Maths Methods – Notes

A1 – Functions and Graphs
A1.1 Graphs and Properties of Functions
22 Topics | 1 Quiz
1.1.1 Introduction to Graph Sketching
1.1.2 Sketching the Graph
1.1.3 Properties of a Graph
1.1.4 Introduction to Power Functions
1.1.5 Drawing Power Functions (for Positive Integers) and its Graph Properties
1.1.6 Drawing Power Functions (for Negative Integers) and its Graph Properties
1.1.7 Drawing Power Functions (for n=1/k where k is a Positive Integer) and its Graph Properties
1.1.8 Drawing Power Functions (for n=-1/k where k is a Positive Integer) and its Graph Properties
1.1.9 Power Functions (for n=p/q where p, q are Positive Integers)
1.1.10 Summary of Power Function Graph Properties
1.1.11 Inverses of Power Functions
1.1.12 Exponential Functions
1.1.13 Logarithmic Functions
1.1.14 Trigonometric Functions – Degrees and Radians
1.1.15 Trigonometric Functions – Sine, Cosine and Tangent
1.1.16 Trigonometric Functions – Symmetry Properties
1.1.17 Trigonometric Functions – Other Properties
1.1.18 Graphs of Sine and Cosine Functions
1.1.19 Graphs of Tangent Functions
1.1.20 Additional Graph Types – Circles
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A1.2 Polynomial Functions
 5 Topics | 1 Quiz
1.2.1 Quadratic Function Basics
1.2.2 Re-expressing Quadratic Functions
1.2.3 Cubic Functions Basics
1.2.4 Polynomials of Higher Degree
1.2.5 Determining the Rule of the Polynomial
Quiz – A1.2 Polynominal Functions
A1.3 Transformation of Graphs
 12 Topics
1.3.1 Transformation 1: Translation
1.3.2 Transformation 2: Dilation
1.3.3 Transformation 3: Reflection
1.3.4 Illustrate Combination of Transformations
1.3.5 Determine Combination of Transformations
1.3.6 Transformations of Power Functions
1.3.7 Transformations of Polynomial Functions
1.3.8 Transformations of Exponential Functions
1.3.9 Transformations of Logarithmic Functions
1.3.10 Transformations of Sine and Cosine
1.3.11 Transformations of Tangent
1.3.12 Inverse Transformations
A1.4 Relationship of Transformations
 8 Topics
1.4.1 Transformations with a Single Parameter
1.4.2 Introduction to Matrices
1.4.3 Matrix Addition, Subtraction, and Scalar Multiplication
1.4.4 Matrix Multiplications
1.4.5 The Identity Matrix
1.4.6 Using Matrices for Transformations
1.4.7 Composition of Mappings
1.4.8 Inverse of 2×2 Matrices for Transformations
A1.5 Real Life Applications using Function Models
 8 Topics
1.5.1 Applications of Polynomial Functions
1.5.2 Applications of Circular Functions
1.5.3 Special Exponential Functions
1.5.4 Special Logarithm Functions
1.5.5 Composite Functions
1.5.6 Sum and Product of Functions
1.5.7 Graph Sketching for Sum of Functions
1.5.8 Graph Sketching for Product of Functions
A2 – Algebra
A2.1 Relations and Functions
 7 Topics
2.1.1 Set Notations
2.1.2 Sets of Numbers
2.1.3 Describing a Set and Function
2.1.4 Different Types of Relations
2.1.5 Different Types of Functions
2.1.6 Inverse Functions
2.1.7 Graphing Inverse Functions
A2.2 Polynomial Functions and Algebraic Operations
 5 Topics
2.2.1 Polynomial Function Basics
2.2.2 Arithmetic of Polynomial Functions
2.2.3 Division of Polynomial Functions
2.2.4 Remainder Theorem and Factor Theorem
2.2.5 The Rational-Root Theorem
A2.3 Functional Relations
 4 Topics
2.3.1 Introduction to Functional Relations
2.3.2 Index Laws
2.3.3 Logarithm Laws
2.3.4 Trigonometric Function Laws
A2.4 Compositions of Functions
 1 Topic
2.4.1 Composite Functions
A2.5 Solving Equation Systems
 7 Topics
2.5.1 Application of Functions
2.5.2 Simultaneous Equations: Polynomials
2.5.3 Solution of Trigonometric Equations (Sine and Cosine) – Basic
2.5.4 Solution of Trigonometric Equations (Sine and Cosine) – More Complicated
2.5.5 Solution of Trigonometric Equations (Tangent)
2.5.6 Finding Intercepts for Trigonometric Equations
2.5.7 Solving Exponential and Logarithmic Equations
A2.6 Literal and Parametric Equation Systems
 5 Topics
2.6.1 Linear Literal Equation Systems
2.6.2 Linear Coordinate Geometry
2.6.3 Literal Equation Systems: Polynomials
2.6.4 Families of Functions and Solving Literal Equations
2.6.5 Systems with a Single Parameter
A2.7 Solving Simultaneous Linear Equations
 2 Topics
2.7.1 Simultaneous Linear Equations of Two Variables
2.7.2 Simultaneous Linear Equations of More Variables
A3 – Calculus
A3.1 Rates of Changes, Tangents and Derivative Functions
 9 Topics
3.1.1 Average Rate of Change
3.1.2 Instantaneous Rate of Change
3.1.3 Limit Notation
3.1.4 Chord, Secant, and Tangent
3.1.5 Derivative Basics
3.1.6 Further Exploring Derivatives
3.1.7 Algebra of Limits (Not Required)
3.1.8 Continuity and Differentiability (Not Required)
3.1.9 Estimating Derivatives (Not Required)
A3.2 Graphs of Derivatives and Antiderivatives
 3 Topics
3.2.1 Graphs of Derivative Functions
3.2.2 Graphs of Derivatives for Typical Functions
3.2.3 Graphs of Antiderivative Functions
A3.3 Derivatives of Functions
 5 Topics
3.3.1 Differentiation Rules for Polynomials
3.3.2 Finding Gradient of a Tangent Line
3.3.3 Differentiation Rules for Exponentials and Logarithms
3.3.4 Estimating Derivative for Exponential (Not Required)
3.3.5 Differentiation Rules for Circular Functions
A3.4 Differentiation Rules
 4 Topics
3.4.1 Sums and Differences
3.4.2 Chain Rule
3.4.3 Product Rule
3.4.4 Quotient Rule
A3.5 Application of Differentiation on Graph Properties
 12 Topics
3.5.1 Finding Tangents
3.5.2 Finding Normals
3.5.3 Rates of Change, Motion in a Straight Line
3.5.4 Motion in a Straight Line
3.5.5 Increasing and Decreasing Functions
3.5.6 Stationary and Turning Points
3.5.7 Plotting Graphs of the Derivative Functions
3.5.8 Local Maximum and Minimum Points
3.5.9 Absolute Maximum and Minimum Points
3.5.10 Second Derivatives and Concavity
3.5.11 Maximum and Minimum in Real Life
3.5.12 Maximum Rates of Increase or Decrease
A3.6 Antiderivatives of Functions
 2 Topics
3.6.1 Antiderivatives of Specific Functions
3.6.2 Antiderivatives of Functions with ax+b replacing x
A3.7 Sum of Area and Definite Integrals
 4 Topics
3.7.1 Estimating Area as Sum of Rectangles
3.7.2 Definite Integrals as an Accurate Estimate
3.7.3 Definite Integrals and Area
3.7.4 Definite Integrals and Sum of Areas
A3.8 Anti-Differentiation
 1 Topic
3.8.1 Anti-Differentiation Concepts
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1.1.1 Introduction to Graph Sketching

Maths Methods – Notes A1.1 Graphs and Properties of Functions 1.1.1 Introduction to Graph Sketching
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