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Intermediate Algebra

Key Terms

Intermediate AlgebraKey Terms
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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Key Terms

absolute value
The absolute value of a number is its distance from 00 on the number line.
additive identity
The number 0 is the additive identity because adding 0 to any number does not change its value.
additive inverse
The opposite of a number is its additive inverse.
coefficient
The coefficient of a term is the constant that multiplies the variable in a term.
complex fraction
A fraction in which the numerator or the denominator is a fraction is called a complex fraction.
composite number
A composite number is a counting number that is not prime. It has factors other than 1 and the number itself.
constant
A constant is a number whose value always stays the same.
denominator
In a fraction, written ab,ab, where b≠0,b≠0, the denominator b is the number of equal parts the whole has been divided into.
divisible by a number
If a number m is a multiple of n, then m is divisible by n.
equation
An equation is two expressions connected by an equal sign.
equivalent fractions
Equivalent fractions are fractions that have the same value.
evaluate an expression
To evaluate an expression means to find the value of the expression when the variables are replaced by a given number.
expression
An expression is a number, a variable, or a combination of numbers and variables using operation symbols.
factors
If a·b=m,a·b=m, then a and b are factors of m.
fraction
A fraction is written ab,ab, where b≠0,b≠0, and a is the numerator and b is the denominator. A fraction represents parts of a whole.
integers
The whole numbers and their opposites are called the integers.
irrational number
An irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.
least common denominator
The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.
least common multiple
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.
like terms
Terms that are either constants or have the same variables raised to the same powers are called like terms.
multiple of a number
A number is a multiple of n if it is the product of a counting number and n.
multiplicative identity
The number 1 is the multiplicative identity because multiplying 1 by any number does not change its value.
multiplicative inverse
The reciprocal of a number is its multiplicative inverse.
negative numbers
Numbers less than 00 are negative numbers.
numerator
In a fraction, written ab,ab, where b≠0,b≠0, the numerator a indicates how many parts are included.
opposite
The opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.
order of operations
The order of operations are established guidelines for simplifying an expression.
percent
A percent is a ratio whose denominator is 100.
prime factorization
The prime factorization of a number is the product of prime numbers that equals the number.
prime number
A prime number is a counting number greater than 1 whose only factors are 1 and the number itself.
principal square root
The positive square root is called the principal square root.
rational number
A rational number is a number of the form pq,pq, where p and q are integers and q≠0.q≠0. Its decimal form stops or repeats.
real number
A real number is a number that is either rational or irrational.
reciprocal
The reciprocal of a fraction is found by inverting the fraction, placing the numerator in the denominator and the denominator in the numerator.
simplify an expression
To simplify an expression means to do all the math possible.
square of a number
If n2=m,n2=m, then m is the square of n.
square root of a number
If n2=m,n2=m, then n is a square root of m.
term
A term is a constant, or the product of a constant and one or more variables.
variable
A variable is a letter that represents a number whose value may change.
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