Exam Style Practice Questions, Notes and Past Paper for IBDP Maths - MAA and MAI 2025

Please see below the program documentation for a discussion of the math curriculum changes effective September 2019 for the IB Class of 2021.

The following chart summarizes the new courses and provides guidance in course selection:

The following pages summarize the content of the new courses.

Mathematics: Analysis and approaches

The number and algebra SL looks at: scientific notation, arithmetic and geometric sequences and series and their applications including financial applications, laws of logarithms and  exponentials, solving exponential equations, simple proof, approximations and errors, and the binomial theorem. The number and algebra HL looks at: permutations and combinations, partial fractions, complex numbers, proof by induction, contradiction and counter-example, and solution of systems of linear equations.

The functions SL looks at: equations of straight lines, concepts and properties of functions and their graphs, including composite, inverse, the identity, rational, exponential, logarithmic and quadratic functions. Solving equations both analytically and graphically, and transformation of graphs. The functions HL looks at: the factor and remainder theorems, sums and products of roots of polynomials, rational functions, odd and even functions, self-inverse functions, solving function inequalities and the modulus function.

The geometry and trigonometry SL looks at: volume and surface area of 3d solids, right­ angled and non -right -angled trigonometry including bearings and angles o f elevation and depression, radian measure, the unit circle and Pythagorean identity, double angle identities for sine and cosine, composite trigonometric functions, solving trigonometric equations. The geometry and trigonometry HL looks at: reciprocal trigonometric ratios, inverse trigonometric function s, compound angle identities ,double angle identity for tangent, symmetry properties of trigonometric graphs, vector theory, applications with lines and planes, and vector algebra.

The statistics and probability SL looks at: collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation, regression, calculating probabilities, probability diagrams, the normal distribution with standardization of variables, and the binomial distribution. The statistics and probability HL looks at: Bayes theorem, probability distributions, probability density functions, expectation algebra.

The calculus SL looks at: informal ideas of limits and convergence, differentiation including analysing graphical behaviour of functions, finding equations of normals and tangents, optimization, kinematics involving displacement, velocity, acceleration and total distance travelled, the chain, product and quotient rules, definite and indefinite integration. The calculus HL looks at: introduction to continuity and differentiability, convergence and divergence, differentiation from first principles, limits and L’Hopital’s rule, implicit differentiation, derivatives of inverse and reciprocal trigonometric functions, integration by substitution and parts, volumes o f revolution, solution of first order differential equations using Euler’s method, by separating variables and using the integrating factor, Maclaurin series.

Mathematics: Applications and interpretation

The number and algebra SL looks at: scientific notation, arithmetic and geometric sequences and series and their applications in finance including loan repayments, simple treatment of logarithms and exponentials, simple proof, approximations and errors. The number and algebra HL looks at: laws of logarithms, complex numbers and their practical applications, matrices and their applications for solving systems of equations, for geometric transformations, and their applications to probability.

The functions SL looks at: creating, fitting and using models with linear, exponential, natural logarithm, cubic and simple trigonometric functions. The functions HL looks at: use of log-log graphs, graph transformations, creating, fitting and using models with further trigonometric, logarithmic, rational, logistic and piecewise functions.

The geometry and trigonometry SL looks at: volume and surface area of 3d solids, right­ angled and non -right-angled trigonometry including bearings, surface area and volume of composite 3d solids, establishing optimum positions and paths using Voronoi diagrams.

The geometry and trigonometry HL looks at: vector concepts and their applications in kinematics, applications o f adjacency matrices, and tree and cycle algorithms.

The statistics and probability SL looks at: collecting data and using sampling techniques, presenting data in graphical form, measures of central tendency and spread, correlation using Pearson’s pro duct-moment and Spearman’s rank correlation coefficients, regression, calculating probabilities, probability diagrams, the normal distribution, Chi-squared test for independence and goodness of fit. The statistics and probability HL looks at: the binomial and Poisson distributions, designing data collection methods, tests for reliability and validity, hypothesis testing and confidence intervals.

The calculus SL looks at: differentiation including analyzing graphical behavior of functions and optimization , using simple integration and the trapezium/ trapezoidal rule to calculate areas of irregular shapes. The calculus HL looks at: kinematics and practical problems involving rates of change, volumes of revolution, setting up and solving models involving differential equations using numerical and analytic methods, slope fields, coupled and second-order differential equations in context.