IB Mathematics Analysis and Approaches HL Functions

IB Mathematics Analysis and Approaches HL – Functions

2.1 Straight Lines
2.2 Functions
2.3 Quadratic Functions
2.4 Quadratic Equations
2.5 Graphs
2.6 Transformations
2.7 Polynomials

83 Lessons

Course Materials


Gradient of Lines


Parallel Lines

Perpendicular Lines

Vertical Lines and Horizontal Lines

Finding Equations of Lines

General Form of a Line

Finding Gradient from an Equation


Relations and Functions

Function Notation

Domain and Range

Functions and Equations

Functional Equations

Inverse Functions

Relations and Their Inverses

Functions and Their Inverses

Understanding Inverse Functions

Composite Functions

Even Functions and Odd Functions


Key Features of Quadratic Graphs

Quadratic Graphs from Tables of Values

Quadratic Graphs Vertices Origin

Restricting Functions

Quadratic Graphs Up Down

Parabola Touches X-axis

Parabola in Vertex Form

Parabola in Intercept Form

X-intercept Y-intercept

Axis of Symmetry

Vertex of a Parabola

Quadratic Graphs by Completing the Square

Finding Quadratics from Graphs

Where Quadratic Graphs Meet


Positive Definite and Negative Definitive Quadratics


What are Quadratic Equations?

Finding Solutions by Inspecting Graphs

Quadratic Equations in Factorised Form

Quadratic Equations in Square Form (ax^2 + c = 0)

Quadratic Identities

Substitutions into Quadratics

Solving by Factorisation

Solving by Completing the Square

Quadratic Formula

Problem Solving with Quadratics

Forming Quadratic Equations

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