# Algebraic Reasoning and Modeling

- Author:
- Kevin Hopkins

- Topic:
- Algebra

All Units of Algebraic Reasoning and Modeling (formerly 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 (http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP001849.html) .
I (Dr. Hopkins) 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

### Unit 1-Sections 1.1-2.10

- Gradebook Scenerios
- Finding the Median and Mean-Section 1.1
- Finding the Mean of Grouped Data-Section 1.1
- Function Table-Section 1.3
- Function Graphs-Section 1.3
- Function Rule-Section 1.3
- Increasing Functions-Section 1.5
- Concavity-Section 1.5
- Slope-Section 2.3
- Slope Intercept form from Table-Section 2.5
- Slope Intercept Form-Section 2.5
- Line Equation-Section 2.5
- Equation of Line-Section 2.5-2.8
- Perpendicular and Parallel Lines-Section 2.7-2.8
- Line Match-Sections 2.5-2.8

### Unit 2-Sections 3.1-4.5

- Solving a system of equations-Section 3.1-3.2 in College Alg
- Inequalities-Section 3.3
- Scientific Notation-Section 4.1
- Absolute Value-Section 4.1
- Simplify Expressions with Exponents-Section 4.2
- Simplify Expressions with Exponents, More Diffic-Section 4.2
- Simplify Expressions, More Complicated-Section 4.2-4.3
- Fractional Exponents-Section 4.3
- Square Roots-Section 4.3

### Unit 3-Sections 4.6, 5.1-6.3

- Exponential from Two Points-Sections 5.1, 2, 4
- Exponential Equations-Sections 5.1, 2, 4
- Exponential Equations Matching-Sections 5.1-5.4
- Exponential vs Linear from Table-Section 5.3
- Exponential vs Linear-Section 5.3
- Demonstration-Section 5.4
- Exponential Growth/Decay Rate-Section 5.5
- Demonstration-Section 5.6
- Demonstration-Section 5.7
- Compound Interest-Section 5.7
- Exponential to Logarithm-Section 4.6 & 6.1
- Logarithm to Exponential-Section 4.6 & 6.1
- Simple Logarithms-Section 6.1
- Solving Logarithm Equations-Section 6.1
- Exponential Equations-Section 6.1
- Expanding Natural Logarithms-Section 6.2
- Contract Natural Logarithms-Section 6.2

### Unit 4-Sections 7.1-9.5

- Section 7.1-Power Functions-Area
- Section 7.1-Volume as a Power Function
- Section 7.1-Applying Power Functions.
- Section 7.3-Power Function Demonstration-Positive Even Power
- Section 7.3-Power Function Demonstration-Positive Odd Powers
- Section 7.3-Power Function Demonstration-Positive Powers
- Section 7.4-Power vs Exponential Function Demonstration
- Section 7.6-Power Function Demonstration-Negative Even Power
- Section 7.6-Power Function Demonstration-Negative Odd Powers
- Section 7.6-Power Function Demonstration-Negative Powers
- Sections 7.3-7.6: Graphs of Power Functions
- Section 7.3-7.6: Matching graphs of Power Functions
- Section 7.6-All function types together to identify.
- Section 8.1-Demonstration-Quadratics
- Section 8.1, 3, 4-Quadratics and Parabolas
- Section 8.4-Addition of Complex Numbers
- Section 8.4-Multiplication of Complex Numbers
- Section 8.4-Division of Complex Numbers
- Section 9.1-Demonstration: Translations
- Section 9.1-Demonstration: Reflections
- Section 9.1-Demonstration: Stretches
- Section 9.1-2: Function Transformation
- Section 9.1-2: More Difficult Function Transformation
- Section 9.1-9.5: Combining Functions
- Section 9.5-Inverses
- Section 9.5-Finding Inverse

### Multiple Choice Questions for Review