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  5. Corequisite Support for College Algebra: Concepts through Functions


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For corequisite courses in College Algebra.

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Concepts through Functions, A Corequisite Solution encompasses full text content for College Algebra and the Corequisite Support course, classroom activities, study skills, and thoughtfully prebuilt, pre-assigned assignments to help students progress through the essential material. Instructors are given complete flexibility in implementation, no matter how their coreq course is set up.


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Table of contents

Study Skills for Mathematics

SS1 How Learning Math is Different

SS2 The Growth Mindset and Grit

SS3 Resources Available for Help

SS4 Time Management

SS5 How to Be An Effective Listener and How to Take Notes

SS6 How to Do Math Homework the Right Way

SS7 How to Read a Math Book

SS8 How to Study for a Math Exam

SS9 Overcoming Math and Test Anxiety

Elementary Algebra Review

R.1 Sets and Classifications of Numbers

  • Use set notation
  • Classify numbers
  • Approximate decimals by rounding or truncating
  • Plot points on the real number line
  • Use inequalities to order real numbers

R.2 Properties of Real Numbers

  • Compute the absolute value of a real number
  • Add and subtract signed numbers
  • Multiply and divide signed numbers
  • State the associative and distributive properties

R.3 Perform Operations on Rational Numbers

  • Write rational numbers written as fractions in lowest terms
  • Multiply and divide rational numbers written as fractions
  • Add or subtract rational numbers written as fractions

R.4 Order of Operations

  • Evaluate real numbers with exponents
  • Use the order of operations to evaluate expressions

R.5 Algebraic Expressions

  • Translate English expressions into mathematical language
  • Evaluate algebraic expressions
  • Simplify algebraic expressions by combining like terms
  • Determine the domain of a variable

R.6 Square Roots

  • Evaluate square roots of perfect squares
  • Determine whether a square root is rational, irrational, or not a real number
  • Find square roots of variable expressions
  • Use the product rule to simplify square roots

R.7 Geometry Essentials

  • Use the Pythagorean Theorem and Its Converse
  • Know Geometry Formulas
  • Understand Congruent Triangles and Similar Triangles

R.8  Laws of Exponents

  • Simplify Exponential Expressions Using the Product Rule
  • Simplify Exponential Expressions Using the Quotient Rule
  • Evaluate Exponential Expressions with a Zero or Negative Exponent
  • Simplify Exponential Expressions Using the Power Rule
  • Simplify Exponential Expressions Containing Products or Quotients
  • Simplify Exponential Expressions Using the Laws of Exponents

R.9 Adding and Subtracting Polynomials  

  • Define monomial and determine the coefficient and degree of a monomial
  • Define polynomial and determine the degree of a polynomial
  • Simplify polynomials by combining like terms

R.10 Multiplying Polynomials

  • Multiply a monomial by a polynomial
  • Multiply two binomials
  • Multiply two polynomials
  • Multiply special products

Preparing for Chapter F     

F.P1 Linear Equations in One Variable

  • Determine whether a number is a solution to an equation
  • Solve linear equations
  • Determine whether an equation is a conditional equation, an identity, or a contradiction
  • Solve for a variable in a formula

F.P2 Greatest Common Factor; Factoring by Grouping

  • Factor out the greatest common factor
  • Factor by grouping

F.P3 More Factoring

  • Factor trinomials of the form x2 + bx + c  
  • Factor perfect square trinomials
  • Factor the difference of two squares  

F.P4 Polynomial Equations

  • Solve polynomial equations using the zero-product property  
  • Solve quadratic equations using the square root property

F.P5 Solving Quadratic Equations by Completing the Square

  • Complete the square in one variable
  • Solve quadratic equations by completing the square

Chapter F.  Foundations: A Prelude to Functions

F.1 The Distance and Midpoint Formulas

  • Use the distance formula
  • Use the midpoint formula

F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry

  • Graph equations by plotting points
  • Find intercepts from a graph
  • Find intercepts from an equation
  • Test an equation for symmetry
  • Know how to graph key equations

F.3 Lines

F.4 Circles

Preparing for Chapter 1

1.P1 Linear Inequalities in One Variable

  • Represent inequalities using the real number line and interval notation
  • Understand the properties of inequalities
  • Solve linear inequalities
  • Solve problems involving linear inequalities

1.P2 nth Roots

  • Evaluate nth roots
  • Simplify expressions of the form   

1.P3 An Introduction to Problem Solving

  • Translate English sentences into mathematical statements
  • Model and solve direct translation problems
  • Model and solve mixture problems (optional)
  • Model and solve uniform motion problems
  • Use geometry formulas to solve problems

Chapter 1. Functions and Their Graphs

1.1 Functions

1.2 The Graph of a Function

1.3 Properties of Functions

1.4 Library of Functions; Piecewise-defined Functions

1.5 Graphing Techniques: Transformations

1.6 Mathematical Models: Building Functions

1.7 Building Mathematical Models Using Variation

Preparing for Chapter 2

2.P1 Factoring Trinomials Where the Leading Coefficient is Not One

Factor trinomials for the form ax2 + bx + c, a ≠ 1

2.P2 The Complex Number System  

  • Evaluate the square root of negative real numbers
  • Add or subtract complex numbers
  • Multiply complex numbers
  • Divide complex numbers
  • Evaluate the powers of i

Solve quadratic equations using the Square Root Property

2.P3 Solving Quadratic Equations by the Quadratic Formula

  • Solve quadratic equations using the quadratic formula
  • Use the discriminant to determine the nature of solutions of a quadratic equation

2.P4 Solving Equations Quadratic in Form

  • Solve equations that are quadratic in form

2.P5 Compound Inequalities  

  • Determine the intersection or union of two sets
  • Solve compound inequalities involving “and”
  • Solve compound inequalities involving “or”
  • Solve problems using compound inequalities

Chapter 2. Linear and Quadratic Functions

2.1 Properties of Linear Functions and Linear Models

2.2 Building Linear Models from Data

2.3 Quadratic Functions and Their Zeros

2.4 Properties of Quadratic Functions

2.5 Inequalities Involving Quadratic Functions

2.6 Building Quadratic Models from Verbal Descriptions and from Data

2.7 Complex Zeros of a Quadratic Function

2.8 Equations and Inequalities Involving the Absolute Value Function

Preparing for Chapter 3

3.P1 Factoring

  • Factoring trinomials using substitution
  • Factoring the sum and difference of two cubes

3.P2 Dividing Polynomials; Synthetic Division

  • Divide a polynomial by a monomial
  • Divide polynomials using long division
  • Divide polynomials using synthetic division

3.P3 Multiplying and Dividing Rational Expressions

  • Determine the domain of a rational expression
  • Simplify rational expressions
  • Multiply rational expressions
  • Divide rational expressions

3.P4 Adding and subtracting rational expressions

  • Add or subtract rational expressions with a common denominator
  • Find the least common denominator of two or more rational expressions
  • Add or subtract rational expressions with different denominators

3.P5 Complex Rational Expressions

  • Simplify a complex rational expression by simplifying the numerator and denominator separately (Method I)
  • Simplify a complex rational expression using the least common denominator (Method II)

3.P6 Rational Equations

  • Solve equations containing rational expressions
  • Solve equations involving rational functions

Chapter 3. Polynomial and Rational Functions

3.1 Polynomial Functions and Models

3.2 The Real Zeros of a Polynomial Function

3.3 Complex Zeros; Fundamental Theorem of Algebra

3.4 Properties of Rational Functions

3.5 The Graph of a Rational Function

3.6 Polynomial and Rational Inequalities

Preparing for Chapter 4

4.P1 Rational Exponents

  • Evaluate expressions of the form a1/n
  • Evaluate expressions of the form am/n

4.P2 Simplifying Expressions Using the Laws of Exponents

  • Simplify expressions involving rational exponents
  • Simplify radical expressions
  • Factor expressions containing rational exponents

4.P3 Simplifying Radical Expressions Using Properties of Radicals

  • Use the product property to multiply radical expressions
  • Use the product property to simplify radical expressions
  • Use the quotient property to simplify radical expressions

4.P4 Adding, Subtracting, and Multiplying Radical Expressions

  • Add or subtract radical expressions
  • Multiply radical expressions

4.P5 Rationalizing Radical Expressions

  • Rationalize a denominator containing one term
  • Rationalize a denominator containing two terms

Chapter 4. Exponential and Logarithmic Functions

4.1 Composite Functions 

4.2 One­to­One Functions; Inverse Functions 

4.3 Exponential Functions 

4.4 Logarithmic Functions 

4.5 Properties of Logarithms 

4.6 Logarithmic and Exponential Equations 

4.7 Compound Interest 

4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay 

4.9 Building Exponential, Logarithmic, and Logistic Functions from Data

Chapter 5. Conics

 5.1 Conics

 5.2 The Parabola 

5.3 The Ellipse

 5.4 The Hyperbola

Chapter 6. Systems of Equations and Inequalities

6.1 Systems of Linear Equations: Substitution and Elimination 

6.2 Systems of Linear Equations: Matrices 

6.3 Systems of Linear Equations: Determinants 

6.4 Matrix Algebra 

6.5 Partial Fraction Decomposition 

6.6 Systems of Nonlinear Equations 

6.7 Systems of Inequalities 

6.8 Linear Programming

Chapter 7. Sequences; Induction; the Binomial Theorem

7.1 Sequences 

7.2 Arithmetic Sequences 

7.3 Geometric Sequences; Geometric Series 

7.4 Mathematical Induction 

7.5 The Binomial Theorem

Chapter 8. Counting and Probability

8.1 Counting

8.2 Permutations and Combinations

8.3 Probability

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