IB Mathematics: Analysis and Approaches HL
154 lessons across 5 topics
1. Number and Algebra
1Algebraic Solutions To Systems2Applications Of Sequences And Series3Argand Diagrams4Arithmetic Sequences And Series5Binomial Theorem6Complex Roots Of Polynomials7Compound Interest And Depreciation8Counting Principles9De Moivre’s Theorem10Direct Proof11Extension Of The Binomial Theorem12Forms Of Complex Numbers13Geometric Sequences And Series14Geometry Of Complex Numbers15Introduction To Complex Numbers16Introduction To Logarithms17Language Of Sequences And Series18Laws Of Indices19Laws Of Logarithms20Modulus And Argument21Partial Fractions22Permutations And Combinations23Proof By Contradiction24Proof By Induction25Roots Of Complex Numbers26Solving Exponential Equations27Standard Form28Systems Of Linear Equations
2. Functions
29Completing The Square30Composite Functions31Composite Transformations Of Graphs32Discriminants33Equations Of A Straight Line34Exponential Functions35Factor Theorem36Factorising Quadratics37Graphing Functions38Inverse Functions39Language Of Functions40Logarithmic Functions41Modelling With Functions42Modulus Equations And Inequalities43Modulus Functions44Modulus Transformations45Polynomial Division46Polynomial Functions47Polynomial Inequalities48Quadratic Functions49Quadratic Inequalities50Rational Functions51Reciprocal And Square Transformations52Reciprocal Functions53Reflections Of Graphs54Remainder Theorem55Roots Of Polynomials56Solving Equations With Functions57Solving Inequalities Graphically58Solving Quadratic Equations59Stretches Of Graphs60Symmetry Of Functions61Translations Of Graphs
3. Geometry and Trigonometry
62Angles Between Lines And Planes63Applications Of Trigonometry And Pythagoras64Arcs And Sectors65Compound Angle Formulae66Coordinate Geometry67Double Angle Formulae68Exact Values69Geometric Proof With Vectors70Graphs Of Trigonometric Functions71Intersections Of Lines And Planes72Introduction To Vectors73Inverse Trigonometric Functions74Linear Trigonometric Equations75Magnitude Of A Vector76Modelling With Trigonometric Functions77Non Right-angled Trigonometry78Pairs Of Lines In 3d79Position And Displacement Vectors80Pythagoras And Right-angled Trigonometry81Quadratic Trigonometric Equations82Radian Measure83Reciprocal Trigonometric Functions84Relationships Between Trigonometric Ratios85Shortest Distances With Lines86Shortest Distances With Planes87Simple Identities88Strategy For Trigonometric Equations89The Scalar Product90The Unit Circle91The Vector Product92Three-dimensional Coordinate Geometry93Transformations Of Trigonometric Functions94Trigonometric Proof95Vector Applications To Kinematics96Vector Equations Of Lines97Vector Equations Of Planes98Volume And Surface Area
4. Statistics and Probability
99Bayes’ Theorem100Bivariate Data101Calculating Binomial Probabilities102Calculations With The Normal Distribution103Conditional Probability104Correlation105Discrete Probability Distributions106Frequency Tables107Interpreting Data108Linear Transformations Of Data109Mean And Variance Of A Distribution110Outliers111Probability And Types Of Events112Probability Density Functions113Regression114Sample Space Diagrams115Sampling And Data Collection116Standardisation Of Normal Variables117Statistical Measures118The Binomial Distribution119The Normal Distribution120Univariate Data
5. Calculus
121Advanced Applications Of Integration122Analytical Solutions To Differential Equations123Applications Of Differentiation124Applications Of Integration125Applications Of The Chain Rule126Basic Limits And Continuity127Calculus For Kinematics128Concavity And Points Of Inflection129Definite Integrals130Derivatives And Graphs131Differentiating Further Functions132Differentiating Special Functions133First Principles Differentiation134Further Applications Of Differentiation135Further Applications Of Integration136Further Limits137Further Techniques Of Integration138Higher-order Derivatives139Implicit Differentiation140Integrating Further Functions141Integrating Special Functions142Integrating With Partial Fractions143Introduction To Differentiation144Introduction To Integration145Kinematics Toolkit146L’hôpital’s Rule147Maclaurin Series148Maclaurin Series From Differential Equations149Modelling With Differential Equations150Modelling With Differentiation151Numerical Solutions To Differential Equations152Techniques Of Differentiation153Techniques Of Integration154Volumes Of Revolution