Outline
Discovering Mathematics for IB DP AA & AI
Dive into IB Diploma Programme Mathematics with our GeoGebra book, tailored for both Analysis & Approaches and Applications & Interpretations courses. This interactive guide offers dynamic activities and exercises, blending conceptual understanding with practical application. Explore calculus, statistics, and real-world problems through engaging tutorials and visualizations. Designed for self-study and classroom use, it's the perfect tool for students aiming to master their IB DP Mathematics exams with confidence.
Table of Contents
Algebra
- Arithmetic (AA/AI SL 1.2)
- Graph Trans (AASL 2.11, AIHL 2.8)
- Rational functions (AAHL 2.13) quadratic over linear
- Binomial theorem (AAHL 1.10)
- Rational functions (AA HL 2.13) (Linear over quadratic)
- Graph trans. (AAHL 2.16)
- Geometric (AA/AI SL 1.3)
- Investigating general parabola (AASL 2.6)
- Factorising quadratics, sketching and inequalities
- Completing the square and vertex form (AASL 2.6)
- Sum of geometric series (AA SL 1.8, AI HL 1.11)
- Log rules (AA SL 1.7, AI HL 1.9)
- Indices laws (AASL 1.5/1.7)
- Binomial theorem (AASL 1.5)
- Inverse functions
- Composite functions
- Rational functions AASL
- Chain rule (AASL/HL)
- Log graph transformations
- The Cosine Rule
- Discriminant
- Equations of straight lines (AASL2.1)
- Complex numbers AAHL 1.11,1.12
Calculus
- Tangent and normals at a point (AA/AI SL 5.4)
- Second derivative - AASL 5.7/5.8 AI HL 5.10
- Trapezium rule (AI SL 5.8)
- Phase portraits (AI HL 5.17)
- Maclaurin series
- Partial fractions (AAHL 1.11)
- Eulers method visualised (AI HL 5.16)
- Derivative of x^n
- Product rule (AASL/HL)
- Quotient rule (AASL/HL)
- Integration of functions of f(ax+b) AASL 5.10
- Integral calculus - Area AASL5.11
- Integration by parts AAHL5.20
Statistics
Geometry and trigonometry
- Trigonometric graphs (domains, ranges sin,cos,tan,arctan,arcsin,arccos,cosec,sec,cot)
- Motion with variable velocity in 2D
- Vector applications in kinematics
- Adding sinusoidal waves (AI HL 1.13)
- 3D Vectors (addition, subtraction, multiplication by scalar, unit vectors and magnitude)
- Degrees-Radians, area of sector and length of arcs
- Distance and midpoints (3D) - AI/AA SL 3.1
- Angle between a line and a plane
- Angle between lines (3D)
- Angle between two lines (2D)
- Equation of perpendicular bisector (AI SL 3.5)
- Powers of matrices (AI HL 1.15)
- Further explorations with Voronoi (AI SL 3.6)
- Voronoi (exploring) - AI SL 3.6
- Transformation matrices (AI HL 3.9)
- Eigenvalues and vectors (AI HL 1.15)
- Angles in the four quadrants (Unit circle)
- Discover double angles (AASL 3.6)
- The Sine Rule
- The Cosine Rule
- Trigonometric graphs (Radians and degrees)
Number
Applying to the real world
Graph Theory
- Graph theory (AIHL 3.15, 3.16) - Part 1 Definitions and basics
- Graph theory (AIHL 3.15, 3.16) - Part 2 Adjacency
- Graph theory (AIHL 3.15, 3.16) - Part 3 Minimum Spanning Trees
- Graph theory (AIHL 3.15, 3.16) - Part 4 Travelling Salesman Problem
- Graph theory (AIHL 3.15, 3.16) - Part 5 Chinese Postman Problem