Course: Math 32, Precalculus
MWF 8:10-9 in 4 Leconte
Instructor: Alex Kruckman
kruckman@math.berkeley.edu
Office hours: Tuesdays 11-12 in 775 Evans, Fridays 10-12 in the Student Learning Center
GSIs: Jue Chen (Sections 101 and 102 - MW 9-10 and 10-11 in 3111 Etcheverry)
juechen@math.berkeley.edu
Office hours: Mondays 2:10-4 in 1006 Evans
Oran Gannot (Sections 105 and 106 - MW 1-2 and 2-3 in 5 Evans)
ogannot@math.berkeley.edu
Office hours: Fridays 1:30-3:30 in 787 Evans
Per Stinchcombe (Sections 102 and 103 - MW 11-12 and 12-1 in 5 Evans)
per@math.berkeley.edu
Office hours: Mondays 10-11 and Wednesdays 1-2 in 1056 Evans
Textbook: Precalculus: A Prelude to Calculus, by Sheldon Axler.
You can get a significant discount (more than half off!) if you purchase it through this website:
http://www.wiley.com/WileyCDA/Section/id-811889.html
Note: The book is currently backordered on Wiley. If you don't have the book yet, please find another source as soon as possible!
Enrollment: Unfortunately, I do not have control over the course roster. If you are waitlisted or need to switch sections, you have to wait for something to open up and make the change yourself on Telebears. You may only switch into a section with free seats, and you must attend the section for which you are registered.
Grading: Your grade for the course will be based on homework and quizzes, two midterms, and a final.
10% - Homework
20% - Quizzes
20% - Midterm 1
20% - Midterm 2
30% - Final Exam
Homework: Homework is due most Wednesdays (see schedule). Hand it in to your GSI at the beginning of section self-graded (see below).
Your lowest two homework scores will be dropped at the end of the semester. No late homework will be accepted.
Self-grading policy: When you hand in your homework, write a whole number (no half points) 1-3 clearly at the top of the first page.
0: You'll get a 0 if you don't turn the homework in.
1: I only did a small number of problems, or I put very little effort into the homework.
2: I put some effort into the homework, but I skipped some problems.
3: I made a serious attempt at all of the problems.
Please be honest. The difference between a 1, a 2, and a 3 will be quite clear to your GSI.
Quizzes: Quizzes will be given in section most Wednesdays (see schedule). Quizzes will be 10 minutes long, will be graded out of 6 points, and will consist of two questions taken directly from the homework.
Your lowest two quiz scores will be dropped at the end of the semester. No make-up quizzes will be given.
Exams: The midterm exams will be 1 hour each, held in class on Friday 9/28 and Friday 10/26. The final will be 3 hours, held Monday 12/10 7-10pm in 155 Dwinelle. The difficulty of exam problems will be similar to the difficulty of homework problems.
Please be sure you can attend the exams! No make-up exams will be given for any reason. However, if your (percentage) score on the final is better than your (percentage) score on one of the midterms, your lowest midterm score will be replaced by your score on the final at the end of the semester.
No calculators or cheat sheets will be allowed (or necessary!) on quizzes or exams. However, I may provide a sheet with important formulas for the exams, especially in the trigonometry section of the course, where it would be very difficult to memorize all the relevant identities. I will also avoid assigning homework problems which require a calculator.
Where to get help: This course will be challenging! Here are some resources.
Special arrangements: Some of the grading policies above may be adjusted in the case of extended medical absence.
If you have special testing arrangements through DSP, talk to me as soon as possible. I will need at least a week to set up alternative testing arrangements.
Schedule: The course consists of three units, loosely organized around three classes of functions.
The lecture schedule is approximate - we may get ahead or behind. But the assignment due dates and exam days will not change.
| Date: | Lecture Topic: | Homework/Quiz/Exam: |
| Friday 8/24 | Introduction and 0.1 - The Real Line | |
| Monday 8/27 | 0.2 and 0.3 - Algebra of Real Numbers and Inequalities | |
| Wednesday 8/29 | 1.1 - Functions | Homework and Quiz #1: 0.1-3 |
| Friday 8/31 | 1.2 - The Coordinate Plane and Graphs | |
| Monday 9/3 | No class | |
| Wednesday 9/5 | 1.3 - Function Transformations and Graphs | Homework and Quiz #2: 1.1-2 |
| Friday 9/7 | 1.4 - Composition of Functions | |
| Monday 9/10 | 1.5 - Inverse Functions (Guest Lecture) | |
| Wednesday 9/12 | 1.6 - A Graphical Approach to Inverse Functions | Homework and Quiz #3: 1.3-5 |
| Friday 9/14 | 2.1 - Linear Functions and Lines | |
| Monday 9/17 | 2.2 - Quadratic Functions and Parabolas | |
| Wednesday 9/19 | 2.3 - Integer Exponents | Homework and Quiz #4: 1.6, 2.1-2 |
| Friday 9/21 | 2.4 - Polynomials | |
| Monday 9/24 | 2.5 - Rational Functions | |
| Wednesday 9/26 | Midterm review | Homework and Quiz #5: 2.3-5 |
| Friday 9/28 | Midterm 1 (in class) | Midterm 1: Chapters 0, 1, and 2 |
| Monday 10/1 | 3.1 - Rational and Real Exponents | |
| Wednesday 10/3 | 3.2 - Logarithms as Inverses of Exponentiation | No Homework, No Quiz |
| Friday 10/5 | 3.3 - Algebraic Properties of Logarithms | |
| Monday 10/8 | 3.4 - Exponential Growth | |
| Wednesday 10/10 | 3.5 - Additional Applications of Exponents and Logarithms | Homework and Quiz #6: 2.5, 3.1-3 |
| Friday 10/12 | 4.1 - Distance, Length, and Circles | |
| Monday 10/15 | 4.2 - Areas of Simple Regions | |
| Wednesday 10/17 | 4.3 - e and the Natural Logarithm | Homework and Quiz #7: 3.4-5, 4.1-2 |
| Friday 10/19 | 4.4 - Approximations with e and ln | |
| Monday 10/22 | 4.5 - Exponential Growth Revisited | |
| Wednesday 10/24 | Midterm review | Homework and Quiz #8: 4.3-5 |
| Friday 10/26 | Midterm 2 (in class) | Midterm 2: Chapters 3 and 4 |
| Monday 10/29 | 5.1 - The Unit Circle | |
| Wednesday 10/31 | 5.2 - Radians | No Homework, No Quiz |
| Friday 11/2 | 5.3 - Cosine and Sine | |
| Monday 11/5 | 5.4 - More Trigonometric Functions | |
| Wednesday 11/7 | 5.5 - Trigonometry in Right Triangles | Homework and Quiz #9: 5.1-3 |
| Friday 11/9 | 5.6 - Trigonometric Identities | |
| Monday 11/12 | No class | |
| Wednesday 11/14 | 5.7 - Inverse Trigonometric Functions | Homework and Quiz #10: 5.4-6 |
| Friday 11/16 | 5.8 - Inverse Trigonometric Identities | |
| Monday 11/19 | 6.1 - Using Trigonometry to Compute Area | Homework and Quiz #11: 5.7-8 |
| Wednesday 11/21 | 6.2 - The Law of Sines and the Law of Cosines | |
| Friday 11/23 | No class | |
| Monday 11/26 | 6.3 - Double-Angle and Half-Angle Formulas | |
| Wednesday 11/28 | 6.4 - Addition and Subtraction Formulas | Homework and Quiz #12: 6.1-3 |
| Friday 11/30 | 6.5 - Transformations of Trigonometric Functions | |
| Wednesday 12/5 | Final exam review | |
| Monday 12/10 | Final Exam: 7-10pm (in 155 Dwinelle) | Final Exam: Chapters 0-6 |
Homework assignments:
Section 0.1 - 3, 9, 10
Section 0.2 - 6, 16, 18, 28, 32, 38, 40, 41, 45, 47
Section 0.3 - 2, 4, 6, 8, 16, 26, 30, 32, 40, 43, 44
Section 1.1 - 2, 4, 6, 16, 18, 20, 24, 28, 30, 32, 34, 36, 38, 40, 46, 48, 50, 52, 54, 56, 60, 62, 63, 66, 67, 70, 71
Section 1.2 - 12, 20, 26, 28, 30, 32, 38, 40, 42, 44, 45, 46, 47
Section 1.3 - 16, 20, 24, 28, 32, 36, 40, 44, 48, 50, 56, 58, 59
Section 1.4 - 2, 6, 10, 12, 14, 18, 26, 32, 34, 38, 42, 45, 48, 49, 50
Section 1.5 - 2, 8, 14, 16, 18, 20, 30, 31, 32, 33
Section 1.6 - 26, 28, 30, 32, 34, 36, 37, 38, 39
Section 2.1 - 4, 6, 8, 10, 12, 26, 28, 32, 34, 36, 38, 41, 42, 43, 44, 45, 46, 54
Section 2.2 - 2, 6, 10, 14, 18, 28, 30, 32, 34, 36, 45, 47, 49, 51
Section 2.3 - 2, 4, 6, 10, 14, 16, 20, 22, 26, 32, 34, 38, 42, 44, 52, 54, 64, 65
Section 2.4 - 2, 6, 10, 14, 16, 18, 20, 22, 24, 26, 28, 35, 39, 40
Section 2.5 - 30, 32, 34, 46
Plus these additional exercises: Graphing Polynomials
Section 2.5 - 2, 20, 38, 40
Section 3.1 - 2, 4, 6, 8, 24, 26, 32, 34, 36, 38, 40, 44
Section 3.2 - 2, 6, 10, 14, 18, 20, 38, 42, 46, 50, 60, 62
Section 3.3 - 12, 14, 20, 22, 24, 26, 28, 30, 34, 36, 38
Section 3.4 - 4, 14, 16, 20, 22, 24, 32, 35
Section 3.5 - 2, 4, 6, 8, 10, 12, 18, 31, 32, 34
Section 4.1 - 2, 4, 6, 10, 12, 14, 18, 20, 24, 26, 32, 38, 49, 51
Section 4.2 - 2, 6, 10, 12, 14
Notes:
--- Problems 3.4 # 16, 20, 22, and 24, and 3.5 #4, 6, and 8 require calculators. For these problems, it is sufficient to write down an expression describing the answer instead of approximating the answer with a calculator. If you'd like to do the approximation, but you don't have a calculator, I suggest you acquaint yourself with Wolfram Alpha.
--- Problems 3.5 #10, 12, 18, 32, and 34 deal with applications that we did not talk about in class. You will have to read the relevant parts of Section 3.5 to do these problems.
Additional Resources: