IB Maths AI Definitions

1: All sub-topics combined

View the definitions for all 12 of the IB maths ai topic 1 subtopics combined.

1.1: Scientific notation

Master operations with scientific notation. Learn to manipulate numbers in standard form efficiently and confidently.

1.2: Arithmetic sequences

Explore the world of arithmetic sequences and series. Discover the formulae for nth terms, sums, and sigma notation to describe patterns in numbers.

1.3: Geometric sequences

Dive into geometric sequences and their powerful properties. Master the formulae for nth terms, finite sums, and the convergence of infinite series.

1.4: Interest

Apply sequences and series to real-world financial contexts. Understand simple and compound interest, depreciation, and how to model imperfect arithmetic patterns in practice.

1.5: Introduction to exponents & logs

Build your foundation in exponents and logarithms. Understand the laws of integer exponents and learn to evaluate logarithms with base 10 and e.

1.6: Handling numbers

Develop precision in your numerical work. Master rounding, significant figures, upper and lower bounds, percentage errors, and estimation techniques.

1.7: Use of technology

Harness technology for financial mathematics and equation solving. Apply amortization and annuities, and solve systems of equations and polynomials using your GDC.

1.8: Advanced exponents & logs (HL)

Deepen your command of logarithms. Master the laws of logarithms and simplify expressions involving rational exponents with confidence.

1.9: Introduction to complex numbers (HL)

Enter the world of complex numbers. Explore Cartesian, polar, and exponential forms, and discover how complex numbers arise as solutions to quadratic equations.

1.10: Advanced complex numbers (HL)

Extend your understanding of complex numbers. Add sinusoidal functions and explore the geometric interpretation of complex operations.

1.11: Introduction to matrices (HL)

Discover the algebra of matrices. Master operations, determinants, inverses, and use matrices to solve systems of linear equations.

1.12: Advanced matrices (HL)

Unlock eigenvalues and eigenvectors. Explore the characteristic polynomial, diagonalization, and applications to powers of matrices.

2: All sub-topics combined

View the definitions for all 8 of the IB maths ai topic 2 subtopics combined.

2.1: Forms of lines

Master the equations of straight lines in all their forms. Explore gradients, intercepts, and the conditions for parallel and perpendicular lines.

2.2: Introduction to functions

Build your understanding of functions from the ground up. Explore domain, range, notation, inverse functions, and the key features of graphs.

2.3: Introduction to modelling functions

Model the real world with mathematical functions. Explore linear, quadratic, exponential, cubic, and sinusoidal models to describe patterns and make predictions.

2.4: Modelling applications

Put mathematical models to the test. Develop, fit, validate, and interpret models in real-world contexts, and use them to make informed predictions.

2.5: Further functions (HL)

Combine and reverse functions with confidence. Master composite functions, formal notation, and finding inverse functions with domain restriction.

2.6: Graph transformations (HL)

Transform your understanding of graphs. Master translations, reflections, stretches, and composite transformations to manipulate any function.

2.7: Advanced modelling functions (HL)

Expand your modelling toolkit with powerful new functions. Explore half-life, logarithmic, sinusoidal, logistic, and piecewise models.

2.8: Logarithmic graphs (HL)

Scale and linearize data using logarithms. Interpret log-log and semi-log graphs to identify exponential and power relationships in data.

3: All sub-topics combined

View the definitions for all 13 of the IB maths ai topic 3 subtopics combined.

3.1: Fundamentals of geometry

Navigate three-dimensional space with confidence. Calculate distances, midpoints, volumes, surface areas, and angles between lines and planes.

3.2: Introduction to trigonometry

Build your trigonometric foundations. Apply sine, cosine, and tangent ratios alongside the sine rule, cosine rule, and triangle area formulae.

3.3: Applied trigonometry

Put trigonometry to work in real-world contexts. Solve problems involving angles of elevation and depression, and construct labelled diagrams from written descriptions.

3.4: Circles

Measure the circle with precision. Calculate arc lengths and sector areas to describe circular geometry.

3.5: Perpendicular bisectors

Construct and apply perpendicular bisectors. Derive their equations and use them in coordinate geometry problems.

3.6: Voronoi diagrams

Partition the plane with Voronoi diagrams. Explore nearest neighbour interpolation and apply your understanding to the toxic waste dump problem.

3.7: Unit circle (HL)

Define trigonometric functions through the unit circle. Explore radians, the Pythagorean identity, and solve trigonometric equations graphically.

3.8: Geometric transformations (HL)

Transform geometry using matrices. Apply reflections, stretches, enlargements, translations, rotations, and interpret the geometric meaning of determinants.

3.9: Vectors (HL)

Enter the world of vectors. Master components, operations, scalar and vector products, and their geometric interpretations.

3.10: Vector lines (HL)

Describe lines in vector form and model motion. Apply vector equations to kinematics with constant and variable velocity in two and three dimensions.

3.11: Graph theory (HL)

Map connections with graph theory. Explore vertices, edges, degrees, trees, and the fundamental structures of graphs and networks.

3.12: Adjacency matrices (HL)

Represent graphs with matrices. Analyse walks, weighted graphs, and construct transition matrices for connected and directed graphs.

3.13: Algorithms & problems (HL)

Solve classic graph theory problems. Apply algorithms for minimum spanning trees, the Chinese postman problem, and the travelling salesman problem.

4: All sub-topics combined

View the definitions for all 14 of the IB maths ai topic 4 subtopics combined.

4.1: Fundamentals of statistics

Lay the foundations of statistical analysis. Explore populations, samples, data types, central tendency, and measures of spread.

4.2: Visualising statistics

Bring data to life with visual tools. Master histograms, cumulative frequency graphs, and box-and-whisker diagrams to reveal patterns and distributions.

4.3: Distribution properties

Quantify the spread of data with precision. Understand interquartile range, standard deviation, variance, and how constant changes affect distributions.

4.4: Introduction to linear statistics

Uncover relationships in bivariate data. Master Pearson's and Spearman's correlation coefficients, scatter diagrams, and regression lines for prediction.

4.5: Probability

Quantify uncertainty with the language of probability. Apply Venn diagrams, tree diagrams, and the rules for combined, conditional, and independent events.

4.6: Probability distributions

Model randomness with probability distributions. Explore discrete random variables, the binomial distribution, and the normal distribution with probability calculations.

4.7: Hypotheses & tests

Test your hypotheses with statistical rigour. Master chi-squared tests, t-tests, p-values, and significance levels to draw valid conclusions from data.

4.8: Data collection & categorisation (HL)

Design robust data collection methods. Understand reliability, validity, and the appropriate categorisation of data for statistical tests.

4.9: Advanced linear statistics (HL)

Fit curves to data with confidence. Explore non-linear regression, sum of square residuals, and the coefficient of determination to evaluate model fit.

4.10: Linear transformations & combinations (HL)

Transform and combine random variables. Master expected values, variances, unbiased estimators, and the central limit theorem.

4.11: Confidence intervals (HL)

Estimate population parameters with precision. Construct and interpret confidence intervals for the mean of a normal population.

4.12: Poisson distribution (HL)

Model rare events with the Poisson distribution. Explore its mean, variance, and the property that the sum of independent Poisson variables is also Poisson.

4.13: Distribution tests (HL)

Test population parameters with rigour. Apply hypothesis tests for means, proportions, and correlations, and understand Type I and Type II errors.

4.14: Transition matrices (HL)

Model state changes with Markov chains. Calculate steady state and long-term probabilities using transition matrices and systematic analysis.

5: All sub-topics combined

View the definitions for all 9 of the IB maths ai topic 5 subtopics combined.

5.1: Introduction to derivatives

Take your first steps into the world of calculus. Understand limits, interpret derivatives as gradient functions and rates of change, and master the power rule.

5.2: Applying derivatives

Put derivatives to work in context. Find tangents, locate turning points, and solve optimisation problems using first and second derivatives.

5.3: Fundamentals of integration

Discover integration as the reverse of differentiation. Calculate areas under curves, evaluate definite integrals, and approximate areas using the trapezoidal rule.

5.4: Advanced derivatives (HL)

Expand your differentiation skills. Apply the chain, product, and quotient rules to trigonometric, exponential, and logarithmic functions, and use the second derivative test.

5.5: Further integration (HL)

Integrate a broader range of functions. Master definite and indefinite integrals of power, trigonometric, and exponential functions, and apply integration by inspection.

5.6: Applying integration (HL)

Calculate areas and volumes using integration. Find regions enclosed by curves and compute volumes of revolution about the x and y-axes.

5.7: Kinematics (HL)

Apply calculus to the study of motion. Solve problems involving displacement, velocity, and acceleration.

5.8: Introduction to differential equations (HL)

Model change with differential equations. Set up models from context, solve by separation of variables, and approximate solutions using Euler's method and slope fields.

5.9: Advanced differential equations (HL)

Analyse coupled systems using phase portraits. Explore equilibrium points, trajectories, eigenvalue classification, and second-order differential equations.