Welcome to Math 32 (Precalculus)!

Syllabus | Schedule | Homework | Practice Exams

Time and place:
Lecture: MWF 8:10-9:00 in 105 Stanley

Section 101: MW 9:10-10:00 in 3105 Etcheverry
Section 102: MW 10:10-11:00 in 3107 Etcheverry
Section 103: MW 11:10-12:00 in 3109 Etcheverry
Section 104: MW 12:10-1:00 in 4 Evans
Section 105: MW 1:10-2:00 in 3107 Etcheverry
Section 106: MW 2:10-3:00 in 105 Latimer
Section 107: MW 9:10-10:00 in 289 Cory
Section 108: MWF 2:10-4:00 in 230C Stephens (this is a PDP section)
Section 109: MW 3:10-4:00 in 4 Evans

You need to be registered for lecture, plus one of these nine sections.

Instructor:
Alex Kruckman (That's me)
kruckman@math.berkeley.edu
Office hours: Mondays 10-12 in 747 Evans

GSIs: Piotr Achinger (Sections 104 and 105)
achinger@math.berkeley.edu
Office hours: Mondays 2-3 and Fridays 3-4 in 941 Evans

Ahmed Bakhaty (Section 108)
abakhaty@berkeley.edu
Office hours: Tuesdays 1-3 in 868 Evans

Adam Lesnikowski (Sections 103 and 107)
adam@math.berkeley.edu
Website: http://math.berkeley.edu/~adam/fall2013.html
Office hours: See website

Eugenia Rosu (Sections 101 and 102)
rosu@math.berkeley.edu
Office hours: Mondays 11-12 and Tuesdays 2-3 in 787 Evans

Benjamin Tsou (Sections 106 and 109)
btsou@math.berkeley.edu
Office hours: Fridays 3-5 in 716 Evans

Textbook: Precalculus: A Prelude to Calculus, Second Edition, by Sheldon Axler.
Note that we are using the second edition of Axler's text, not the first edition as in previous semesters. Berkeley has arranged a cheaper custom edition of the text, which is available at the Cal bookstore or directly from the publisher: http://www.wiley.com/WileyCDA/Section/id-811889.html. The content in the custom edition is identical to that in the second edition.

Enrollment: There is currently a waitlist for the course. It is very unlikely that additional discussion sections will be opened, but it is likely that students on the waitlist will get seats in their sections due to students dropping the class in the first week. If you are on the waitlist and are serious about taking the course, you should come to class on the first day, go to the section you are on the waitlist for, do the first homework, etc.

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.

The Student Learning Center: The SLC offers drop-in tutoring Monday-Thursday 10-4 in Chavez 103. They also offer a 1-unit adjunct course, Math 98, designed to be taken simultaneously with Math 32. Many students find the adjunct course useful, but enrolling in it is entirely optional. Information is available at http://slc.berkeley.edu/math_stat/math32.htm.

Assignments and 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 automatically 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 single lowest quiz score will be automatically dropped at the end of the semester. No make-up quizzes will be given.

Exams: The midterm exams will be 50 minutes each, held in class on Friday 10/4 and Friday 11/1. The final exam will be 3 hours, held Monday 12/16 7-10pm in 230 Hearst Gym.
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 automatically replaced by your score on the final at the end of the semester.

A note on calculators: No calculators will be allowed (or necessary!) on quizzes or exams. I will avoid assigning homework problems which require a calculator, but you may sometimes find that a calculator is useful for checking your work or doing a decimal approximation. If you don't have a physical calculator, I recommend Wolfram|Alpha, which knows a surprising amount of math.

And a note on cheat sheets: In some courses, students are allowed to make "cheat sheets" of relevant formulas and techniques and bring them to the exam. No cheat sheets will be allowed in Math 32 - for most of the course, the formulas and techniques we use are fairly simple. You should be able to remember them by remembering why they're true! But we'll encounter some more complicated formulas when we study trigonometry, and I will provide a page of useful trigonometric identities on the final exam.

Special arrangements:

  • Some of the grading policies above may be adjusted in the case of excused medical absence.
  • If you have special testing arrangements through DSP, come see me as soon as possible. I will need at least a week to set up alternative testing arrangements.
  • If you are a student athlete who will be missing a quiz or exam due to a sporting event, we can usually arrange for you to take the test on the road, proctored by a coach or academic adviser. Please put your GSI (in the case of a quiz) or me (in the case of an exam) in touch with your coach at least a week before the scheduled absence so we can make arrangements.

    Schedule: The course consists of three units, loosely organized around three classes of functions.

  • Functions and algebra. Weeks 0-5 (culminating with Midterm 1). After a brief review of the real number system, we'll study the general theory of functions, introducing inverse functions and examining the relationship between a function and its graph. Then we'll focus on algebraic functions: linear functions, quadratics, polynomials, and rational functions. This is Chapter 0, Chapter 1, and Chapter 2 of the text.
  • Exponents and logarithms. Weeks 6-9 (culminating with Midterm 2). We'll study the exponential functions and their inverses, the logarithms. In particular, we'll see how exponentials and logarithms appear in various real-world applications of mathematics. After a digression about computing area in the plane and a preview of calculus by way of estimating areas under curves, we'll introduce the number e and the natural logarithm. If we have time, we'll continue with our preview of calculus, introducing the notions of sequence and series. This is Chapter 3, Appendix A, and part of Chapter 7 of the text.
  • Trigonometry. Weeks 10-14 (culminating with the Final). This subject brings together properties of circles, right triangles, areas, and distances in a beautiful way. It also introduces us to a third class of functions, the trig functions. We'll define sin, cos, tan, etc., study their relationships by proving trig identities, and use them to solve geometry problems. This is Chapter 4, Chapter 5, and part of Chapter 6 of the text.

    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 8/30 Introduction and Chapter 0 - The Real Numbers
    Monday 9/2 No class
    Wednesday 9/4 0.3 - Inequalities and Absolute Values Homework #1: 0.2, No Quiz
    Friday 9/6 1.1 - Functions
    Monday 9/9 1.2 - The Coordinate Plane and Graphs
    Wednesday 9/11 1.3 - Function Transformations and Graphs Homework #2 and Quiz #1: 0.3, 1.1-2
    Friday 9/13 1.3 - Examples, Even and Odd Functions
    Monday 9/16 1.4/1.5 - Composition and Inverses
    Wednesday 9/18 1.5/1.6 - More on Inverse Functions Homework #3 and Quiz #2: 1.3-4
    Friday 9/20 2.1 - Linear Functions and Lines
    Monday 9/23 2.2 - Quadratic Functions (but no conics - we'll come back to these later)
    Wednesday 9/25 2.4 - Polynomials (Part 1) Homework #4 and Quiz #3: 1.5-6, 2.1-2
    Friday 9/27 2.4 - Polynomials (Part 2)
    Monday 9/30 2.5 - Rational Functions
    Wednesday 10/2 Midterm review Homework #5 and Quiz #4: 2.4-5
    Friday 10/4 Midterm 1 (in class) Midterm 1: Chapters 0, 1, and 2
    Monday 10/7 2.3/3.1 - Exponential Functions and Logarithms
    Wednesday 10/9 3.2 - Applications of the Power Rule for Logarithms No Homework, No Quiz
    Friday 10/11 3.3 - Applications of the Product and Quotient Rules for Logarithms
    Monday 10/14 3.4 - Exponential Growth
    Wednesday 10/16 2.2/Appendix A - Distances, Circles and Ellipses, and Circumference Homework #6 and Quiz #5: 2.3, 3.1-3
    Friday 10/18 Appendix A/3.5 - Area and Area Under Curves
    Monday 10/21 3.5/3.6 - Defining e and ln via Area Under Curves, Approximations
    Wednesday 10/23 3.7 - Exponential Growth Revisited Homework #7 and Quiz #6: 2.2, App. A, 3.4-5
    Friday 10/25 7.1 - Sequences
    Monday 10/28 7.2 - Series
    Wednesday 10/30 Midterm review Homework #8 and Quiz #7: 3.6-7, 7.1-2
    Friday 11/1 Midterm 2 (in class) Midterm 2: Chapter 3, Appendix A, Sections 7.1-2
    Monday 11/4 4.1 - The Unit Circle
    Wednesday 11/6 4.2 - Radians No Homework, No Quiz
    Friday 11/8 4.3 - Cosine and Sine
    Monday 11/11 No class
    Wednesday 11/13 4.4 - More Trigonometric Functions Homework #9 and Quiz #8: 4.1-3
    Friday 11/15 4.5 - Trigonometry in Right Triangles
    Monday 11/18 4.6 - Trigonometric Identities
    Wednesday 11/20 5.1 - Inverse Trigonometric Functions Homework #10 and Quiz #9: 4.4-5
    Friday 11/22 5.2 - Inverse Trigonometric Identities
    Monday 11/25 5.3 - Using Trigonometry to Compute Area Homework #11 and Quiz #10: 4.6, 5.1
    Wednesday 11/27 5.4 - The Law of Sines and the Law of Cosines No Homework, No Quiz (moved to Monday)
    Friday 11/29 No class
    Monday 12/2 5.5 - Double-Angle and Half-Angle Formulas
    Wednesday 12/4 5.6 - Addition and Subtraction Formulas Homework #12 and Quiz #11: 5.2-4
    Friday 12/6 6.1 - Transformations of Trigonometric Functions
    Wednesday 12/11 Final exam review
    Monday 12/16 Final Exam: 7-10pm (230 Hearst Gym) Final Exam: All sections

    Homework assignments:

  • Homework #1 (due Wednesday 9/4):
    Section 0.2 - 6, 8, 12, 14, 18, 20, 24, 26, 28, 30, 32, 34, 38, 40, 46, 48, 52, 53, 55, 58

  • Homework #2 (due Wednesday 9/11):
    Section 0.3 - 2, 4, 6, 8, 10, 20, 24, 28, 30, 36, 42, 48, 52, 56, 58
    Section 1.1 - 2, 6, 10, 20, 22, 24, 26, 34, 38, 40, 42, 44, 46, 48, 50, 62, 64, 69, 70
    Section 1.2 - 12, 14, 18, 22, 24, 47, 48, 49

  • Homework #3 (due Wednesday 9/18):
    Section 1.3 - 2, 6, 8, 12, 14, 30, 36, 40, 42, 56, 58, 67, 72
    Section 1.4 - 6, 10, 18, 20, 24, 32, 34, 46, 48, 55, 56, 57, 58, 59, 66, 67, 68

  • Homework #4 (due Wednesday 9/25):
    Section 1.5 - 2, 4, 6, 8, 10, 36, 37, 38, 41, 45
    Section 1.6 - 2, 4, 6, 8, 10, 12, 37, 48
    Section 2.1 - 4, 6, 12, 14, 16, 28, 32, 36, 38, 40, 46, (optional: 54)
    Section 2.2 - 2, 14, 18, 20, 30, 32, 36, 52, 86, 88

  • Homework #5 (due Wednesday 10/2):
    Section 2.4 - 2, 6, 12, 16, 22, 24, 26, 28, 31, 32, 33, 42, 43, 63, 64, 72
    Section 2.5 - 2, 6, 10, 16, 22, 28, 30, 32, 34, 36, 38, 40
    Plus the three exercises in this supplemental handout: Graphing Polynomials

  • Homework #6 (due Wednesday 10/16):
    Section 2.3 - 4, 6, 10, 14, 26, 30, 82, 84, 96, 98, 115, 116
    Section 3.1 - 10, 14, 18, 22, 26, 30, 32, 36, 38, 40, 80, 83, 85, 89
    Section 3.2 - 4, 10, 26, 43, 47, 48
    Section 3.3 - 10, 28, 30, 32, 36, 38, 44, 48, 65, 71, 73

  • Homework #7 (due Wednesday 10/23):
    Section 3.4 - 4, 14, 16, 22, 24, 32
    Section 2.2 - 56, 58, 68, 72, 74, 97
    Appendix A - 2, 6, 14, 16, 18, 24, 38, 40, 46, 50, 72
    Section 3.5 - 12, 16, 20, 24, 40, 50, 53, 54, 55, 56

  • Homework #8 (due Wednesday 10/30):
    Section 3.6 - 2, 4, 6, 8, 12, 16, 36
    Section 3.7 - 2, 4, 12, 26, 18, 37
    Section 7.1 - 2, 4, 12, 14, 22, 24, 26, 32, 44, 46, 50, 54, 61
    Section 7.2 - 2, 8, 12, 22, 28, 36, 38, (44, 48, 64, 65, 66) - problems in parentheses are optional

  • Homework #9 (due Wednesday 11/13):
    Section 4.1 - 2, 4, 8, 10, 12, 14, 53
    Section 4.2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 32, 34, 47, 51
    Section 4.3 - 2, 4, 6, 8, 10, 12, 18, 22, 24, 35, 36, 38, 39, 42, 44, 45

  • Homework #10 (due Wednesday 11/20):
    Section 4.4 - 8, 10, 14, 18, 20, 24, 28, 30, 34, 38, 43, 44, 45
    Section 4.5 - 2, 4, 14, 16, 18, 20, 24, 26, 28, 37, 38, 41

  • Homework #11 (due Monday 11/25):
    Section 4.6 - 6, 8, 10, 12, 14, 22, 30, 38, 46, 50, 58, 66, 70, 71, 72, 75, 80, 81, 85, 88 - and interpret the result of 88 as a statement about the relationship between the graphs y = sin(x) and y = cos(x)
    Section 5.1 - 2, 4, 18, 20, 36, 42, 49, 52, 53, 54, 55 - for the problems with calculator icons, you can leave your answers in terms of inverse trig functions

  • Homework #12 (due Wednesday 12/4):
    Section 5.2 - 2, 6, 10, 14, 18, 24, 26, 28, 30
    Section 5.3 - 8, 10, 12, 16, 20, 22, 26, 28, 30, 32, 34, 36, 38, 41, 42, 45, 47, 48
    Section 5.4 - 4, 8, 12, 16, 22, 29, 30, 31, 43, 44
    for the problems with calculator icons, you can leave your answers in terms of trig and inverse trig functions

  • Recommended problems for RRR week (not to be turned in):
    Section 5.5 - 10, 12, 14, 16, 18, 20, 22, 24, 26, 64, 66, 68, 72, 73, 76, 79, 105
    Section 5.6 - 6, 8, 10, 12, 26, 30, 32, 39, 46, 57, 58
    Section 6.1 - 2, 4, 6, 8, 14, 16, 22, 24, 26, 34

    Practice Exams / Resources:

    Notes:
    - In Fall 2012, we did not cover rational functions before Midterm 1, so this topic appears on Practice Midterm 2 and Fall 2012 Midterm 2, instead of on Practice Midterm 1 and Fall 2012 Midterm 1. This semester, rational functions will be covered on Midterm 1.
    - In previous semester, we did not cover sequences and series (Sections 7.1 and 7.2), so these topics do not appear on any practice exams. This semester, sequences and series will be covered on Midterm 2. For extra practice on these topics, I recommend doing problems from the textbook.

  • Midterm 1 review
  • Practice Midterm 1 and Solutions
  • Fall 2012 Midterm 1 and Solutions
  • Spring 2013 Midterm 1 and Solutions
  • Midterm 2 review
  • Practice Midterm 2 and Solutions
  • Fall 2012 Midterm 2 and Solutions
  • Spring 2013 Midterm 2 and Solutions
  • Final review
  • Trig study guide, courtesy of Ahmed Bakhaty
  • Practice Final and Solutions
  • Fall 2012 Final and Solutions
  • Spring 2013 Final and Solutions

    Exam Solutions (for the current semester):

  • Midterm 1 Solutions (and the exam)
  • Midterm 2 Solutions (and the exam)
  • Final (and the exam)