دانلود کتاب Maths in focus : mathematics extension preliminary course

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0 - Preface.pdf (p.1-15)
Maths in Focus
Maths in Focus: Mathematics Extension 1 Preliminary Course
Copyright Page
Contents
Preface
Acknowledgements
Credits
Features of this Book
Syllabus Matrix
Study Skills
1 - Basic Arithmetic.pdf (p.16-57)
Chapter 1 Basic Arithmetic
Introduction
Real Numbers
Directed Numbers
Fractions, Decimals and Percentages
Powers and Roots
Absolute Value
Test Yourself 1
Challenge Exercise 1
2 - Algebra and Surds.pdf (p.58-107)
Chapter 2 Algebra and Surds
Introduction
Simplifying Expressions
Binomial Products
Factorisation
Completing the Square
Algebraic Fractions
Substitution
Surds
Test Yourself 2
Challenge Exercise 2
3 - Equations.pdf (p.108-153)
Chapter 3 Equations
Introduction
Simple Equations
Substitution
Inequations
Equations and Inequations Involving Absolute Values
Exponential Equations
Quadratic Equations
Extension: Further Inequations
Quadratic Inequations
Simultaneous Equations
Test Yourself 3
Challenge Exercise 3
4 - Geometry 1.pdf (p.154-212)
Chapter 4 Geometry 1
Introduction
Notation
Types of Angles
Parallel Lines
Types of Triangles
Congruent Triangles
Similar Triangles
Types of Quadrilaterals
Polygons
Areas
Test Yourself 4
Challenge Exercise 4
5 - Functions and Graphs.pdf (p.213-298)
Chapter 5 Functions and Graphs
Introduction
Functions
Graphing Techniques
Linear Function
Quadratic Function
Absolute Value Function
The Hyperbola
Circles and Semi-circles
Other Graphs
Limits and Continuity
Extension: Further Graphs
Regions
Test Yourself 5
Challenge Exercise 5
6 - Trigonometry.pdf (p.299-398)
Chapter 6 Trigonometry
Introduction
Trigonometric Ratios
Right-angled Triangle Problems
Applications
Exact Ratios
Angles of Any Magnitude
Trigonometric Equations
Trigonometric Identities
Non-right-angled Triangle Results
Applications
Area
Extension: Trigonometry in Three Dimensions
Extension: Sums and Differences of Angles
Extension: Further Trigonometric Equations
Test Yourself 6
Challenge Exercise 6
7 - Linear Functions.pdf (p.399-445)
Chapter 7 Linear Functions
Introduction
Distance
Midpoint
Gradient
Equation of a Straight Line
Parallel and Perpendicular Lines
Intersection of Lines
Perpendicular Distance
Extension: Angle Between Two Lines
Extension: Ratios
Test Yourself 7
Challenge Exercise 7
8 - Introduction to Calculus.pdf (p.446-501)
Chapter 8 Introduction to Calculus
Introduction
Gradient
Differentiation from First Principles
Short Methods of Differentiation
Tangents and Normals
Further Differentiation and Indices
Composite Function Rule
Product Rule
Quotient Rule
Extension: Angle Between 2 Curves
Test Yourself 8
Challenge Exercise 8
9 - Properties of the Circle.pdf (p.502-545)
Chapter 9 Properties of the Circle
Introduction
Extension: Parts of a Circle
Extension: Arcs, Angles and Chords
Extension: Chord Properties
Extenstion: Concyclic Points
Extension: Tangent Properties
Test Yourself 9
Challenge Exercise 9
10 - The Quadratic Function.pdf (p.546-581)
Chapter 10 The Quadratic Function
Introduction
Graph of a Quadratic Function
Quadratic Inequalities
The Discriminant
Quadratic Identities
Sum and Product of Roots
Equations Reducible to Quadratics
Test Yourself 10
Challenge Exercise 10
11 - Locus and the Parabola.pdf (p.582-658)
Chapter 11 Locus and the Parabola
Introduction
Locus
Circle as a Locus
Parabola as a Locus
General Parabola
Tangents and Normals
Extension: Parametric Equations of the Parabola
Extension: Chords, Tangents and Normals
Extension: Properties of the Parabola
Extension: Locus Problems
Test Yourself 11
Challenge Exercise 11
12 - Polynomials 1.pdf (p.659-711)
Chapter 12 Polynomials 1
Introduction
Extension: Definition of a Polynomial
Extension: Division of Polynomials
Extension: Remainder and Factor Theorems
Extension: Graph of Polynomial
Extension: Roots of Coefficients of Polynomial Equations
Test Yourself 12
Challenge Exercise 12
13 - Permutations and Combinations.pdf (p.712-744)
Chapter 13 Permutations and Combinations
Introduction
Extension: Fundamental Counting Principle
Extension: Permutations
Extension: Combinations
Test Yourself 13
Challenge Exercise 13
14 - Assessment 1.pdf (p.745-749)
Practice Assessment Task Set 1
15 - Assessment 2.pdf (p.750-753)
Practice Assessment Task Set 2
16 - Assessment 3.pdf (p.754-759)
Practice Assessment Task Set 3
17 - Assessment 4.pdf (p.760-766)
Practice Assessment Task Set 4
18 - Answers.pdf (p.767-861)
Answers
Chapter 1: Basic arithmetic
Chapter 2: Algebra and surds
Chapter 3: Equations
Chapter 4: Geometry 1
Practice assessment task set 1
Chapter 5: Functions and graphs
Chapter 6: Trigonometry
Chapter 7: Linear functions
Chapter 8: Introduction to calculus
Practice assessment task set 2
Chapter 9: Properties of the circle
Chapter 10: The quadratic function
Chapter 11: Locus and the parabola
Practice assessment task set 3
Chapter 12: Polynomials 1
Chapter 13: Permutations and combinations
Practice assessment task set 4