# Pre-Calculus

## MAT 103 - Pre-Calculus

Fahmil Shah

Summer 2019

MAT 103 OER

Level 1 – Adopt

This OER course using a new textbook is based on the section of MAT103 that I taught in Spring 2019. I will be teaching the course again in Fall 2019 and will adapt the assignments/readings presented here when I teach the course again. I am willing to share new versions of the materials that are created in the Fall as well.

### Course Description

Pre-Calculus is a preparatory course for Calculus. It builds upon the intermediate level of Algebra and makes intensive use of technology to conceptualize functions and methods of function manipulation with emphasis on quantitative change. Topics include a library of functions (linear, quadratic, exponential, logarithmic, polynomial, rational and trigonometric), transformations, compositions, inverses and combinations of functions and solving triangles. This course requires use of technology that is equal or better than TI83 graphing calculator.

### Instructional Objectives

(a) Demonstrate knowledge of the basic properties of functions in order to apply this knowledge to analyze and graph different types of functions;

(b) Use the built-in graphing capabilities of a graphing calculator in order to graph and analyze functions;

(c) Review and deepen understanding of linear functions;

(d) Perform operations on functions,

(e) Recognize and analyze polynomial functions;

(f) Use logarithmic and exponential functions to model real-world situations; and

(g) Demonstrate an understanding of the six trigonometric functions.

### Link to OER Textbook

*Precalculus *by Stitz & Zeager (http://www.stitz-zeager.com/szprecalculus07042013.pdf)

### Alignment of Open Textbook with Instructional Objectives

From above, the objectives for the course are:

(a) Demonstrate knowledge of the basic properties of functions in order to apply this knowledge to analyze and graph different types of functions;

(b) Use the built-in graphing capabilities of a graphing calculator in order to graph and analyze functions;

(c) Review and deepen understanding of linear functions;

(d) Perform operations on functions,

(e) Recognize and analyze polynomial functions;

(f) Use logarithmic and exponential functions to model real-world situations; and

(g) Demonstrate an understanding of the six trigonometric functions.

This course utilizes* *content from the following sections of *Precalculus*, and assignments have been created based on textbook problems using problems from the textbook. These assignments have been submitted in a summary document, as well as in **separate** word documents (as originally distributed). **The tentative timeline corresponds to a 13-week Autumn Access course.**

Chapter and Sections | Tentative Timeline | Corresponding Assignments from Spring 2019 |

Chapter 1 – Relations and Functions Sections 1.1 to 1.7 | Weeks 1-2 | Homework Assignments 1, 2, 3 Problem Sets 1, 2, 3, 4, 5 |

Chapter 2 – Linear and Quadratic Equations Sections 2.1 to 2.3 | Weeks 3-4 | Homework Assignments 4, 5 Problem Sets 6, 7, 8, 9 |

Chapter 3 – Polynomial Functions Sections 3.1 to 3.4 | Week 5 | Homework Assignment 6 Problem Sets 9, 10, 11, 12, 13, 14 |

Chapter 4 – Rational Functions Sections 4.1 and 4.2 | Weeks 6-7 | Homework Assignment 7 Problem Sets 15, 16 |

Chapter 5 – Further Topics in Functions Sections 5.5 and 5.2 | Week 8 | Homework Assignment 8 Problem Sets 17, 18 |

Chapter 6 – Exponential and Logarithmic Functions Sections 6.1 to 6.5 | Weeks 9-10 | Homework Assignment 9 Problem Set 20, 21 |

Chapter 7 – Hooked on Conics Section 7.1 | Week 11 | N/A |

Chapter 10 – Foundations of Trigonometry Sections 10.1 to 10.5 | Weeks 12-13 | N/A |

The table below presents the alignment between the course objectives and the *Precalculus *textbook.

Objective | Corresponding Precalculus Chapters |

Demonstrate knowledge of the basic properties of functions in order to apply this knowledge to analyze and graph different types of functions | Chapter 1 |

Use the built-in graphing capabilities of a graphing calculator in order to graph and analyze functions | Chapters 1, 2, 3, 4, 5, 6, 10 |

Review and deepen understanding of linear functions | Chapter 2 |

Perform operations on functions | Chapter 1, 5 |

Recognize and analyze polynomial functions | Chapter 3 |

Use logarithmic and exponential functions to model real-world situations | Chapter 6 |

Demonstrate an understanding of the six trigonometric functions | Chapter 10 |

### Corresponding Problem Sets and Homework Assignments from Precalculus

Included as word files. An overview document is also included, which has the assignments consolidated into a single document. Assignments may be modified in subsequent implementations of the course.

## Problem Sets

### Problem Set 1

Section 1.1 (pp. 14-15) - #1, 3, 7, 15, 20

### Problem Set 2

Section 1.1 (p. 16) - #23, 25

Section 1.2 (pp. 29-32) - #1, 7, 15, 21, 25, 27, 31, 33

### Problem Set 3

Section 1.3 (pp. 49-52) – 1, 3, 9, 11, 15, 17, 19, 39, 41

Section 1.4 (p. 63) – 3, 5, 7

### Problem Set 4

Section 1.4 (pp. 64-68) - #19, 21, 31, 63, 69

### Problem Set 5

Section 1.5 (pp. 84-85) - #1, 5, 15, 17, 25, 47

### Problem Set 6

Section 2.1 (pp. 163-168) – 13, 17, 33, 35, 45, 47

### Problem Set 7

Section 2.2 (p. 183) – 1, 5, 9, 15, 23, 27

### Problem Set 8

Section 2.3 (pp. 200-202) – 1, 7, 11, 17, 23

### Problem Set 9

Section 2.3 (p. 201) – 19, 21

Section 3.1 (p. 246) – 1, 3, 5, 7, 9

### Problem Set 10

Section 3.1 (pp. 246-247) – 9, 11, 15, 21, 29

### Problem Set 11

Section 3.1 (p. 246) – 13, 17, 19

Section 3.2 (p. 265) – 1, 5, 7, 9, 13

### Problem Set 12

Section 3.2 (p. 265) – 21, 23, 25

Section 3.3 (p. 280) – 15, 29, 25

### Problem Set 13

Section 3.4 (p. 296) – 35, 43, 47

### Problem Set 14

Section 3.4 (p. 296) – 35, 43, 47

### Problem Set 15

Section 4.1 (p. 314) – 1, 3, 5, 11, 17

### Problem Set 16

Section 4.2 (p. 333) #3, 7, 9, 11

### Problem Set 17

Section 5.1 (pp. 369-370) #3,7, 17, 21, 27, 35, 39, 41

### Problem Set 18

Section 5.2 (pp. 394) # 1, 3, 9, 11, 13, 17

### Problem Set 19

Section 6.1 (pp. 429-430) #1, 3, 7, 11, 13, 17, 19, 29, 59

### Problem Set 20

Section 6.2 (p. 445) #19, 25

Section 6.3 (p. 456) #1, 27

Section 6.4 (p. 466) #3, 19

### Problem Set 21

Section 6.5 (pp. 482-484) #1, 9, 21, 23, 31

## Homework

### Homework 1

Section 1.1 (pp. 14-16) - #2, 6, 12, 18, 22, 24

Section 1.2 (pp. 29-31) - #2, 10, 15, 22, 26, 32, 34

### Homework 2

Section 1.3 (pp. 49-52) - #2, 8, 14, 18, 20, 26, 30

Section 1.4 (pp. 64-68) - #20, 30, 38, 42, 58, 66

### Homework 3

Section 1.5 (pp. 84-86) - #4, 8, 18, 22, 24, 46

Section 1.6 (pp. 107-113) - #2, 16, 42, 48, 50, 52, 54, 56, 88, 90

### Homework 4

Section 2.1 (163-168) - #4, 14, 28, 44, 48, 56

### Homework 5

Section 2.2 (p.183) – 4, 12, 24, 28

Section 2.3 (pp. 200 – 201) – 2, 6, 14, 22

### Homework 6

Section 3.1 (p. 246) – 14, 24

Section 3.2 (pp. 265-266) – 2, 8, 16, 32, 38

Section 3.3 (p. 280) – 12, 14

Section 3.4 (p. 295) – 6, 14, 16, 28, 30

### Homework 7

Section 4.1 (p. 314) #2, 8, 12, 20

Section 4.2 (p. 333) #2, 6, 12

### Homework 8

Section 5.1 (pp. 369 – 370) #2, 12, 18, 24, 44, 48

Section 5.2 (p. 394) #2, 8, 18

### Homework 9

Section 6.1 (pp. 429-430) #44, 46, 50

Section 6.2 (pp. 445-446) #18, 26, 30

Section 6.3 (p. 456) #12, 22

Section 6.4 (p. 466) #8, 18

Section 6.5 (p. 482) #3, 4, 8, 10, 22

This work is licensed under a Creative Commons Attribution 4.0 International License.