Ontario High School Algebra by J. T. Crawford, B.A. is a comprehensive guide to the subject of Algebra for high school students in Ontario. This book provides a thorough understanding of the fundamental concepts and principles of Algebra, making it an essential resource for students looking to excel in this subject. The book covers all the important topics in Algebra, including functions, relations, systems of linear equations, quadratic functions, exponential and logarithmic functions, and more.
One of the key strengths of this book is its clear and concise explanations of complex mathematical concepts. The author has done an excellent job of breaking down each topic into manageable sections, making it easier for students to grasp the material. Additionally, the book is filled with numerous examples and practice problems, which help students to reinforce their understanding of the concepts covered.
Another advantage of this book is its focus on problem-solving. The author provides students with a step-by-step approach to solving algebraic equations, helping them to develop the skills and confidence they need to tackle even the most challenging problems. The book also includes a comprehensive set of review questions and problems, which allow students to test their understanding of the material and identify areas where they may need additional practice.
TABLE OF CONTENTS
CHAPTER I Algebraic Notation
- Arithmetical and Algebraic Signs and Symbols
- Fundamental Laws
- Factor and Pro- duct
- Power and Index
- Coefficient
- Addition and Subtraction of like Terms
- Use of Brackets
CHAPTER II Simple Equations
- Meaning of Equation, Solving an Equation, Root of an Equation
- Axioms used
- Verifying Results
- Problems solved by Equations
CHAPTER III Positive and Negative Numbers
- Graphical Representation of Positive and Negative Numbers
- Concrete Examples of Negative Numbers
- Signs of Operation and Signs of Quahty
- Absolute Value
CHAPTER IV Addition and Subtraction 36
- Addition of Quantities with like Signs
- Compound Addition
- Addition with unlike Signs
- Indicated Additions
- Subtraction the Inverse of Addition
- Rule for Subtraction
- Removal of Brackets
CHAPTER V Multiplication and Division
- Multiplication of Simple Positive Quantities
- Index Law for Multiplication
- Rule of Signs
- Compound Multiplication
- Verifications
- Division by a Simple Quantity
- Index Law for Division
CHAPTER VI Simple Equations {continued)
- Equation and Identity
- Transposing Terms
- Simple Fractional Equations
- Steps in the Solution of an Equation
- Algebraic statements of Arithmetical Theorems
CHAPTER VII Simultaneous Equations
- Equations with two Unknowns
- Method of Solution
- Ehmination
- Fractional Simultaneous Equations
CHAPTER VIII Type Products and Simple Factoring
- Monomial Factors
- Product of two Binomials
- Factors of Trinomials
- Radical Sign
- Square of a Binomial
- Square Root of a Trinomial
- Difference of two Squares
- Numerical Applications
CHAPTER IX Simple Applications of Factoring
- Highest Common Factor
- Algebraic Fractions
- Lowest Terms
- Multiplication and Division of Fractions
- Lowest Common Multiple
- Addition and Subtraction of Fractions
- Mixed Expressions
CHAPTER X Review of the Simple Rules
- Brackets
- Collecting Coefficients
- Multiplication with Detached Coefficients
- Division by a Compound Quantity
- Verifying Division
- Inexact Division
CHAPTER XI Factoring (continued) 128
- Factors by Grouping
- Complete Squares
- DifEerence of Squares
- Incomplete Squares
- Trinomials
- Sum. and Difference of Cubes
- The Factor Theorem
- Easy Quadratic Equations
CHAPTER XII Simultaneous Equations {continued)
- Elimination by Substitution and by Comparison
- Equations with three Unknowns
- Special Forms of Equations
CHAPTER XII Geometrical Representation of Number
- Function of x
- Variables and Constants
- Arithmetical Graphs
- The Axes
- Graph of an Equation
- Coordinates
- Plotting Points
- Linear Equation
- Graphical Solution of Simultaneous Equations
- Special Forms of Equations
CHAPTER XIV Highest Common Factor and Lowest Common Multiple
- By Factoring
- By Elimination
- Product of the H.C.F. and L.C.M
CHAPTER XV Fractions
- Changes in the Form of a Fraction
- Lowest Terms
- Addition and Subtraction
- Special Types
- Cyclic Order
- Multiplication and Division
- Complex Fractions
CHAPTER XVI Fractional Equations
- Cross Multiplication
- Special Forms of Fractional Equations
- Literal Equations with one Unknown
CHAPTER XVII PAGE Extraction of Roots 216
- Square Root by Inspection
- by the Formal Method
- Verifying Results
- Cube of a Binomial
- Cube Root
- Higher Roots
CHAPTER XVIII Quadratic Surds
- Surd and Rational Quantities
- Mixed and Entire Surds
- Like Surds
- Addition and Subtraction
- Square Root Table
- Conjugate Surds
- Rationalizing a De-nominator
- Surd Equations
CHAPTER XIX Quadratic Equations
- Standard Form
- Solution by Factoring
- By Completing the Square
- Irrational Roots
- Inadmissible Solutions
CHAPTER XX Ratio and Proportion
- Methods of Comparing Magnitudes
- Comparison of Ratios
- Proportion
- Finding a Ratio by Solving an Equation
- Mean Proportional
- Ratio Theorems
CHAPTER XXT The General Quadratic Equation 268
- Solution of Literal Quadratics
- Solution by Formula
- Imaginary Roots
- Equations Solved like Quadratics
CHAPTER XXII Simultaneous Quadratics
- Three Types of Simultaneous Quadratics
- Special Methods
- Graphical Solutions
CHAPTER XXIII Indices
- The Index Laws
- Fractional, Zero and Negative Indices
- Operations with Fractional and Negative Indices
- Contracted Methods
CHAPTER XXIV Surds and Surd Equations
- Surds of different Orders
- Varying Forms of Surds
- Surd Equations
- Extraneous Roots
- Square Root of a Binomial Surd
- Imaginary Surds
- Impossible Problems
CHAPTER XXV Theory of Quadratic Equations
- Sum and Product of the Roots
- Reciprocal Roots
- Functions of the Roots
- Character of the Roots
- The Discriminant
- Factors of the Quadratic Expression
CHAPTER XXVI Supplementary Chapter
- Factors of the Product of two Trinomials
- Sum and Difference of Cubes
- Factors by Grouping
- The Factor Theorem
- Symmetry
- Factoring by Symmetry
Download Now Book in PDF
In addition to its clear explanations and focus on problem-solving, this book is also designed to be user-friendly. The layout is clear and easy to follow, making it simple for students to find the information they need. The book also includes numerous illustrations and graphs, which help to visually reinforce the concepts being covered.
For students who are looking to download the book in PDF format, it is readily available online. This makes it easy for students to access the material wherever they are, whether at home, at school, or on the go. Additionally, the PDF format makes it simple for students to take notes and highlight important sections, helping them to study more effectively.
In conclusion, Ontario High School Algebra by J. T. Crawford, B.A. is an excellent resource for high school students looking to excel in this subject. With its clear explanations, focus on problem-solving, and user-friendly design, this book is a must-have for any student studying Algebra in Ontario. So, what are you waiting for? Download the PDF version of this book today and start your journey towards a deeper understanding of Algebra.
