Outline

# Calculus I with Apex Calculus

- Author:
- Kevin Hopkins

- Topic:
- Calculus

A workbook created in Spring 2017 to use for Calculus I using Apex Calculus textbook. Most of the worksheets in this book also appear in other places.
Feel free to email me at khopkins@sbuniv.edu if you think there is an error in any worksheet (please be as specific as possible-a screenshot of the error would be most helpful). I tested them quite a bit, but there could be things that come up that I didn’t encounter in my testing.
I would also like to know if you used these and found them useful. If so, can you think of ways I could expand them?
Some are "self check" and others have you enter the answer and GeoGebra does the checking. I would encourage you to watch an introductory video (http://youtu.be/zzz42Y_qZJw) to get a feel for how the worksheets operate.

## Table of Contents

### Exam 1 Material-Review of Algebra and Limits

- Representing a Function in Four Ways-Section 1.1
- Tables as Functions: Solving and Evaluating-Section 1.1
- Graphs as Functions: Solving and Evaluating-Section 1.1
- Formulas as Functions: Solving and Evaluating-Section 1.1
- Basic Toolkit Functions-Section 1.1 with Trig Added
- Graphing Functions-Section 1.1
- Finding Domain and Range of Functions: Section 1.1
- Algebra of Function
- Shifts or Translations-Section 1.2
- Reflections-Section 1.2
- Stretch/Compression-Section 1.2
- Simpler Determining the Transformation-Section 1.2
- More Difficulty Determine Transformation-Section 1.2
- Slope of a Line Given Two points-Section 1.3
- Slope Intercept form from Table-Section 1.3
- What do m and b do to graph of a line-Section 1.3
- Line Equation-Section 1.3
- Equation of Line from points-Section 1.3
- Matching graph with line equation-Section 1.3
- Simplify Expressions with Exponents-Section 1.4
- Simplify Expressions with Exponents, More Difficult-Section 1.4
- Simplify Expressions, More Complicated-Section 1.4
- Shifted Form of Quadratic-Section 1.5
- Demonstration-Quadratics-Section 1.5
- Quadratics and Parabolas-Section 1.5
- Polynomial Inequalities-Section 1.6
- Graphs of the Exponential-Section 1.7
- Matching Exponential Equations-Section 1.7
- Compounding Periods-Section 1.7
- Logarithm to Exponential-Section 1.8
- Exponential to Logarithm-Section 1.8
- Solving Exponential Equations-Section 1.8
- Trig Review
- Section 1.1-Piecewise Defined Functions
- Section 1.1-Limits using numerical method
- Section 1.1-Functions with no limit at a point
- Section 1.1-Estimating Limits from Given Functions
- Section 1.1 and 1.3-Work with difference quotient
- Section 1.4-One-sided limits
- Section 1.5-The Intermediate Value Theorem

### Exam 2 Material-Section 1.6, 1.2, Chapter 2

- Section 1.6-Limit as x approaches infinity
- Section 1.6-Horizontal asymptotes
- Section 1.2-Precise definition of the limit
- Section 1.6-Precise definition of the limit as x approaches infinity
- Section 1.6-Precise definition of infinite limit
- Section 1.1, 4, and 2.1-Secant lines compared to tangent lines
- Section 2.1-Limits with Difference Quotients
- Section 2.1 in Apex-Sketching Graph of Derivative
- Section 2.3-2.5 from Apex-Derivative Practice
- Section 2.5-Chain Rule
- Section 2.6-Implicit Differentiation
- Section 2.6-Implicit Differentiation

### Exam 3 Material-Section 2.7-Section 4.4

- Section 2.7 in Apex-Inverse Functions
- Section 3.1 Apex-Absolute Extreme Values
- Section 3.2-Mean Value Theorem
- Section 3.3 Apex-Increasing versus Decreasing
- Section 3.4 Apex-Concavity
- Section 3.5-Curve Sketching
- Section 4.1 Apex-Newton's Method
- Section 4.2: Apex-Related Rates-Ladder Falling
- Section 4.2 Apex-Related Rates-Man Walking
- Section 4.2 Apex-Related Rates-Rotating Spotlight
- Section 4.2 Apex-Related Rates-Boat Pulling
- Section 4.3 Apex-Applied Max Min
- Section 4.4 Apex-Differential

### Exam 4 Material-Section 5.1-5.5, 6.1, 7.1-7.3

- Apex Section 5.1-Antiderivatives-Multiple Choice Problems
- Apex Section 5.1-Indefinite Integral
- Apex Section 5.2-Areas
- Apex Section 5.3-Riemann Sums
- Apex Section 5.3-Riemann Sums-Random Width Intervals
- Apex Section 5.4-Part 2 of Fundamental Theorem of Calculus
- Apex Section 5.4: Part 1 of Fundamental Theorem of Calculus
- Apex Section 5.5-Numerical integration
- Apex Section 6.1-Integration using substitution
- Apex Section 7.1-Areas
- Apex Section 7.2-Method of Disks
- Apex Section 7.2-Method of Washers
- Apex Section 5.3-Method of Shells