IB Math AI HL study plan

Compute and interpret mean, median, mode, quartiles, range, interquartile range, and standard deviation for raw and grouped data sets

Classify data types and choose appropriate graphical displays (box plots, histograms, cumulative frequency curves) for a given context

Calculate and interpret Pearson's product-moment correlation coefficient and the coefficient of determination, and distinguish correlation from causation

Derive the least-squares regression line of y on x and use it to make predictions, stating the meaning of gradient and intercept in context

Apply the multiplication and addition rules, conditional probability, and independence to multi-stage problems

Construct and use tree diagrams and Venn diagrams, including set notation for unions, intersections, and complements

Use Bayes' theorem in context to reverse conditional probabilities

Model discrete random variables, computing expected value E(X) and variance Var(X) from a probability distribution table

Recognise when to apply the binomial and normal distributions and compute probabilities in each case

Standardise normal variables using z-scores and find probabilities and inverse-normal values from a calculator

Use the normal approximation to the binomial where appropriate, checking conditions

Compute expected value and variance of a binomial variable and interpret them in context

Differentiate polynomial, exponential, logarithmic, and trigonometric functions using the chain, product, and quotient rules

Interpret the derivative as a rate of change and as a gradient, and find equations of tangents and normals

Locate and classify stationary points using first and second derivative tests

Apply calculus to optimisation and kinematics problems in real contexts

Set up and evaluate a hypothesis test for a population mean or proportion, stating null and alternative hypotheses and interpreting the p-value

Apply the sine and cosine rules and the area formula to non-right triangles, including the ambiguous case

Solve trigonometric equations in a given domain and convert between degrees and radians

Use the unit circle and exact values, and apply Pythagorean and double-angle identities

Integrate standard functions and apply definite integrals to find areas under curves and between curves

Compute volumes of revolution about the x-axis using definite integrals

Compute distances, midpoints, and equations of lines in 2D and 3D, including the angle between two vectors

Use the scalar product to test perpendicularity and find projections

Solve 3D geometry problems involving lines, planes, and angles in context

Sketch and analyse quadratic, exponential, and rational functions, identifying intercepts, asymptotes, and symmetry

Find inverse functions, composite functions, and state domain and range restrictions

Transform graphs (translations, stretches, reflections) and describe transformations from equations

Solve exponential and logarithmic equations and apply log laws to model growth and decay

Solve systems of linear equations and apply sequences and series, including arithmetic and geometric sums

Use the binomial theorem to expand expressions and find a specified term

Complete two full-length timed practice papers under exam conditions

Review every error and classify it as conceptual, procedural, or calculator-related

Rehearse the internal assessment structure: research question, mathematical processes, and evaluation criteria

Consolidate calculator techniques for statistics, distributions, and calculus

Build a final one-page formula recall sheet from memory