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.

Availability: Out of Stock Usually Dispatched In: 3 - 7 Business Days ISBN: 9781740981750 Publisher: Academic Task Force Categories: ATARAssessment PreparationMathematicsTest PrepPreparation & Study Guides
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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.

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
    • 21.4 Proof by Contradiction
    • 21.5 Mathematical Induction
  • Answers
  • 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.
View Year 11 ATAR Course Study Guide - Mathematics Specialist


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
View Year 11 ATAR Course Revision Series - Mathematics Specialist

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

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