My name is Martin Vito Cruz and I'm the instructor for Math 32 this semester. The class meets on Mondays, Wednesdays, and Fridays from 8-9AM in 9 Lewis.

The URL for this page is http://math.berkeley.edu/~vitocruz/math32spring2007/class.html.

The textbook we'll be using is Precalculus by David Cohen, 6th edition.

There are three sections for the class:

  • Section 101: Meets TuTh 8-9AM in B51 Hildebrand; GSI: K. Beal
  • Section 102: Meets TuTh 2-3PM in 110 Barker; GSI: K. Beal
  • Section 103: Meets TuTh 8-9AM in 289 Cory; GSI: I. Dan-Cohen

Office hours

My office is in 835 Evans. I have office hours on Mondays from 9:30-10:30AM and on Wednesdays from 10:30-11:30AM. You are also welcome to email me and set up an appointment for a different time.

Important announcements

  • The final is on Friday, May 11 from 8-11AM. We will begin at 8AM so you will have the full three hours to finish the exam. It is in 60 Evans. The final will be comprehensive so in addition to looking at the old finals, you may also want to look at old practice midterms.
  • Here are solutions for the Fall 2005, Spring 2006, and Summer 2006 finals.
  • To help you study for the upcoming final, here are finals from previous semesters: Fall 2004 practice part 1, Fall 2004 practice part 2, Fall 2005 practice, Fall 2005, Spring 2006, Summer 2006, Fall 2006. I'll post solutions to some of them later. Note that the Fall 2004 semester covered a lot more material than we're going to cover. The other semesters on the other hand covered exactly the same material as this semester so you should be able to do all the problems from Fall 2005 and later.
  • Here are solutions for the first midterm and second midterms.
  • We didn't get to section 7.7 today, so the homework from that section has been moved to the next assignment (HW #10), and the upcoming midterm will only cover sections 4.4-7.5.
  • The second midterm is next week on Friday, March 23. I sent an email to the class about taking the midterm early, but in case you didn't get it, please email me as soon as possible if you need to take the exam early. The exam will cover sections 4.4-7.7.
  • Here are some previous exams to help you study for the upcoming midterm: Fall 2005 (practice), Fall 2005, Spring 2006, Summer 2006, Fall 2006. If you want to check your answers, here are solutions for some of those: Fall 2005, Spring 2006, Summer 2006, Fall 2006. Note that since we're at a slightly different place in the book than those classes were at about this time, the practice exams have material that we haven't gotten to yet and will not be on our exam.
  • Since we didn't quite finish 4.7 today, I moved the problems from section 4.7 from homework #5 to homework #6.
  • Here are solutions for some of the sample midterms: Spring 2006, Summer 2006, Fall 2006.
  • The first midterm is next week on Friday, February 16. To help you study, here are copies of midterm 1 from previous semesters: Fall 2004, Fall 2005, Fall 2005 (practice), Spring 2006, Summer 2006, Fall 2006.

Course overview

We will cover most of the material in the textbook. The goal is to prepare you to take a calculus class at the university level. I'm hoping that by the end of the class, you'll have a good understanding of equations, inequalities, functions, and graphs in general, and for the important special cases (linear functions, polynomials, rational functions, exponentials/logarithms, and the trig functions).

In my experience, there are a few things you have to do to do well in this class (or in any other math class).

  • Go to lectures, discussions, and office hours. Lectures are where you learn how to do things and why things are the way they are. Discussions are where you get to practice using the things you learned in lecture. Office hours are where you get to clarify topics you're still a little fuzzy about. If there's something you're not quite sure about, ask me or ask your GSI (this is what office hours are especially good for).
  • Do a lot of problems. Math is something that needs to be practiced. You will probably need to do more problems than just the ones assigned for homework. When doing homework, you should try as much as possible to do the problems without looking at your notes or the book. If you can't do this, you will probably have a hard time with the exams.
  • Don't fall behind. A lot of the material we'll learn later in the class depends on the earlier material.

Grades

Your grade will be based on homework, quizzes, midterms, and the final. The break down will be

  • Homework: 20%
  • Quizzes: 20%
  • Midterm 1: 15%
  • Midterm 2: 15%
  • Final: 30%

I'm aiming for a flat grading scale: this means an overal grade of 90% or above will get you an A, 80% or above a B, 70% or above a C, 60% or above a D, and anything lower an F. I'm hoping that the class average will be around an 80%.

Homework and quizzes

Homework will be assigned weekly. Late homework will not be accepted, but your lowest two homework scores will be dropped. It is important that you try to do all the assigned problems (this is where office hours can be helpful).

For the list of homework assignments, look at the calendar section below. The homework is given underneath the week that it is due.

There will also be weekly quizzes. Your lowest two quiz scores will be dropped.

Exams

There will be three exams: two 1-hour midterms and a 3-hour final. The final will be on Friday, May 11 from 8-11AM. This is not flexible -- if you have a conflict, come talk to me as soon as possible.

The two midterms will be on February 16 and March 23.

You will not be allowed to use notes, books, or calculators on the exams (just pencils/pens and erasers).

Calendar and homework assignments

  • Week 1: 1/15-1/19
    • 1/15: No class
    • 1/17: Introduction, 1.1, 1.2 (real numbers, intervals, absolute value)
    • 1/19: 1.3, 1.4, 1.5 (solving equations, rectangular coordinates, distance formula, graphs)
  • Week 2: 1/22-1/26
    • 1/22: 1.6, 1.7 (equations of lines, symmetry)
    • 1/24: 2.1, 2.2 (more techniques for solving equations)
    • 1/26: 2.3, 2.4 (solving inequalities)
    Homework #1 (due 1/23) (These problems are from Appendix B in the back and from the first two sections of Chapter 1.)
    • B.1: 7, 17, 32
    • B.2: 6, 33, 41
    • B.3: 1, 8, 25
    • B.4: 1, 3
    • B.5: 1, 13, 24
    • 1.1: 12, 18, 46, 51
    • 1.2: 10, 25, 26, 38
  • Week 3: 1/29-2/2
    • 1/29: 2.4, 3.1 (more inequalities, definition and examples of functions)
    • 1/31: 3.1, 3.2 (domain, range, graphs of functions)
    • 2/2: 3.3, 3.4 (shapes of graphs, graphing using reflections and translations)
    Homework #2 (due 1/30)
    • 1.3: 8, 22, 29
    • 1.4: 3, 8, 12
    • 1.5: 3, 6, 10, 18
    • 1.6: 4, 12, 15, 22, 26, 35
    • 1.7: 3, 10, 18, 24
    • 2.1: 8, 14, 36, 39
    • 2.2: 2, 26, 34, 50, 66
  • Week 4: 2/5-2/9
    • 2/5: 3.5, 3.6 (function composition, inverse functions)
    • 2/7: 4.1, 4.2 (linear functions, quadratic functions, completing the square)
    • 2/9: 1.7, 4.4, 4.5 (equations of circles, applications [minimization/maximization])
    Homework #3 (due 2/6)
    • 2.3: 2, 7, 8, 20, 26
    • 2.4: 5, 10, 33, 56
    • 3.1: 5, 6, 12, 15, 22, 27, 34
    • 3.2: 18, 26, 36
  • Week 5: 2/12-2/16
    • 2/12: 4.5, 4.6 (more min/maximization, polynomials)
    • 2/14: 4.6, 4.7 (more polynomials, rational functions)
    • 2/16: Midterm 1
    Homework #4 (due 2/13)
    • 3.3: 4, 9, 10, 22
    • 3.4: 4, 14, 23, 24
    • 3.5: 10, 12, 16, 20, 24
    • 3.6: 4, 8, 13, 16, 18
    • 4.1: 2, 12, 21
    • 4.2: 6, 16, 23, 36
  • Week 6: 2/19-2/23
    • 2/19: No class
    • 2/21: 4.7, 5.1 (rational, exponential functions)
    • 2/23: 5.2, 5.3, 5.4 (e^x, logarithms)
    Homework #5 (due 2/20)
    • 1.7: 40, 44, 47
    • 4.4: 2, 4, 5
    • 4.5: 8, 13, 16
    • 4.6: 12, 30, 39
  • Week 7: 2/26-3/2
    • 2/26: 5.4, 5.5 (properties of logarithms, solving exponential and logarithmic equations)
    • 2/28: 5.5, 5.3 (more equations, logarithmic scales)
    • 3/2: 5.7 (exponential growth and decay)
    Homework #6 (due 2/27)
    • 4.7: 10, 20, 29
    • 5.1: 6, 12, 19, 31
    • 5.2: 1-8, 18, 20
  • Week 8: 3/5-3/9
    • 3/5: 6.1, 6.2 (trig definitions, basic identities)
    • 3/7: 6.3, 6.4 (applications, unit circle definition, reference angles)
    • 3/9: 6.5 (proving trig identities)
    Homework #7 (due 3/6)
    • 5.3: 10, 15, 22, 27, 46, 47
    • 5.4: 4, 7, 16, 22, 48, 53
    • 5.5: 2, 4, 9, 17, 24, 32
  • Week 9: 3/12-3/16
    • 3/12: 7.1, 7.2, 7.3 (radians, circle geometry, trig functions in terms of radians)
    • 3/14: 7.3, 7.4 (graphs of sin x and cos x)
    • 3/16: 7.5 (graphs of A sin (Bx - C), A cos (Bx - C))
    Homework #8 (due 3/13)
    • 5.7: 1, 4, 26
    • 6.1: 4, 9, 15, 26
    • 6.2: 6, 14, 20, 25, 44
    • 6.3: 7, 10, 19, 30
    • 6.4: 1-4, 12, 41, 46, 52
  • Week 10: 3/19-3/23
    • 3/19: 7.7, 8.1 (graphs of tan (Bx -C), addition/subtraction formulas for sine and cosine)
    • 3/21: 8.1, 8.2 (more on addition/subtraction formulas)
    • 3/23: Midterm 2
    Homework #9 (due 3/20)
    • 6.5: 4, 11, 16, 26
    • 7.1: 8, 11, 14, 33
    • 7.2: 2, 7, 11
    • 7.3: 4, 7, 10, 30, 39
    • 7.4: 3, 6, 9-12, 22
    • 7.5: 6, 25, 26, 41, 42
  • Week 11: 3/26-3/30
    • Spring break!
  • Week 12: 4/2-4/6
    • 4/2: 8.4 (solving trig equations)
    • 4/4: 8.5 (inverse trig functions)
    • 4/6: 8.5 (more on inverse trig functions)
    Homework #10 (due 4/3)
    • 7.7: 2, 3
    • 8.1: 4, 15, 28, 36
    • 8.2: 3, 10, 25, 31, 34
  • Week 13: 4/9-4/13
    • 4/9: 9.1, 9.5 (law of sines/cosines, polar coordinates)
    • 4/11: 9.6 (polar graphs)
    • 4/13: 10.1 (systems of linear equations in 2 unknows)
    Homework #11 (due 4/10)
    • 8.4: 2, 8, 14, 17, 45
    • 8.5: 4, 7, 11, 14, 20, 25, 36, 44
  • Week 14: 4/16-4/20
    • 4/16: 10.2 (Gaussian elimination)
    • 4/18: 10.3 (Augmented matrices)
    • 4/20: 10.6 (Systems of nonlinear equations)
    Homework #12 (due 4/17)
    • 9.1: 1, 6, 8, 10, 12, 16
    • 9.5: 2, 4-6, 7, 19, 26
    • 9.6: 6, 15, 27, 30
  • Week 15: 4/23-4/27
    • 4/23: 10.7 (Systems of inequalities)
    • 4/25: 12.1, 12.2 (Complex numbers, polynomials, long division, synthetic division)
    • 4/27: 12.3 (Remainder theorem, factor theorem)
    Homework #13 (due 4/24)
    • 10.1: 4, 14, 22, 25, 30
    • 10.2: 4, 9, 14, 17, 24, 31, 36
    • 10.3: 11, 16, 20, 22
  • Week 16: 4/30-5/4
    • 4/30: 12.3 (More on the remainder/factor theorems)
    • 5/2: 12.4, 12.5, 12.6
    • 5/4: 13.2
    Homework #14 (due 5/1)
    • 10.6: 4, 6, 13, 16, 18, 19, 21
    • 10.7: 4, 14, 16, 20, 24
    • 12.1: 2, 10, 17, 22, 40, 41, 52, 60
    • 12.2: 6, 15, 28, 33, 38
  • Week 17: 5/7-5/8
    • 5/7:13.1
    Homework #15 (due 5/8)
    • 12.3: 16, 21, 30, 35
    • 12.4: 1, 12, 20, 23
    • 12.5: 7, 17, 20
    • 12.6: 6, 15
  • Final exam: 5/11 8-11AM