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Mathematics: Analysis and Approaches

43 premium lessons live for IB Diploma Mathematics: Analysis and Approaches. Learn visually, read concise notes, then practise with criterion marking on every topic.

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ContentsMaths AA HL · 43 topics

Unit 1 · 8 topics

Number and algebra

◆Sequences and series: arithmetic and geometric1 sim1.1CONTINUE Exponents and logarithms1.2 The binomial theorem2 sims1.3 Counting principles, permutations and combinations1.4 Proof: induction, contradiction and counterexample1.5 Complex numbers: Cartesian, polar and Euler form1 sim1.6 Complex numbers: De Moivre's theorem and roots1 sim1.7 Systems of linear equations1.8

Unit 2 · 8 topics

Functions

Linear functions and equations of straight lines1 sim2.1 Functions: domain, range, composite and inverse1 sim2.2 Quadratic functions and equations1 sim2.3 Transformations of graphs2.4 Rational functions and their graphs2.5 Exponential and logarithmic functions2.6 Polynomial functions, factor and remainder theorems2.7 Solving equations and inequalities; modulus functions2.8

Unit 3 · 9 topics

Geometry and trigonometry

Geometry of 3D solids: volume and surface area1 sim3.1 Trigonometry: sine and cosine rules2 sims3.2 The unit circle and radian measure1 sim3.3 Trigonometric functions and their graphs1 sim3.4 Trigonometric identities and equations3.5 Compound and double angle identities; inverse trig3.6 Vectors: properties and operations3.7 Vector equations of lines3.8 Scalar and vector products; planes1 sim3.9

Unit 4 · 8 topics

Statistics and probability

Descriptive statistics2 sims4.1 Bivariate data: correlation and linear regression1 sim4.2 Probability, Venn diagrams and tree diagrams1 sim4.3 Discrete random variables and expected value4.4 The binomial distribution1 sim4.5 The normal distribution1 sim4.6 Conditional probability and Bayes' theorem1 sim4.7 Continuous random variables and probability density functions1 sim4.8

Unit 5 · 10 topics

Calculus

Limits and differentiation from first principles1 sim5.1 Differentiation rules: chain, product and quotient1 sim5.2 Tangents, normals and the second derivative5.3 Optimization and kinematics1 sim5.4 Integration as antidifferentiation5.5 Definite integrals: areas and volumes of revolution2 sims5.6 Further differentiation: implicit, related rates and L'Hopital2 sims5.7 Integration techniques: substitution, by parts and partial fractions1 sim5.8 Differential equations and slope fields5.9 Maclaurin series1 sim5.10

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Mathematics: Analysis and Approaches (Maths AA) — free IB HL course