Is the SL content included?

Yes. HL students sit the SL content too, so every SL syllabus point is here. Chapters only HL students need are tagged HL only.

Are these IB past paper questions?

No. They are written by our teachers in the IB style, so you can practise without using up the past papers you will want for timed mocks.

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You keep your account and your scores. Courses you have not bought lock until you buy them. Nothing renews automatically, and you are never charged without choosing to pay.

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IB Diploma · Mathematics

IBDP Maths AI HL

IBDP Maths AI HL on Preppeo is a bank of 2,006 practice questions across 5 topics and 73 chapters, with worked solutions. Sign in and the whole course is free for 7 days.

questions: 2,006; questions
topics: 5; topics
chapters: 73; chapters
difficulty levels: 3; difficulty levels

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What you get

Syllabus: The current IB Mathematics: Applications and Interpretation guide (first exams 2021), all five topics, SL and HL content.
Questions: Written answers, in parts, with marks shown
Solutions: Mark-by-mark solutions in the IB style (M1, A1)
Progress: Your accuracy in every topic, so you know which one to practise next.

Three levels of difficulty

Start a chapter on basics and work up to exam-style questions.

Basics 1,187
Medium 441
Exam-style 378

Syllabus

5 topics, 73 chapters. Open a topic to see its chapters; numbers follow the official syllabus. The bar beside each chapter shows its mix of basics, medium and exam-style questions.

1Number and Algebra14 chapters · 450 questions

1.1Standard form, currency conversions, units9
1.2Arithmetic sequences and series17
1.3Geometric sequences and series14
1.4Financial applicationsCompound interest, depreciation, annuities (basic)18
1.5Exponents and logarithms (including change of base)33
1.6Approximation, rounding, percentage error58
1.7Amortization and annuities with finance equationsHL only61
1.8Logarithmic and exponential models, solving log equationsHL only31
1.9Laws of logarithms (advanced manipulation)HL only11
1.10Simplifying expressions with exponents and surdsHL only47
1.11Sum of infinite geometric series, partial fractionsHL only9
1.12Complex numbers (Cartesian and polar form, De Moivre's)HL only84
1.13MatricesHL onlyBasic operations, determinant, inverse35
1.14Eigenvalues, eigenvectors, diagonalizationHL only23

2Functions10 chapters · 428 questions

2.1Equation of a line, gradient, intercepts, parallel/perpendicular28
2.2Concept of function, domain/range, inverse, composite34
2.3GraphsIntercepts, asymptotes, maxima/minima99
2.4Modelling with functionsLinear, quadratic, exponential49
2.5ModellingCubic, sinusoidal, logistic, piecewise, direct/inverse variation75
2.6Modelling skillsChoosing a model, parameters, evaluating fit24
2.7Composite functions, identity, self-inverseHL only16
2.8Transformations of graphs (translation, reflection, dilation)HL only33
2.9Logarithmic transformation of data to linearizeHL only41
2.10Sinusoidal models (amplitude, period, phase shift)HL only29

3Geometry and Trigonometry16 chapters · 452 questions

3.13D distance, midpoint, volume16
3.2Volume and surface area of 3D solids (prism, cone, sphere, pyramid)44
3.3Right-angled trigonometry, sine rule, cosine rule, area of triangle55
3.4Bearings, angles of elevation/depression, 3D applications37
3.5Equation of perpendicular bisector, midpoint locus9
3.6Voronoi diagrams, toxic-waste / nearest-neighbour problems37
3.7Radian measure, arc length, sector areaHL only23
3.8Reciprocal trig ratios, Pythagorean identities, double-angleHL only34
3.9VectorsHL onlyMagnitude, direction, dot product, angle between vectors42
3.10Vector equation of a line, intersection, skew linesHL only7
3.11Vector kinematics, displacement, velocity, scalar product applicationsHL only22
3.12Graph theoryHL onlyVertices, edges, walks, paths, trails, circuits10
3.13Adjacency matrices, weighted graphs, transition matricesHL only11
3.14Tree, minimum spanning tree (Kruskal, Prim), Chinese postman, TSPHL only23
3.15Eulerian, Hamiltonian, shortest path (Dijkstra)HL only8
3.16Symmetry / transformation matrices in 2DHL only74

4Statistics and Probability17 chapters · 370 questions

4.1Sampling techniques, population vs sample, sampling bias7
4.2Presentation of dataHistograms, box plots, cumulative frequency13
4.3Measures of central tendency and dispersion (mean, median, SD, IQR)26
4.4Linear correlation, Pearson's r, equation of regression line35
4.5ProbabilityTheoretical, experimental, Venn diagrams, tree diagrams71
4.6Combined events, independent vs dependent, conditional probability30
4.7Discrete random variables, expected value22
4.8Binomial distribution, mean and variance18
4.9Normal distribution, standardization, inverse normal41
4.10Spearman's rank correlation, hypothesis testing, p-valuesHL only18
4.11Chi-squared test (goodness-of-fit, independence), t-testHL only17
4.12Estimators (unbiased), confidence intervals, central limit theoremHL only18
4.13Poisson distribution (mean = variance)HL only13
4.14Hypothesis testing on means / proportionsHL only16
4.15Transition matrices (Markov chains), steady-stateHL only12
4.16Bayes' theorem (advanced conditional probability)HL only7
4.17Linear combinations of normal variablesHL only6

5Calculus16 chapters · 306 questions

5.1Limits, gradient at a point, derivative as a rate of change19
5.2Differentiation of polynomials (power rule)3
5.3Tangents, normals, increasing/decreasing, max/min via derivative31
5.4Integration as anti-differentiation, indefinite integrals22
5.5Definite integration, area under curve, area between curves48
5.6Differentiation rulesHL onlyProduct, quotient, chain37
5.7Differentiation of trig, exponential, logarithmic functionsHL only20
5.8Optimization, second derivative, points of inflectionHL only34
5.9Kinematics (displacement, velocity, acceleration via integration)HL only35
5.10Numerical methods (trapezoidal rule)HL only3
5.11Differential equations (separable), exponential growth/decayHL only21
5.12Euler's method (slope fields), numerical solutionsHL only10
5.13Phase portraits (1st-order ODEs)HL only3
5.14Coupled differential equations (2x2 systems)HL only7
5.15Eigenvalues for 2x2 ODE systems, phase portraitsHL only10
5.16Slope fields, qualitative analysis of ODEsHL only3

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2.1 Equation of a line, gradient, intercepts, parallel/perpendicular· Basics

State the gradient and $y$ -intercept of the line with equation $y = \frac{2 x - 3}{6}$ . [3 marks]

See all 10 free questions

Questions

Is the SL content included?: Yes. HL students sit the SL content too, so every SL syllabus point is here. Chapters only HL students need are tagged HL only.
Are these IB past paper questions?: No. They are written by our teachers in the IB style, so you can practise without using up the past papers you will want for timed mocks.
What happens when the free week ends?: You keep your account and your scores. Courses you have not bought lock until you buy them. Nothing renews automatically, and you are never charged without choosing to pay.
How long can I buy a course for?: 1 month, 3 months, 6 months, 1 year or 2 years. Longer access costs less per month. If you buy again before your access ends, the new time is added on to the end.
How do I pay?: Through Razorpay, by UPI, card, net banking or wallet. Cards issued outside India work too.