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IB Maths AA · questions by skill and topic
IB Maths AA question types
All 4,075 original, past-paper-style questions sorted by the skill each one practises, topic by topic: 340 question types in total. Pick a type to open the topic with only those questions shown, each with its full mark scheme.
Ready to combine skills? Concept clusters: 64 original multi-part questions, each built on one setup that needs several subchapters at once.
The skills
Understanding concepts and notationDefinitions, properties, notation and vocabulary.
Applying standard methodsOne well-known method, carried out accurately.
Manipulating and solving algebraicallyRearrange, simplify, factorise and solve exactly.
Working with graphs and diagramsSketch, read, transform and interpret graphs and diagrams.
Solving multi-step problemsPlan a route through several techniques.
Modelling real-world contextsBuild or use a model of a real situation and answer in context.
Proving and showing resultsShow that, prove and verify: a complete, logical argument.
Interpreting and justifyingExplain what a result means, justify it and comment on validity.
Exam tip: a topic can feel secure while one skill in it is weak. If you can do the calculations but lose marks on explanations or graphs, practise that question type on its own.
Jump to a topic
- 1 Number and algebra (IB Maths AA SL)
- 2 Functions (IB Maths AA SL)
- 3 Geometry and trigonometry (IB Maths AA SL)
- 4 Statistics and probability (IB Maths AA SL)
- 5 Calculus (IB Maths AA SL)
- 1 Number and algebra (IB Maths AA HL)
- 2 Functions (IB Maths AA HL)
- 3 Geometry and trigonometry (IB Maths AA HL)
- 4 Statistics and probability (IB Maths AA HL)
- 5 Calculus (IB Maths AA HL)
IB Maths AA SL
2,037 questions. By skill: Understanding concepts and notation 19, Applying standard methods 621, Manipulating and solving algebraically 173, Working with graphs and diagrams 61, Solving multi-step problems 567, Modelling real-world contexts 509, Proving and showing results 76, Interpreting and justifying 11.
IB Maths AA SL · Topic 1
Number and algebra
488 questions · 28 question types · all questions
Applying standard methods · 64 questions
- 1.9 The binomial theorem: standard methods (19)
- 1.1 Standard form: standard methods (16)
- 1.5 Exponents and introduction to logarithms: standard methods (10)
- 1.8 Infinite geometric series: standard methods (7)
- 1.3 Geometric sequences and series: standard methods (6)
- 1.2 Arithmetic sequences and series: standard methods (5)
Manipulating and solving algebraically · 78 questions
- 1.7 Rational exponents and laws of logarithms: algebraic manipulation (42)
- 1.9 The binomial theorem: algebraic manipulation (24)
- 1.5 Exponents and introduction to logarithms: algebraic manipulation (5)
- 1.1 Standard form: algebraic manipulation (3)
- 1.8 Infinite geometric series: algebraic manipulation (3)
Solving multi-step problems · 61 questions
Modelling real-world contexts · 232 questions
- 1.4 Financial applications: modelling in context (74)
- 1.3 Geometric sequences and series: modelling in context (45)
- 1.2 Arithmetic sequences and series: modelling in context (31)
- 1.1 Standard form: modelling in context (22)
- 1.7 Rational exponents and laws of logarithms: modelling in context (22)
- 1.8 Infinite geometric series: modelling in context (22)
- 1.5 Exponents and introduction to logarithms: modelling in context (11)
- 1.9 The binomial theorem: modelling in context (4)
IB Maths AA SL · Topic 2
Functions
278 questions · 33 question types · all questions
Understanding concepts and notation · 2 questions
Applying standard methods · 29 questions
Manipulating and solving algebraically · 55 questions
- 2.5 Composite and inverse functions: algebraic manipulation (25)
- 2.8 Reciprocal and rational functions: algebraic manipulation (10)
- 2.7 Quadratic equations and the discriminant: algebraic manipulation (7)
- 2.10 Solving equations: algebraic manipulation (4)
- 2.9 Exponential and logarithmic functions: algebraic manipulation (4)
Working with graphs and diagrams · 34 questions
Solving multi-step problems · 47 questions
- 2.7 Quadratic equations and the discriminant: multi-step problems (12)
- 2.1 Equations of straight lines: multi-step problems (11)
- 2.5 Composite and inverse functions: multi-step problems (6)
- 2.6 Quadratic functions: multi-step problems (5)
- 2.10 Solving equations: multi-step problems (4)
- 2.8 Reciprocal and rational functions: multi-step problems (4)
- 2.11 Transformations of graphs: multi-step problems (3)
Modelling real-world contexts · 110 questions
- 2.10 Solving equations: modelling in context (29)
- 2.4 Key features and intersections: modelling in context (18)
- 2.9 Exponential and logarithmic functions: modelling in context (15)
- 2.7 Quadratic equations and the discriminant: modelling in context (12)
- 2.6 Quadratic functions: modelling in context (10)
- 2.1 Equations of straight lines: modelling in context (7)
- 2.2 Functions, domain, range and inverse: modelling in context (7)
- 2.8 Reciprocal and rational functions: modelling in context (5)
- 2.11 Transformations of graphs: modelling in context (4)
- 2.5 Composite and inverse functions: modelling in context (3)
IB Maths AA SL · Topic 3
Geometry and trigonometry
311 questions · 24 question types · all questions
Applying standard methods · 69 questions
- 3.4 Radian measure, arcs and sectors: standard methods (19)
- 3.2 Right-angled and non-right-angled trigonometry: standard methods (12)
- 3.6 Trigonometric identities: standard methods (12)
- 3.5 The unit circle and the ambiguous case: standard methods (10)
- 3.3 Applications of trigonometry: standard methods (8)
- 3.1 Three-dimensional geometry: standard methods (6)
Manipulating and solving algebraically · 35 questions
Working with graphs and diagrams · 11 questions
Solving multi-step problems · 126 questions
- 3.1 Three-dimensional geometry: multi-step problems (26)
- 3.3 Applications of trigonometry: multi-step problems (23)
- 3.5 The unit circle and the ambiguous case: multi-step problems (23)
- 3.4 Radian measure, arcs and sectors: multi-step problems (20)
- 3.2 Right-angled and non-right-angled trigonometry: multi-step problems (16)
- 3.6 Trigonometric identities: multi-step problems (11)
- 3.8 Trigonometric equations: multi-step problems (7)
Modelling real-world contexts · 56 questions
- 3.7 Circular functions and their graphs: modelling in context (24)
- 3.3 Applications of trigonometry: modelling in context (11)
- 3.4 Radian measure, arcs and sectors: modelling in context (6)
- 3.5 The unit circle and the ambiguous case: modelling in context (4)
- 3.6 Trigonometric identities: modelling in context (4)
- 3.1 Three-dimensional geometry: modelling in context (3)
- 3.2 Right-angled and non-right-angled trigonometry: modelling in context (3)
IB Maths AA SL · Topic 4
Statistics and probability
480 questions · 29 question types · all questions
Understanding concepts and notation · 7 questions
Applying standard methods · 278 questions
- 4.2 Presentation of data: standard methods (49)
- 4.4 Correlation and regression of y on x: standard methods (36)
- 4.3 Measures of central tendency and dispersion: standard methods (27)
- 4.6 Combined events and diagrams: standard methods (27)
- 4.11 Conditional probability and independence: standard methods (24)
- 4.9 The normal distribution: standard methods (24)
- 4.10 Regression of x on y: standard methods (23)
- 4.8 The binomial distribution: standard methods (23)
- 4.1 Sampling, data and outliers: standard methods (18)
- 4.7 Discrete random variables: standard methods (15)
- 4.5 Probability and expected occurrences: standard methods (7)
- 4.12 Standardization and inverse normal: standard methods (5)
Solving multi-step problems · 159 questions
- 4.12 Standardization and inverse normal: multi-step problems (22)
- 4.9 The normal distribution: multi-step problems (22)
- 4.7 Discrete random variables: multi-step problems (21)
- 4.6 Combined events and diagrams: multi-step problems (20)
- 4.11 Conditional probability and independence: multi-step problems (16)
- 4.3 Measures of central tendency and dispersion: multi-step problems (16)
- 4.8 The binomial distribution: multi-step problems (12)
- 4.2 Presentation of data: multi-step problems (10)
- 4.10 Regression of x on y: multi-step problems (9)
- 4.4 Correlation and regression of y on x: multi-step problems (6)
- 4.1 Sampling, data and outliers: multi-step problems (3)
Modelling real-world contexts · 14 questions
IB Maths AA SL · Topic 5
Calculus
480 questions · 32 question types · all questions
Understanding concepts and notation · 8 questions
Applying standard methods · 181 questions
- 5.10 Indefinite integrals and reverse chain rule: standard methods (28)
- 5.9 Kinematics: standard methods (28)
- 5.5 Introduction to integration: standard methods (20)
- 5.2 Increasing and decreasing functions: standard methods (19)
- 5.4 Tangents and normals: standard methods (18)
- 5.6 Differentiation rules: standard methods (15)
- 5.7 The second derivative and graphs: standard methods (15)
- 5.3 Differentiating polynomials and integer powers: standard methods (14)
- 5.1 Limits and the derivative: standard methods (9)
- 5.11 Definite integrals and areas: standard methods (9)
- 5.8 Stationary points, inflexion and optimization: standard methods (6)
Manipulating and solving algebraically · 5 questions
Working with graphs and diagrams · 6 questions
Solving multi-step problems · 174 questions
- 5.4 Tangents and normals: multi-step problems (40)
- 5.9 Kinematics: multi-step problems (36)
- 5.6 Differentiation rules: multi-step problems (24)
- 5.11 Definite integrals and areas: multi-step problems (16)
- 5.10 Indefinite integrals and reverse chain rule: multi-step problems (15)
- 5.2 Increasing and decreasing functions: multi-step problems (12)
- 5.3 Differentiating polynomials and integer powers: multi-step problems (9)
- 5.7 The second derivative and graphs: multi-step problems (9)
- 5.5 Introduction to integration: multi-step problems (8)
- 5.8 Stationary points, inflexion and optimization: multi-step problems (3)
Modelling real-world contexts · 97 questions
- 5.8 Stationary points, inflexion and optimization: modelling in context (29)
- 5.9 Kinematics: modelling in context (20)
- 5.1 Limits and the derivative: modelling in context (14)
- 5.7 The second derivative and graphs: modelling in context (13)
- 5.2 Increasing and decreasing functions: modelling in context (12)
- 5.11 Definite integrals and areas: modelling in context (3)
IB Maths AA HL
2,038 questions. By skill: Understanding concepts and notation 1, Applying standard methods 662, Manipulating and solving algebraically 142, Working with graphs and diagrams 41, Solving multi-step problems 638, Modelling real-world contexts 379, Proving and showing results 172, Interpreting and justifying 3.
IB Maths AA HL · Topic 1
Number and algebra
342 questions · 36 question types · all questions
Applying standard methods · 95 questions
- 1.14 Conjugate roots, De Moivre’s theorem, powers and roots: standard methods (21)
- 1.13 Polar and Euler forms: standard methods (14)
- 1.10 Counting principles and the extended binomial theorem: standard methods (12)
- 1.11 Partial fractions: standard methods (12)
- 1.1 Standard form: standard methods (11)
- 1.9 The binomial theorem: standard methods (8)
- 1.12 Complex numbers in Cartesian form: standard methods (4)
- 1.3 Geometric sequences and series: standard methods (4)
- 1.8 Infinite geometric series: standard methods (3)
Manipulating and solving algebraically · 23 questions
- 1.12 Complex numbers in Cartesian form: algebraic manipulation (6)
- 1.11 Partial fractions: algebraic manipulation (4)
- 1.14 Conjugate roots, De Moivre’s theorem, powers and roots: algebraic manipulation (4)
- 1.5 Exponents and introduction to logarithms: algebraic manipulation (4)
- 1.7 Rational exponents and laws of logarithms: algebraic manipulation (4)
Working with graphs and diagrams · 1 question
Solving multi-step problems · 62 questions
- 1.16 Systems of linear equations: multi-step problems (13)
- 1.11 Partial fractions: multi-step problems (9)
- 1.14 Conjugate roots, De Moivre’s theorem, powers and roots: multi-step problems (9)
- 1.13 Polar and Euler forms: multi-step problems (6)
- 1.9 The binomial theorem: multi-step problems (5)
- 1.7 Rational exponents and laws of logarithms: multi-step problems (4)
- 1.8 Infinite geometric series: multi-step problems (4)
- 1.10 Counting principles and the extended binomial theorem: multi-step problems (3)
- 1.3 Geometric sequences and series: multi-step problems (3)
Modelling real-world contexts · 85 questions
- 1.4 Financial applications: modelling in context (26)
- 1.16 Systems of linear equations: modelling in context (20)
- 1.7 Rational exponents and laws of logarithms: modelling in context (11)
- 1.1 Standard form: modelling in context (6)
- 1.3 Geometric sequences and series: modelling in context (6)
- 1.12 Complex numbers in Cartesian form: modelling in context (3)
- 1.5 Exponents and introduction to logarithms: modelling in context (3)
- 1.8 Infinite geometric series: modelling in context (3)
Proving and showing results · 76 questions
IB Maths AA HL · Topic 2
Functions
328 questions · 35 question types · all questions
Understanding concepts and notation · 1 question
Applying standard methods · 33 questions
Manipulating and solving algebraically · 46 questions
- 2.15 Solving inequalities g(x) ≥ f(x): algebraic manipulation (10)
- 2.5 Composite functions and inverse functions: algebraic manipulation (10)
- 2.16 Modulus, reciprocal and other graph transformations: algebraic manipulation (9)
- 2.7 Quadratic equations, inequalities and the discriminant: algebraic manipulation (4)
- 2.14 Odd and even functions, inverse and self-inverse functions: algebraic manipulation (3)
- 2.2 Functions, domain, range and inverse functions: algebraic manipulation (3)
Working with graphs and diagrams · 32 questions
Solving multi-step problems · 86 questions
- 2.12 Polynomial functions, factor and remainder theorems, sum and product of roots: multi-step problems (21)
- 2.13 Rational functions with oblique and horizontal asymptotes: multi-step problems (15)
- 2.14 Odd and even functions, inverse and self-inverse functions: multi-step problems (14)
- 2.1 Equations of straight lines, parallel and perpendicular lines: multi-step problems (8)
- 2.5 Composite functions and inverse functions: multi-step problems (8)
- 2.7 Quadratic equations, inequalities and the discriminant: multi-step problems (6)
- 2.16 Modulus, reciprocal and other graph transformations: multi-step problems (4)
- 2.6 The quadratic function and its forms: multi-step problems (3)
Modelling real-world contexts · 109 questions
- 2.4 Key features of graphs and intersections using technology: modelling in context (21)
- 2.15 Solving inequalities g(x) ≥ f(x): modelling in context (14)
- 2.8 The reciprocal function and rational functions: modelling in context (12)
- 2.10 Solving equations graphically and analytically: modelling in context (10)
- 2.12 Polynomial functions, factor and remainder theorems, sum and product of roots: modelling in context (8)
- 2.13 Rational functions with oblique and horizontal asymptotes: modelling in context (8)
- 2.16 Modulus, reciprocal and other graph transformations: modelling in context (8)
- 2.3 Graphs of functions and sketching from a context: modelling in context (6)
- 2.2 Functions, domain, range and inverse functions: modelling in context (5)
- 2.7 Quadratic equations, inequalities and the discriminant: modelling in context (4)
- 2.1 Equations of straight lines, parallel and perpendicular lines: modelling in context (3)
- 2.9 Exponential and logarithmic functions: modelling in context (3)
Proving and showing results · 20 questions
IB Maths AA HL · Topic 3
Geometry and trigonometry
443 questions · 43 question types · all questions
Applying standard methods · 129 questions
- 3.17 Equations of a plane: standard methods (24)
- 3.14 Vector equation of a line: standard methods (15)
- 3.9 Reciprocal and inverse trigonometric functions: standard methods (15)
- 3.12 Vectors: concepts and algebra: standard methods (14)
- 3.4 Radians, arc length and sector area: standard methods (9)
- 3.10 Compound and double angle identities: standard methods (7)
- 3.2 Right-angled and non-right-angled triangles: standard methods (7)
- 3.13 Scalar product: standard methods (6)
- 3.1 Three-dimensional geometry: distance, solids and angles: standard methods (5)
- 3.18 Intersections and angles of lines and planes: standard methods (5)
- 3.15 Intersecting, parallel and skew lines: standard methods (4)
- 3.16 Vector product: standard methods (4)
- 3.3 Applications of trigonometry: elevation, depression and bearings: standard methods (4)
- 3.6 Pythagorean and double angle identities: standard methods (3)
Manipulating and solving algebraically · 41 questions
Working with graphs and diagrams · 7 questions
Solving multi-step problems · 164 questions
- 3.18 Intersections and angles of lines and planes: multi-step problems (37)
- 3.15 Intersecting, parallel and skew lines: multi-step problems (18)
- 3.17 Equations of a plane: multi-step problems (16)
- 3.1 Three-dimensional geometry: distance, solids and angles: multi-step problems (13)
- 3.3 Applications of trigonometry: elevation, depression and bearings: multi-step problems (13)
- 3.4 Radians, arc length and sector area: multi-step problems (12)
- 3.14 Vector equation of a line: multi-step problems (9)
- 3.16 Vector product: multi-step problems (9)
- 3.2 Right-angled and non-right-angled triangles: multi-step problems (9)
- 3.10 Compound and double angle identities: multi-step problems (8)
- 3.13 Scalar product: multi-step problems (4)
- 3.5 The unit circle, exact values and the ambiguous case: multi-step problems (4)
- 3.9 Reciprocal and inverse trigonometric functions: multi-step problems (4)
- 3.6 Pythagorean and double angle identities: multi-step problems (3)
Modelling real-world contexts · 58 questions
- 3.7 Circular functions and their transformations: modelling in context (27)
- 3.14 Vector equation of a line: modelling in context (9)
- 3.10 Compound and double angle identities: modelling in context (5)
- 3.3 Applications of trigonometry: elevation, depression and bearings: modelling in context (5)
- 3.4 Radians, arc length and sector area: modelling in context (3)
Proving and showing results · 44 questions
- 3.6 Pythagorean and double angle identities: proofs and show that (11)
- 3.10 Compound and double angle identities: proofs and show that (9)
- 3.11 Symmetry properties of trigonometric graphs: proofs and show that (6)
- 3.9 Reciprocal and inverse trigonometric functions: proofs and show that (6)
- 3.8 Solving trigonometric equations: proofs and show that (4)
IB Maths AA HL · Topic 4
Statistics and probability
491 questions · 37 question types · all questions
Applying standard methods · 254 questions
- 4.2 Presentation of data: standard methods (43)
- 4.14 Variance, continuous random variables and linear transformations: standard methods (40)
- 4.13 Bayes’ theorem: standard methods (23)
- 4.11 Conditional probability and independence: standard methods (21)
- 4.4 Correlation and regression of y on x: standard methods (20)
- 4.6 Combined, conditional and independent events: standard methods (19)
- 4.10 Regression line of x on y: standard methods (18)
- 4.1 Sampling, bias and outliers: standard methods (16)
- 4.8 Binomial distribution: standard methods (16)
- 4.12 Standardization and unknown normal parameters: standard methods (11)
- 4.3 Measures of central tendency and dispersion: standard methods (9)
- 4.7 Discrete random variables: standard methods (9)
- 4.9 The normal distribution: standard methods (8)
Manipulating and solving algebraically · 31 questions
- 4.14 Variance, continuous random variables and linear transformations: algebraic manipulation (9)
- 4.8 Binomial distribution: algebraic manipulation (5)
- 4.12 Standardization and unknown normal parameters: algebraic manipulation (4)
- 4.13 Bayes’ theorem: algebraic manipulation (3)
- 4.2 Presentation of data: algebraic manipulation (3)
Solving multi-step problems · 174 questions
- 4.14 Variance, continuous random variables and linear transformations: multi-step problems (44)
- 4.13 Bayes’ theorem: multi-step problems (29)
- 4.12 Standardization and unknown normal parameters: multi-step problems (20)
- 4.2 Presentation of data: multi-step problems (20)
- 4.6 Combined, conditional and independent events: multi-step problems (11)
- 4.11 Conditional probability and independence: multi-step problems (9)
- 4.7 Discrete random variables: multi-step problems (9)
- 4.8 Binomial distribution: multi-step problems (8)
- 4.9 The normal distribution: multi-step problems (6)
- 4.3 Measures of central tendency and dispersion: multi-step problems (5)
- 4.4 Correlation and regression of y on x: multi-step problems (5)
- 4.10 Regression line of x on y: multi-step problems (4)
Modelling real-world contexts · 26 questions
- 4.13 Bayes’ theorem: modelling in context (6)
- 4.14 Variance, continuous random variables and linear transformations: modelling in context (6)
- 4.8 Binomial distribution: modelling in context (5)
- 4.9 The normal distribution: modelling in context (4)
- 4.12 Standardization and unknown normal parameters: modelling in context (3)
Proving and showing results · 5 questions
IB Maths AA HL · Topic 5
Calculus
434 questions · 43 question types · all questions
Applying standard methods · 151 questions
- 5.16 Integration by substitution and by parts: standard methods (24)
- 5.13 Limits and l’Hôpital’s rule: standard methods (20)
- 5.18 First order differential equations: standard methods (15)
- 5.15 Further derivatives and integrals; partial fractions: standard methods (14)
- 5.14 Implicit differentiation, related rates and optimisation: standard methods (13)
- 5.19 Maclaurin series: standard methods (12)
- 5.12 Limits, first principles and higher derivatives: standard methods (9)
- 5.17 Areas with the y-axis and volumes of revolution: standard methods (8)
- 5.9 Kinematics: standard methods (7)
- 5.5 Introduction to integration: standard methods (6)
- 5.4 Tangents and normals: standard methods (5)
- 5.1 Limits and the derivative: standard methods (4)
- 5.8 Stationary points, inflexion and optimization: standard methods (4)
- 5.10 Indefinite integrals and reverse chain rule: standard methods (3)
Manipulating and solving algebraically · 1 question
Working with graphs and diagrams · 1 question
Solving multi-step problems · 152 questions
- 5.9 Kinematics: multi-step problems (17)
- 5.3 Differentiating polynomials and integer powers: multi-step problems (16)
- 5.16 Integration by substitution and by parts: multi-step problems (13)
- 5.13 Limits and l’Hôpital’s rule: multi-step problems (12)
- 5.14 Implicit differentiation, related rates and optimisation: multi-step problems (12)
- 5.17 Areas with the y-axis and volumes of revolution: multi-step problems (12)
- 5.18 First order differential equations: multi-step problems (12)
- 5.19 Maclaurin series: multi-step problems (12)
- 5.15 Further derivatives and integrals; partial fractions: multi-step problems (9)
- 5.7 The second derivative and graphs: multi-step problems (6)
- 5.4 Tangents and normals: multi-step problems (5)
- 5.6 Differentiation rules: multi-step problems (5)
- 5.8 Stationary points, inflexion and optimization: multi-step problems (5)
- 5.10 Indefinite integrals and reverse chain rule: multi-step problems (4)
- 5.11 Definite integrals and areas: multi-step problems (4)
- 5.5 Introduction to integration: multi-step problems (4)
- 5.2 Increasing and decreasing functions: multi-step problems (3)
Modelling real-world contexts · 101 questions
- 5.14 Implicit differentiation, related rates and optimisation: modelling in context (38)
- 5.1 Limits and the derivative: modelling in context (16)
- 5.8 Stationary points, inflexion and optimization: modelling in context (14)
- 5.9 Kinematics: modelling in context (12)
- 5.18 First order differential equations: modelling in context (8)
- 5.17 Areas with the y-axis and volumes of revolution: modelling in context (5)