IB Math Analysis and Approaches
This course has been newly added to the IB Programme and has, in fact, replaced the old curriculum, known as Math Applications and Interpretations. Unlike the old curriculum, Math AA is less centralised on calculus and has some focus on other topics such as proofs, bionomial theorms, and statistics. Although some calculus-related contents have been removed, it is still considered as one of the most challenging courses in IB Programme. The first examination session of Math AA was in May 2021.
Overview of the Content
When a new curriculum is introduced, the IB provides schools with a detailed list of the content required to be covered for that new curriculum. Most of IB courses are taught in standard level and higher level. The main difference between the two levels is the amount of content, difficulty of questions, and nature of some topics. In the higher level courses, more content is covered and exam questions are more difficult. In some courses, such as math, the difference between higher and standard levels is very noticeable. IB Math AA Syllabus content can be found here.
Here is an overview of the course content:
Functions: Domain and range, rational functions, composite functions, inverse functions, transformations of functions, exponential functions, logarithms, even and odd functions, absolute value functions, partial fractions, etc.
Trigonometry: unit circle and radian measure, reciprocal and inverse trigonometric functions, double and compound angle identities, algebraic manipulations with trigonometric functions, etc.
Real Polynomials: operations with polynomials, zeros, roots, factors, polynomial equality, polynomial division, polynomial theorm, factor theorm, fundamental theory of algebra, graphing polynomial functions, cubic inequalities, biomial theorm, extended binomial theorm, etc.
Complex Numbers: operations with complex numbers, equalities with complex numbers, properties of complex conjugates, complex plane, modulus and argument, geometry in complex plane, polar and Euler's form, De Moivre's theorem, roots of complex numbers, etc.
Vectors and Vector Application: geometric operations with vectors and plane vectors, vectors in space, parallelism, scalar and vector product of two vectors, angle between vectors, equation of vector line, equation of plane, angle between lines and planes, intersecting lines and planes, row operations and solving systems of linear equations, etc.
Reasoning and Proof: proof by deduction, equivalence, counter example and contradiction, proof by mathematical induction, etc.
Counting: product and sum principle, factorial notation, permutations and combinations, etc.
Statistics: smapling and data, grouped data, box and whisker diagrams, outliers, cumulative frequency diagram, variance and standard deviation, bivariate statistics, Pearson's product-moment correlation coefficient, linear regression, etc.
Probability: Experimental and theoretical probability, sample space and events, laws of probability, independent and dependent events, conditional probability, discrete and continuous random variables, probability mass function, expectation, binomial distribution, normal distribution, probability density function, etc.
Calculus: limits, existence of limit, continuity, trogonometic limits, gradient and derivative, differentiation from first principle, differentiability, L'Hopital's rule, increasing and decreasing functions, stationary points, point of inflection, rate of change, optimisation, related rates, implicit differentiation, integration, area under the curve, fundamental theorem of calculus, partial fractions, integration by substition and by parts, definite integrals, solids of revolution, improper integrals, kinematics, maclaurin series, convergence, addition and subtraction of maclaurin series, multiplication and division of maclaurin series, differntial equations, numerical integration, separable differential equations, homogeneous differential equations, first order linear differnetial equations, logistic growth, etc.
IB Math Examination