Overview
Main description
Building a Better Path To Success!
Connecting Knowledge – Sherri prepares her students for success by refreshing their knowledge of arithmetic. By helping students see the connection between arithmetic and algebra, Sherri found that her students were more confident in their abilities as they progressed through the course. This classroom tested practice was integrated into the texts so that both instructors and students could benefit. Messersmith accomplishes this by including arithmetic examples for most sections before the use of algebraic examples. Also, the author has developed through classroom use a series of Basic Skills Worksheets that can easily be integrated into the classroom.
Presenting Concepts in “Bite Size” Pieces – By breaking down the sections into manageable pieces, the author has identified the core places where students traditionally struggle and then assists them in understanding that material to be successful moving forward.
Mastering Concepts - With the textbook and Connect Mathematics hosted by ALEKS, a new online homework and assessment tool, students can practice and master their understanding of algebraic concepts.
Messersmith is rigorous enough to prepare students for the next level yet easy to read and understand. The exposition is written as if a professor is teaching in a lecture to be more accessible to students. The language is mathematically sound yet easy enough for students to understand.
Table of contents
Chapter 1: Real Numbers and Basic Geometry Concepts1.1 Sets of Numbers1.2 Operations on Real Numbers1.3 Algebraic Expressions and Properties of Real Numbers
Chapter 2: Linear Equations and Inequalities in One Variable2.1 Solving Linear Equations in One Variable2.2 Applications of Linear Equations2.3 Geometry Applications and Solving Formulas2.4 More Applications of Linear Equations2.5 Linear Inequalities in One Variable2.6 Compound Inequalities in One Variable2.7 Absolute Value Equations and Inequalities
Chapter 3: Linear Equations in Two Variables and Functions3.1 Introduction to Linear Equations in Two Variables3.2 Slope of a Line and Slope-Intercept Form3.3 Writing an Equation of a Line3.4 Linear and Compound Linear Inequalities in Two Variables3.5 Introduction to Functions
Chapter 4: Solving Systems of Linear Equations4.1 Solving Systems of Linear Equations in Two Variables4.2 Solving Systems of Linear Equations in Three Variables4.3 Applications of Systems of Linear Equations4.4 Solving Systems of Linear Equations Using Matrices
Chapter 5: Polynomials and Polynomial Functions5.1 The Rules of Exponents5.2 More on Exponents and Scientific Notation5.3 Addition and Subtraction of Polynomials and Polynomial Functions5.4 Multiplication of Polynomials and Polynomial Functions5.5 Division of Polynomials and Polynomial Functions
Chapter 6: Factoring Polynomials6.1 The Greatest Common Factor and Factoring by Grouping6.2 Factoring Trinomials6.3 Special Factoring TechniquesPutting It All Together6.4 Solving Quadratic Equations by Factoring6.5 Applications of Quadratic Equations
Chapter 7: Rational Expressions, Equations, and Functions7.1 Simplifying, Multiplying, and Dividing Rational Expressions and Functions7.2 Adding and Subtracting Rational Expressions7.3 Simplifying Complex Fractions7.4 Solving Rational EquationsPutting It All Together7.5 Applications of Rational Equations7.6 Variation
Chapter 8: Radicals and Rational Exponents8.1 Radical Expressions and Functions8.2 Rational Exponents8.3 Simplifying Expressions Containing Square Roots8.4 Simplifying Expressions Containing Higher Roots8.5 Adding, Subtracting, and Multiplying Radicals8.6 Dividing RadicalsPutting It All Together8.7 Solving Radical Equations8.8 Complex Numbers
Chapter 9: Quadratic Equations and Functions9.1 The Square Root Property and Completing the Square
9.2 The Quadratic FormulaPutting It All Together9.3 Equations in Quadratic Form9.4 Formulas and Applications9.5 Quadratic Functions and Their Graphs9.6 Applications of Quadratic Functions and Graphing Other Parabolas9.7 Quadratic and Rational Inequalities
Chapter 10: Exponential, and Logarithmic Functions 10.1 Composite and Inverse Functions10.2 Exponential Functions10.3 Logarithmic Functions10.4 Properties of Logarithms10.5 Common and Natural Logarithms and Change of Base10.6 Solving Exponential and Logarithmic Equation
Chapter 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems11.1 Graphs of Other Useful Functions11.2 The Distance Formula, Midpoint, and Circle 11.3 The Ellipse11.4 The HyperbolaPutting It All Together11.5 Nonlinear Systems of Equations11.6 Second-Degree Inequalities and Systems of Inequalities
Chapter 12: Sequences and Series (Online Only) 12.1 Sequences and Series12.2 Arithmetic Sequences and Series12.3 Geometric Sequences and Series12.4 The Binomial Theorem
A AppendixA.1 Geometry ReviewA.2 Determinants and Cramer’s RuleA.3 Graphing Polynomial FunctionsA.4 Synthetic Division and the Remainder Theorem
