# Year 11 ATAR Course Textbook - Mathematics Specialist

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Year 11 ATAR Course Textbook - Mathematics Specialist is a comprehensive textbook for the year 11 Mathematics Specialist Units 1 & 2 course.

Year 11 ATAR Course Textbook - Mathematics Specialist is a comprehensive textbook for the year 11 Mathematics Specialist Units 1 & 2 course.

#### Contents

• 1 Combinatorics I
• 1.1 The Factorial Notation
• 1.2 The Multiplication Rule
• 1.3 Arrangements/Permutations
• 1.4 The Grouping Technique and the Complement Rule
• 1.4.1 The Grouping Technique
• 1.4.2 The Complement Rule
• 2 Combinatorics II
• 2.1 The Inclusion-Exclusion Principle for Two Sets/Events
• 2.2 The Inclusion-Exclusion Principle for Three Sets/Events4
• 2.3 The Pigeon Hole Principle (Dirichlet’s principle)
• 3 Combinatorics III
• 3.1 The Combinatorial Notation
• 3.2 Combinations or Selections
• 3.3 Combinations and the inclusion-exclusion principle
• 3.4 Combinations and Arrangements
• 3.5 Pascal’s Triangle
• 4 Introduction to Vectors
• 4.1 Arrow Representation of Vectors
• 4.1.1 Scalar multiple of a vector
• 4.1.2 Addition of Vectors (arrow representation)
• 4.1.3 Subtraction of Vectors (arrow representation)
• 4.1.4 Vectors and Triangle Trigonometry
• 4.2 Component Representation of Vectors
• 4.2.1 Unit vectors and Basis vectors
• 4.2.2 Magnitude and direction of a vector
• 4.2.3 Scalar Multiplication and Parallel Vectors
• 4.2.4 Unit Vectors
• 4.2.5 Alternative notation for vector in component form
• 4.2.6 Addition and Subtraction of Vectors
• 4.2.7 Working with Vectors in Component Form
• 5 Position Vectors
• 5.1 Free Vectors and Position Vectors
• 5.2 Internal and External Division of a Line Segment
• 6 Relative Vectors
• 6.1 Relative Position/Displacement Vectors
• 6.2 Relative Velocity
• 7 Vector Applications I
• 7.1 Vectors using Arrow Representation
• 7.2 Vectors in Component Form
• 7.3 Position Vectors
• 8 Vector Applications II
• 8.1 Relative Displacement and Velocity
• 8.2 Interception & Collision Problems using Relative Vectors
• 9 Scalar Product
• 9.1 Scalar Product (Dot Product)
• 9.1.1 Properties of the Scalar Product
• 9.2 Geometric Interpretation of the Scalar Product
• 9.3 Vector Projection
• 10 Vector Applications III
• 10.1 Closest Distance
• 10.2 Vector Components/Projections
• 11 Geometric Proofs & Circle Properties
• 11.1 Geometric Proofs
• 11.2 Properties of angles, parallel lines and triangles
• 11.3 Similar Triangles
• 11.4 Congruent Triangles
• 11.5 Circle Properties
• 12 Geometric Proofs using Vectors
• 12.1 Geometric Proofs involving Vectors I
• 12.2 Geometric Proofs involving Vectors II
• 13 Trigonometric Equations I
• 13.1 Review of Basic Concepts
• 13.2 Solving Trigonometric Equations
• 13.2.1 General Solutions
• 13.3 Reciprocal Trigonometric Functions
• 14 Trigonometric Graphs130
• 14.1 Graphs of basic trigonometric functions
• 14.2 Graphs of Trigonometric functions of the form y = a f (bx + c) + d
• 14.3 Graphs of reciprocal trigonometric functions
• 15 Trigonometric Identities
• 15.1 Pythagorean Identities
• 15.2 Proving Trigonometric Identities
• 15.3 Compound Angle Formulae
• 15.4 The Double and Half-Angle Formulae
• 15.5 Product to Sum and Sum to Product Formulae
• 15.6 Linear combinations of sine and cosine (Auxiliary Angles)
• 16 Matrix Algebra
• 16.1 Definitions
• 16.1.1 Equality of Matrices
• 16.2 Operations on Matrices
• 16.2.1 Matrix Addition and Subtraction
• 16.2.2 Scalar Multiplication
• 16.2.3 Basic Rules for Manipulation of Matrices
• 16.2.4 Matrix Multiplication
• 16.2.5 More Rules for Manipulating Matrices
• 16.2.6 Properties of Special Matrices
• 16.3 The Multiplicative Inverse of a Matrix
• 16.3.1 Determinant of a 2 ? 2 Matrix
• 16.3.2 Formula for the inverse of a 2 ? 2 matrix
• 16.4 Manipulating Matrix Equations
• 17 Systems of Linear Equations
• 17.1 Systems of Two Linear Equations
• 17.2 The Matrix Inversion Method
• 18 Applications using Matrices
• 19 Transformation Matrices
• 19.1 Linear Transformations in the x-y plane
• 19.2 Using Matrices to Represent Linear Transformations
• 19.2.1 Procedure for determining the matrix representation of a linear transformation
• 19.2.2 Linear Transformations considered
• 19.3 Scale Factor for Area
• 19.4 Combining Transformations
• 20 Introduction to Complex Numbers
• 20.1 Introduction to Complex Numbers
• 20.2 Basic Properties of Complex Numbers (Cartesian Form)
• 20.3 Complex Numbers as Ordered Pairs
• 20.4 Quadratic Equations with Complex Roots
• 21 Methods of Proofs
• 21.1 Conjectures
• 21.2 Deductive Proofs
• 21.3 Counter Examples
• 21.5 Mathematical Induction
• Index

## Also Available

#### Year 11 ATAR Course Study Guide - Mathematics Specialist

The purpose of this text is to assist Year 11 students with their preparation for tests and examinations in the Specialist Mathematics course for Western Australia.

#### Year 11 ATAR Course Revision Series - Mathematics Specialist

Year 11 ATAR Course Revision Series - Mathematics Specialist provides a comprehensive set of revision/review questions for the year 11 Mathematics Specialist Units 1 & 2 course

 ISBN 9781740981750 Publisher Academic Task Force Product Type Student Books, Year Level Year 11, Author(s) O. T. Lee

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