IB Mathematics

Analysis and approaches,
Standard Level.

The course for students who like algebra and proof: functions, calculus and the reasoning behind them.

1 pack available, 5 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.

1Sequences, series and logarithmsplanned

Arithmetic and geometric sequences, sigma notation, exponents and logarithms, the binomial theorem.

1Course

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

  • Arithmetic sequences and seriesPremium
  • Geometric sequences and seriesPremium
  • Exponents and logarithmsPremium
  • The binomial theoremPremium

2Marked examples

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

  • Arithmetic sequences and seriesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Geometric sequences and seriesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Exponents and logarithmsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • The binomial theoremExample 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
  • Arithmetic sequences and seriesPractice set, 8 questionsExcellence
  • Geometric sequences and seriesPractice set, 8 questionsExcellence
  • Exponents and logarithmsPractice set, 8 questionsExcellence
  • The binomial theoremPractice set, 8 questionsExcellence
2Functions and their graphsplanned

Domain and range, composite and inverse functions, transformations, quadratic, rational and exponential functions.

1Course

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

  • Domain, range and graphsPremium
  • Composite and inverse functionsPremium
  • Transformations of graphsPremium
  • Quadratic, rational and exponential functionsPremium

2Marked examples

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

  • Domain, range and graphsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Composite and inverse functionsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Transformations of graphsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Quadratic, rational and exponential functionsExample 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
  • Domain, range and graphsPractice set, 8 questionsExcellence
  • Composite and inverse functionsPractice set, 8 questionsExcellence
  • Transformations of graphsPractice set, 8 questionsExcellence
  • Quadratic, rational and exponential functionsPractice set, 8 questionsExcellence
3Trigonometry and trianglesplanned

Sine and cosine rules, radians, the unit circle, identities and trigonometric equations.

1Course

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

  • Sine and cosine rulesPremium
  • Radians, arcs and sectorsPremium
  • The unit circle and identitiesPremium
  • Trigonometric equations and graphsPremium

2Marked examples

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

  • Sine and cosine rulesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Radians, arcs and sectorsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • The unit circle and identitiesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Trigonometric equations and graphsExample 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
  • Sine and cosine rulesPractice set, 8 questionsExcellence
  • Radians, arcs and sectorsPractice set, 8 questionsExcellence
  • The unit circle and identitiesPractice set, 8 questionsExcellence
  • Trigonometric equations and graphsPractice set, 8 questionsExcellence
4Statistics and probabilityplanned

Data and regression, Venn and tree diagrams, binomial and normal distributions.

1Course

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

  • Data, averages and spreadPremium
  • Regression and correlationPremium
  • Probability, Venn and tree diagramsPremium
  • Binomial and normal distributionsPremium

2Marked examples

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

  • Data, averages and spreadExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Regression and correlationExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Probability, Venn and tree diagramsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Binomial and normal distributionsExample 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
  • Data, averages and spreadPractice set, 8 questionsExcellence
  • Regression and correlationPractice set, 8 questionsExcellence
  • Probability, Venn and tree diagramsPractice set, 8 questionsExcellence
  • Binomial and normal distributionsPractice set, 8 questionsExcellence
5Differential calculuswritten

Rates of change, tangents and normals, the chain, product and quotient rules, optimisation, kinematics.

1Course

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

  • Limits and rates of changePremium
  • Rules of differentiationPremium
  • Tangents and normalsPremium
  • The graphs of f, f′ and f″Premium
  • Stationary points and inflexionPremium
  • OptimisationPremium
  • KinematicsPremium

2Marked examples

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

  • Limits and rates of changeExample 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Rules of differentiationExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Tangents and normalsExample 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • The graphs of f, f′ and f″Example 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Stationary points and inflexionExample 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • OptimisationExample 1FreeExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • KinematicsExample 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
  • Limits and rates of changePractice set, 8 questionsExcellence
  • Rules of differentiationPractice set, 8 questionsExcellence
  • Tangents and normalsPractice set, 8 questionsExcellence
  • The graphs of f, f′ and f″Practice set, 8 questionsExcellence
  • Stationary points and inflexionPractice set, 8 questionsExcellence
  • OptimisationPractice set, 8 questionsExcellence
  • KinematicsPractice set, 8 questionsExcellence
5Integral calculusnext to be written

Antiderivatives, definite integrals, areas between curves, kinematics with integrals.

1Course

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

  • AntiderivativesPremium
  • Definite integralsPremium
  • Areas between curvesPremium
  • Kinematics with integralsPremium

2Marked examples

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

  • AntiderivativesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Definite integralsExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Areas between curvesExample 1PremiumExercise 1PremiumExample 2ExcellenceExercise 2ExcellenceExample 3ExcellenceExercise 3Excellence
  • Kinematics with integralsExample 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
  • AntiderivativesPractice set, 8 questionsExcellence
  • Definite integralsPractice set, 8 questionsExcellence
  • Areas between curvesPractice set, 8 questionsExcellence
  • Kinematics with integralsPractice set, 8 questionsExcellence
A teacher page: the markscheme of a question, mark by mark Cover of the Differential calculus pack

for teachers

Differential calculus.

Four papers' worth of differentiation: rates of change, tangents and normals, the chain, product and quotient rules, stationary points, concavity, optimisation and kinematics.

  • 28 questions and 219 marks, sized like real Paper 1 and Paper 2 sections
  • A markscheme in IB conventions, with the alternative methods
  • Key sequences on both calculators for every Paper 2 question
  • A student edition, and a teacher edition in PDF and Word
Student editionanswer spaces, final answers€12
Teacher editionPDF and Word, full markscheme€29
Departmentevery pack, every teacher in one school€249

On sale from December 2026. Six of the questions are free now.

Free sample, teacher edition (PDF)