# Math 170 Calculus I

## Class Resources and Handouts

Algebra Review WorksheetAlgebra Review Worksheet Solutions

Course Syllabus (pdf)

Exam I Review Sheet

Exam II Review Sheet

Exam III Review Sheet

Exam IV Review Sheet

Final Exam Review

Final Exam Review

**Solutions**

### Course Information

Meeting Times: Monday, Tuesday, Wednesday, and Friday, 8:00 - 8:50 am

Location: Hirt 209

Office Hours: Monday 9-10, Tuesday 12:30-1:30, Wednesday 1-3, Thursday 8-9, Friday 1-2

Prerequisite: Minimum math placement score of 76 (freshmen and sophomores only)

Location: Hirt 209

Office Hours: Monday 9-10, Tuesday 12:30-1:30, Wednesday 1-3, Thursday 8-9, Friday 1-2

Prerequisite: Minimum math placement score of 76 (freshmen and sophomores only)

### Course Description

This is the initial course in a sequence of courses on the fundamental ideas of the calculus of one variable. It is here that truly significant applications of mathematics begin. Topics included are functions, continuity, limits, derivatives, maxima and minima and antiderivatives.

### Objectives

On successful completion of the course, students will be able to:

- recognize, define, and apply properties of functions, such as their domain and range, intercepts, and inverses.
- have an intuitive understanding of a limit, and be able to evaluate a variety of limits.
- identify discontinuities of a function presented either graphically or algebraically.
- find the derivative of functions using the limit definition.
- find the derivative of sums, products, and quotients of composite polynomial, trigonometric, exponential, and logarithmic functions.
- understand conceptual relationships between derivatives, rates of change, and tangent lines.
- use properties of functions and derivatives to graph polynomials and rational functions.
- apply differentiation procedures to solve related rates and extreme value problems.
- identify and evaluate limits involving indeterminate forms.
- compute definite and indefinite integrals using formulas and substitution.
- understand the relationship between the integral and the derivative.
- read and interpret mathematical theorems, including checking that hypotheses are satisfied and reaching correct conclusions.

### Prerequisites

To remain enrolled in this course, you must satisfy at least one of the following criteria:

- Began studying at Mercyhurst prior to Fall 2016
- Scored of 76 or better on the ALEKS Mathematics Placement Assessment
- Passed Math 118 (Math for the Natural Sciences), or transfer credit for equivalent
- Passed both Math 111 (College Algebra) and Math 112 (Trigonometry and Functions), or transfer credit for equivalent

### Required Materials

##### Textbook

*Calculus, Early Transcendentals*by Anton, Bivens, and Davis, 10th Edition. We will be covering chapters 0-5 in the textbook. No other supplies are required for the course. You will not be expected to bring your textbook to class. If you prefer to purchase an electronic version of the text, you're welcome to do so.

Be sure to check the edition when purchasing your textbook; other editions have similar material, but the assigned problems may be different.

##### Calculators

You are not required to purchase a calculator for this course, and

**you will not be permitted to use a calculator or other electronic device on any quizzes or exams**. You are strongly encouraged to avoid using a calculator while working on homework.### Quizzes

Keeping up with the homework will ensure that you are prepared for the quizzes, which will feature problems very similar to those in the homework. Quiz grades will not be based strictly on whether or not you found the correct answer. Your work must also be written clearly, and with proper notation, to receive full credit.

Your lowest quiz grade, including a missed quiz, will be dropped when calculating your final grade.

If you miss a quiz, you must make arragements to take it before the graded quizzes are returned to the class; this will typically be the next class meeting.

Your lowest quiz grade, including a missed quiz, will be dropped when calculating your final grade.

If you miss a quiz, you must make arragements to take it before the graded quizzes are returned to the class; this will typically be the next class meeting.

### Exams

There will be four midterm exams given throughout the semester, in addition to the final exam. The material on the exams will be similar to topics covered on quizzes and homework. You will be given review guides for each exam. All exams should be considered to be cumulative; each exam will include some material from the previous exams.

If you need to miss class during a scheduled exam for a documented, excused reason (illness, family emergency, athletics), you will be able to make up the exam. You must schedule a time to retake any exam within one week of the day the exam was given in class.

Your lowest exam grade (including a missed exam) will be replaced by your final exam grade, if your final exam grade is better. A grade of 0 on an exam due to academic dishonesty will not be replaced by the final exam grade.

The final exam is cumulative, including material from all sections covered in class.} Most questions on the final will be taken (with minor modifications) from homework, quizzes, and previous exams.

You are required to take the final exam for this course regardless of your average on earlier exams or quizzes. If you will not be able to take the final exam at its scheduled time, please make alternate arrangements as soon as possible. Final exams may be made up for excused absences only.

The final exam is scheduled for

If you need to miss class during a scheduled exam for a documented, excused reason (illness, family emergency, athletics), you will be able to make up the exam. You must schedule a time to retake any exam within one week of the day the exam was given in class.

Your lowest exam grade (including a missed exam) will be replaced by your final exam grade, if your final exam grade is better. A grade of 0 on an exam due to academic dishonesty will not be replaced by the final exam grade.

The final exam is cumulative, including material from all sections covered in class.} Most questions on the final will be taken (with minor modifications) from homework, quizzes, and previous exams.

You are required to take the final exam for this course regardless of your average on earlier exams or quizzes. If you will not be able to take the final exam at its scheduled time, please make alternate arrangements as soon as possible. Final exams may be made up for excused absences only.

The final exam is scheduled for

**Wednesday, December 12, 8 - 10 am**.### Final Grades

##### Basis of Final Grade

Up to 500 points are available to earn throughout the semester, as follows:

300 points | Midterm Exams |

Four exams, 75 points each | |

Lowest exam grade replaced by final exam, if better | |

100 points | Quizzes |

Nine quizzes, lowest quiz grade dropped | |

Each quiz worth 12.5 points, 0.5 points awarded for attending quiz | |

100 points | Final Exam |

##### Grading Scale

Grade | F | D | D+ | C | C+ | B | B+ | A |

Percentage | 0-59 | 60-66 | 67-69 | 70-76 | 77-79 | 80-86 | 87-89 | 90-100 |

Points | 0 | 300 | 330 | 350 | 380 | 400 | 430 | 450 |

### Resources

#### Software, Videos, and Apps

#### Free Online Calculus Courses

Khan Academy

MIT OpenCourseWare Calculus

edX Calculus 1A: Differentiation

edX Calculus 1B: Integration

MIT OpenCourseWare Calculus

edX Calculus 1A: Differentiation

edX Calculus 1B: Integration

#### Free Textbooks

### Tutoring

The Department of Mathematics offers free tutoring for Calculus I students in Zurn 213. No appointments are needed, just drop by according to the schedule here. You are free to ask tutors questions on any assigned homework and exam review sheets.

### Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

### Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.

## Homework

When we finish a section in the book, you should immediately begin working on the homework problems from the list below.

Your work will not be collected. However, actually working through these problems is the key to your success in this class. Attending every class is not enough; mathematics can only be learned through practice. You should plan to spend a significant amount of time on the homework. It is expected that you spend approximately 8-12 hours per week studying the material outside our class meetings, according the the typical 2-3 hour per credit rule of thumb.

Your work will not be collected. However, actually working through these problems is the key to your success in this class. Attending every class is not enough; mathematics can only be learned through practice. You should plan to spend a significant amount of time on the homework. It is expected that you spend approximately 8-12 hours per week studying the material outside our class meetings, according the the typical 2-3 hour per credit rule of thumb.

**Stay up to date with homework, and get help if you cannot understand a problem after trying it on your own.**Do not ignore a problem that you are struggling with. If you are having trouble with a topic, please come talk to me during office hours, ask questions in class, seek help from a classmate, or go to the department tutors for assistance. You are expected to try to work on all problems on your own first; when coming to my office, be prepared to show me what you've already tried.Section | Page | Problems |

Chapter 0 | ||

0.1 | 12 | 1, 3, 5, 7, 9, 15, 19, 23, 27, 29, 31a-c |

0.2 | 24 | 1, 3, 5, 11, 13, 17, 25, 27, 29, 31, 33, 35, 39, 41, 49, 53, 61, 63 |

0.3 | 35 | 1, 3, 11, 15, 17, 19, 25, 29, 31 |

0.4 | 49 | 1, 3, 5, 9, 13, 17, 19, 25, 27, 31, 39, 41 |

0.5 | 61 | 1, 5, 9, 11, 13, 15, 17, 21, 23, 25, 27, 47, 57 |

Chapter 1 | ||

1.1 | 77 | 1, 3, 5, 7, 9, 17-20, 21, 23, 25, 31 |

1.2 | 87 | 1, 3, 7, 11, 13, 15, 19, 21, 25, 31 |

1.3 | 96 | 1, 3, 5, 9, 13, 15, 21, 31, 33, 37, 43 |

1.4 | 106 | You are not responsible for this section (but try #17 and #21 anyway!) |

1.5 | 118 | 1, 3, 5, 7, 11, 13, 17, 21, 29, 31, 35, 45, 47 |

1.6 | 125 | 1, 7, 9, 13, 17, 19, 21, 23, 27, 31, 37, 49, 67 |

Chapter 2 | ||

2.1 | 141 | 3, 11, 13, 15, 17, 23 |

2.2 | 152 | 1, 3, 7, 9, 11, 21, 23, 25, 29 |

2.3 | 161 | 1, 3, 5, 7, 9, 13, 15, 17, 21, 23, 29, 37, 39, 41, 43, 45, 49 |

2.4 | 168 | 1, 3, 5, 7, 11, 13, 19, 21, 23, 27, 29, 31, 33, 39 |

2.5 | 172 | 1, 5, 11, 15, 17, 21, 23, 27, 29, 31 |

2.6 | 178 | 3, 7, 9, 11, 15, 17, 19, 23, 27, 35, 37, 39, 45, 49, 51, 53, 77 |

Chapter 3 | ||

3.1 | 190 | 3, 5, 7, 9, 11, 13, 15, 17, 27 |

3.2 | 195 | 1, 3, 7, 9, 13, 19, 23, 25, 27, 35, 37, 41 |

3.3 | 201 | 15, 17, 19, 21, 23, 25, 37, 43, 51, 65 |

3.4 | 208 | 1, 5, 13, 15, 17, 19, 25, 27 |

3.5 | 217 | 3, 5, 7, 23, 25, 29, 31, 43 |

3.6 | 226 | 1, 7, 9, 11, 13, 17, 21, 23, 27, 29, 33, 57 |

Chapter 4 | ||

4.1 | 241 | 1, 5, 7, 9, 15, 17, 19, 21, 25, 29, 39 |

4.2 | 252 | 3, 5, 7, 9, 11, 19, 25, 27, 29, 33, 37, 41, 43, 45, 53 |

4.3 | 264 | 1, 3, 5, 9, 13, 19, 23, 25, 31 |

4.4 | 272 | 3, 7, 9, 11, 13, 21, 23, 25, 27, 31, 33 |

4.5 | 283 | 3, 5, 13, 19, 21, 23, 27, 29, 31, 37, 55 |

4.6 | 294 | 1, 3, 13, 17, 19, 33 |

4.8 | 308 | 1, 3, 5, 7, 15, 25, 41 |

Chapter 5 | ||

5.1 | 321 | 7, 9, 13, 15, 17 |

5.2 | 330 | 5, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 43, 45 |

5.3 | 338 | 1, 3, 7, 9, 11, 15, 17, 21, 23, 27, 31, 33, 39, 41, 47, 53, 55, 61, 69, 71 |

5.5 | 360 | 13, 15, 19, 21, 23, 25, 33 |

5.6 | 373 | 7, 9, 13, 15, 17, 19, 23, 29, 31, 59, 61 |

5.7 | 381 | 1, 3, 5, 7, 31, 39 |

5.9 | 393 | 1, 5, 9, 15, 17, 19, 21, 31, 33, 35, 37, 43, 45, 49, 53 |

## Schedule

The exact topic covered on a particular date is subject to change. Exams and quizzes will be given on the day they are scheduled, though the sections appearing on a quiz may differ. Announcements will be made in class regarding any schedule changes.

Date | Topic | Notes |