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IB-DP Mathematics
IB Mathematics
1 Number and Algebra
1.2 Arithmetic Sequences and Series
1.3 Geometric Sequences and Series
1.4 Financial Applications of Geometric Sequences
1.5 Laws of Exponents and Logarithms
MAA Topics
1.7 Exponents and Logarithms, Equations
1.8 Sum of an Infinite Convergent Geometric Series
1.9 Pascal's Triangle and the Binomial Theorem
1HL Complex Numbers
1HL Proofs
MAI Topics
1.6 Approximation, Upper and Lower bounds
1.7 Amortisation and Annuities
1.8 Equations, Systems and Polynomials
1HL Complex Numbers
2 Functions
2.1 The equation of a a straight line
2.2 Functions: notation, domain, range, inverse
MAA Topics
2.5 Composite Functions
2.6 Quadratic functions, Graphs, Applications
2.7 Quadratic Equations, the Quadratic formula, Roots
2.8 Reciprocal and Rational Functions
2.9 Exponential and Logarithmic Graphs
2.10 Solving Logs and Exponents
2.11 Transformation of Graphs
MAI Topics
2.5 Modelling with Functions
3 Geometry and Trigonometry
3.1 Distance, Volume, Area, Angles
3.2 Sin, Cos, Tan and Trigonometry
3.3 Applications of Trigonometry
MAA Topics
3.4 Radian Measure, Arcs, Sectors, Area
3.5 Definition of Sin Cos and Tan
3.6 Double angle identities and Pythagoras
3.7 Trigonometric Functions, Transformations and Modelling
3.8 Trigonometric Equations and Identities
Vectors and Operations
3.HL Vectors
MAI Topics
3.5 Perpendicular bisectors
3.6 Voronoi diagrams
3.HL Vectors
4 Statistics and Probability
4.1 Concepts of population, sample, random sample, discrete and continuous
4.2 Presentation of Data
4.3 Measures of Central tendency and Spread
4.4 Least Squares Regression and Correlation
4.5 Trials, Events, Sample Space, Outcomes
4.6 Venn Diagrams and Conditional Probability
4.7 Discrete Random Variables and Expected Value
4.8 Binomial Distribution
4.9 The Normal Distribution
MAA Topics
4.11Conditional Probability and Independent Events
4.12 Standard Normal Distribution
MAI Topics
4.10 Spearman's Rank Correlation
4.11 Hypothesis Testing
HL4.17 Poisson
5 Calculus
5.1 Limits, Gradients
5.2 Increasing and Decreasing functions
5.3 Derivative of x to the power n
5.4 Tangents and Normals
5.5 Anti Derivation
MAA Topics
5.6 Rules of Differentiation
5.7 Graphs of f, f' and f", Second Derivative
5.8 Maxima, Minima, Inflexion, Optimisation
5.9 Kinematics
5.10 Indefinite Integrals, composites, reverse chain-rule
5.11 Definite Integration, Area under curve
AHL 5.12 First Principles
AHL 5.15 More Derivatives
AHL 5.14 Related Rates
AHL 5.16 Using U substitution
AHL 5.17 Volumes of revolution
MAI Topics
5.6 When f'(x)=0, Maximum and Minimum
5.7 Optimisation
5.8 Approximating Areas w trapezoidal rule
The Exploration
Exploration Ideas
Class Activities ideas
IB-DP Mathematics
1.HL Proofs
AHL 1.15 Proof by induction
AHL 1.15 Proof that Z is imaginary
AHL 1.15 Proof by induction
https://youtu.be/DRfWt77ZqMw
AHL 1.15 Proof that Z is imaginary
https://www.youtube.com/watch?v=hD9C0cvQv04
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