College Algebra-All Units

Kevin Hopkins, David Wright, Jul 10, 2015

All Units of College Algebra included in one location. The book these worksheets were written for is the 5th edition of Kime/Clark's Explorations in College Algebra ([url]http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP001849.html[/url]) . I began developing these in Spring 2012 to use in College Algebra, mainly to give students some additional practice with some of the material. They have been added to and refined some since that time. The videos given were found on a VERY quick search of Khan Academy. Use them to assist you if you need a refresher on the topic the worksheet is covering.

Table of Contents

  1. Unit 1-Sections 1.1-2.10
    1. Gradebook Scenerios
    2. Finding the Median and Mean-Section 1.1
    3. Function Table-Section 1.3
    4. Function Graphs-Section 1.3
    5. Function Rule-Section 1.3
    6. Increasing Functions-Section 1.5
    7. Concavity-Section 1.5
    8. Slope-Section 2.3
    9. Slope Intercept form from Table-Section 2.5
    10. Slope Intercept Form-Section 2.5
    11. Line Equation-Section 2.5
    12. Equation of Line-Section 2.5-2.8
    13. Perpendicular and Parallel Lines-Section 2.7-2.8
    14. Line Match-Sections 2.5-2.8
  2. Unit 2-Sections 3.1-4.5
    1. Solving a system of equations-Section 3.1-3.2 in College Alg
    2. Inequalities-Section 3.3
    3. Scientific Notation-Section 4.1
    4. Absolute Value-Section 4.1
    5. Simplify Expressions with Exponents-Section 4.2
    6. Simplify Expressions with Exponents, More Diffic-Section 4.2
    7. Simplify Expressions, More Complicated-Section 4.2-4.3
    8. Fractional Exponents-Section 4.3
    9. Square Roots-Section 4.3
  3. Unit 3-Sections 4.6, 5.1-6.3
    1. Exponential from Two Points-Sections 5.1, 2, 4
    2. Exponential Equations-Sections 5.1, 2, 4
    3. Exponential Equations Matching-Sections 5.1-5.4
    4. Exponential vs Linear from Table-Section 5.3
    5. Exponential vs Linear-Section 5.3
    6. Demonstration-Section 5.4
    7. Exponential Growth/Decay Rate-Section 5.5
    8. Demonstration-Section 5.6
    9. Demonstration-Section 5.7
    10. Compound Interest-Section 5.7
    11. Exponential to Logarithm-Section 4.6 & 6.1
    12. Logarithm to Exponential-Section 4.6 & 6.1
    13. Simple Logarithms-Section 6.1
    14. Solving Logarithm Equations-Section 6.1
    15. Exponential Equations-Section 6.1
    16. Expanding Natural Logarithms-Section 6.2
    17. Contract Natural Logarithms-Section 6.2
  4. Unit 4-Sections 7.1-9.5
    1. Section 7.1-Power Functions-Area
    2. Section 7.1-Volume as a Power Function
    3. Section 7.1-Applying Power Functions.
    4. Section 7.3-Power Function Demonstration-Positive Even Power
    5. Section 7.3-Power Function Demonstration-Positive Odd Powers
    6. Section 7.3-Power Function Demonstration-Positive Powers
    7. Section 7.4-Power vs Exponential Function Demonstration
    8. Section 7.6-Power Function Demonstration-Negative Even Power
    9. Section 7.6-Power Function Demonstration-Negative Odd Powers
    10. Section 7.6-Power Function Demonstration-Negative Powers
    11. Sections 7.3-7.6: Graphs of Power Functions
    12. Section 7.3-7.6: Matching graphs of Power Functions
    13. Section 7.6-All function types together to identify.
    14. Section 8.1-Demonstration-Quadratics
    15. Section 8.1, 3, 4-Quadratics and Parabolas
    16. Section 8.4-Addition of Complex Numbers
    17. Section 8.4-Multiplication of Complex Numbers
    18. Section 8.4-Division of Complex Numbers
    19. Section 9.1-Demonstration: Translations
    20. Section 9.1-Demonstration: Reflections
    21. Section 9.1-Demonstration: Stretches
    22. Section 9.1-2: Function Transformation
    23. Section 9.1-2: More Difficult Function Transformation
    24. Section 9.1-9.5: Combining Functions
    25. Section 9.5-Inverses
    26. Section 9.5-Finding Inverse
  5. Multiple Choice Questions for Review
    1. MC-Section 6.1-Log Form vs Exp. Form
    2. MC-Section 6.1 & 6.2-Expanding Logarithmic Expressions
    3. MC-Section 6.1 & 6.2-Contracting Logarithmic Expressions
    4. MC-Section 5.7-Compound Interest

1.

Unit 1-Sections 1.1-2.10

  • 1. Gradebook Scenerios
  • 2. Finding the Median and Mean-Section 1.1
  • 3. Function Table-Section 1.3
  • 4. Function Graphs-Section 1.3
  • 5. Function Rule-Section 1.3
  • 6. Increasing Functions-Section 1.5
  • 7. Concavity-Section 1.5
  • 8. Slope-Section 2.3
  • 9. Slope Intercept form from Table-Section 2.5
  • 10. Slope Intercept Form-Section 2.5
  • 11. Line Equation-Section 2.5
  • 12. Equation of Line-Section 2.5-2.8
  • 13. Perpendicular and Parallel Lines-Section 2.7-2.8
  • 14. Line Match-Sections 2.5-2.8

1.1.

Gradebook Scenerios

This is an illustration I use the first day of class to show the importance of participation and homework for the overall course grade in the course.
Gradebook Scenerios
– Kevin Hopkins

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

1.13.

–

1.14.

–

2.

Unit 2-Sections 3.1-4.5

  • 1. Solving a system of equations-Section 3.1-3.2 in College Alg
  • 2. Inequalities-Section 3.3
  • 3. Scientific Notation-Section 4.1
  • 4. Absolute Value-Section 4.1
  • 5. Simplify Expressions with Exponents-Section 4.2
  • 6. Simplify Expressions with Exponents, More Diffic-Section 4.2
  • 7. Simplify Expressions, More Complicated-Section 4.2-4.3
  • 8. Fractional Exponents-Section 4.3
  • 9. Square Roots-Section 4.3

2.1.

Solving a system of equations-Section 3.1-3.2 in College Alg

Solving a system of equations.[br][br]For video on this topic see[br][url]https://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/fast-systems-of-equations/v/solving-linear-systems-by-substitution[/url][br]or [url]http://patrickjmt.com/solving-a-linear-system-of-equations-by-graphing/[/url][br]or [url]http://patrickjmt.com/solving-a-linear-system-of-equations-using-substitution/[/url][br]or[url] http://patrickjmt.com/solving-a-linear-system-of-equations-using-elimination-by-addition/[/url]
– Kevin Hopkins

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

3.

Unit 3-Sections 4.6, 5.1-6.3

  • 1. Exponential from Two Points-Sections 5.1, 2, 4
  • 2. Exponential Equations-Sections 5.1, 2, 4
  • 3. Exponential Equations Matching-Sections 5.1-5.4
  • 4. Exponential vs Linear from Table-Section 5.3
  • 5. Exponential vs Linear-Section 5.3
  • 6. Demonstration-Section 5.4
  • 7. Exponential Growth/Decay Rate-Section 5.5
  • 8. Demonstration-Section 5.6
  • 9. Demonstration-Section 5.7
  • 10. Compound Interest-Section 5.7
  • 11. Exponential to Logarithm-Section 4.6 & 6.1
  • 12. Logarithm to Exponential-Section 4.6 & 6.1
  • 13. Simple Logarithms-Section 6.1
  • 14. Solving Logarithm Equations-Section 6.1
  • 15. Exponential Equations-Section 6.1
  • 16. Expanding Natural Logarithms-Section 6.2
  • 17. Contract Natural Logarithms-Section 6.2

3.1.

Exponential from Two Points-Sections 5.1, 2, 4

Given two points, find C and a for exponential equation.[br][br]For video explanation, see[br][url]https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/exp_growth_decay/v/constructing-linear-and-exponential-functions-from-graph[/url][br]or [br][url]http://patrickjmt.com/finding-the-equation-of-an-exponential-function/[/url]
Exponential from Two Points-Sections 5.1, 2, 4
– Kevin Hopkins

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

3.9.

–

3.10.

–

3.11.

–

3.12.

–

3.13.

–

3.14.

–

3.15.

–

3.16.

–

3.17.

–

4.

Unit 4-Sections 7.1-9.5

  • 1. Section 7.1-Power Functions-Area
  • 2. Section 7.1-Volume as a Power Function
  • 3. Section 7.1-Applying Power Functions.
  • 4. Section 7.3-Power Function Demonstration-Positive Even Power
  • 5. Section 7.3-Power Function Demonstration-Positive Odd Powers
  • 6. Section 7.3-Power Function Demonstration-Positive Powers
  • 7. Section 7.4-Power vs Exponential Function Demonstration
  • 8. Section 7.6-Power Function Demonstration-Negative Even Power
  • 9. Section 7.6-Power Function Demonstration-Negative Odd Powers
  • 10. Section 7.6-Power Function Demonstration-Negative Powers
  • 11. Sections 7.3-7.6: Graphs of Power Functions
  • 12. Section 7.3-7.6: Matching graphs of Power Functions
  • 13. Section 7.6-All function types together to identify.
  • 14. Section 8.1-Demonstration-Quadratics
  • 15. Section 8.1, 3, 4-Quadratics and Parabolas
  • 16. Section 8.4-Addition of Complex Numbers
  • 17. Section 8.4-Multiplication of Complex Numbers
  • 18. Section 8.4-Division of Complex Numbers
  • 19. Section 9.1-Demonstration: Translations
  • 20. Section 9.1-Demonstration: Reflections
  • 21. Section 9.1-Demonstration: Stretches
  • 22. Section 9.1-2: Function Transformation
  • 23. Section 9.1-2: More Difficult Function Transformation
  • 24. Section 9.1-9.5: Combining Functions
  • 25. Section 9.5-Inverses
  • 26. Section 9.5-Finding Inverse

4.1.

Section 7.1-Power Functions-Area

What does changing dimension do to area?
Section 7.1-Power Functions-Area
– Kevin Hopkins

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

4.8.

–

4.9.

–

4.10.

–

4.11.

–

4.12.

–

4.13.

–

4.14.

–

4.15.

–

4.16.

–

4.17.

–

4.18.

–

4.19.

–

4.20.

–

4.21.

–

4.22.

–

4.23.

–

4.24.

–

4.25.

–

4.26.

–

5.

Multiple Choice Questions for Review

Here are multiple choice questions to review topics. I have tried to help you realize that there are various forms for much of what we have been studying. Sometimes I have you pick the one form that is NOT equivalent to the other forms. Other questions are more typical multiple choice where you select the correct answer out of a variety of options.

  • 1. MC-Section 6.1-Log Form vs Exp. Form
  • 2. MC-Section 6.1 & 6.2-Expanding Logarithmic Expressions
  • 3. MC-Section 6.1 & 6.2-Contracting Logarithmic Expressions
  • 4. MC-Section 5.7-Compound Interest

5.1.

MC-Section 6.1-Log Form vs Exp. Form

Multiple choice where only one form is NOT equivalent to the others. Select which form is not equivalent to the rest.
MC-Section 6.1-Log Form vs Exp. Form
– Kevin Hopkins

5.2.

–

5.3.

–

5.4.

–

Information