correlationPractice set, 8 questionsExcellence
  • Chi-squared testsPractice set, 8 questionsExcellence
  • The t-testPractice set, 8 questionsExcellence
4Probability and distributionsplanned

Probability, Venn and tree diagrams, binomial and normal distributions.

1Course

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

  • Probability and diagramsPremium
  • Binomial distributionPremium
  • Normal distributionPremium

2Marked examples

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

  • Probability and diagramsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Binomial distributionExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Normal distributionExample 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
  • Probability and diagramsPractice set, 8 questionsExcellence
  • Binomial distributionPractice set, 8 questionsExcellence
  • Normal distributionPractice set, 8 questionsExcellence
5Calculus for modellingwritten

Derivatives of polynomials, optimisation in context, integration and the trapezoidal rule.

1Course

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

  • Tangents and normalsPremium
  • Increasing and decreasingPremium
  • Optimisation in contextPremium
  • Integration and the trapezoidal rulePremium

2Marked examples

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

  • Tangents and normalsExample 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Increasing and decreasingExample 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Optimisation in contextExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Integration and the trapezoidal ruleExample 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
  • Tangents and normalsPractice set, 8 questionsExcellence
  • Increasing and decreasingPractice set, 8 questionsExcellence
  • Optimisation in contextPractice set, 8 questionsExcellence
  • Integration and the trapezoidal rulePractice set, 8 questionsExcellence