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 277 Cory.

The URL for this page is http://math.berkeley.edu/~vitocruz/math32fall2006/class.html.

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

Office hours

My office is in 835 Evans. I have office hours on Mondays from 9:30-10:30AM, Tuesdays from 12-1PM, and Fridays 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 Wednesday, December 13 from 8-11AM in 10 Evans (not in the usual lecture room). It will cover pretty much all that we've done during the semester (take a look at the materials below to get a better idea of the sorts of things that may be on the final). I'll have office hours next week at the regular time, but I'd be willing to extend them an extra hour if there's big enough demand.
  • Here are solutions to the old finals: Fall 2005, Spring 2006, Summer 2006. I didn't do all the problems because there are a few problems that are pretty much the same between the different exams (so I just did it for one or two of the exams).
  • Here are things from previous semesters you may want to look at to help you prepare for the final: Fall 2004 review session (part 1), Fall 2004 review session (part 2), Fall 2005 practice, Fall 2005 exam, Spring 2006 exam, Summer 2006 exam. Note that the summer exam is shorter than the others since final exams in the summer are only two hours long instead of three.
  • Here are solutions to the 2nd midterm.
  • Here are solutions to the old midterms: Fall 2005, Spring 2006, Summer 2006.
  • The upcoming midterm will cover the sections after 4.2 up to and including section 8.5 (excluding the ones we skipped). For the exam, the trig identities that I expect you to remember are the ones on pg. 594, #1-4, 5(a)-(d), and 6(a)-(b). I'll have extra office hours this week on Wednesday from 4-5PM and Thursday from 4-5PM.
  • Here are the second midterms from past semesters: Fall 2005, Spring 2006, Summer 2006.
  • Here are solutions to the first midterm. Note that there are probably other ways to do some of the problems (e.g., for the inequality involving absolute values, you could have also used the key numbers method).
  • Here are solutions to two of the old midterms: Spring 2006, Summer 2006.
  • The first midterm will cover everything we've done so far up to and including section 4.2
  • The first midterm is coming up. You can take a look at the midterms from previous semesters to get an idea of what the midterms will be like: Fall 2004, Fall 2005 practice, Fall 2005, Spring 2006, Summer 2006.
  • There was a typo in the original syllabus concerning the date of the second midterm. It has been corrected -- the second midterm is during lecture on Friday, November 3 (not Thursday, November 2).

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: 15%
  • Quizzes: 15%
  • Midterm 1: 15%
  • Midterm 2: 15%
  • Final: 40%

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 Wednesday, December 13 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 September 29 and November 3.

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: 8/28-9/1
    • 8/28: Introduction (Review of exponents/factoring)
    • 8/30: 1.1, 1.2, 1.3 (Intervals, absolute values, basic equations)
    • 9/1: 1.4, 1.5, 1.6 (Rectangular coordinates, graphs of equations, lines)
  • Week 2: 9/4-9/8
    • 9/4: No class
    • 9/6: 1.7, 2.1, 2.2 (Symmetry, quadratic functions, more techniques for solving equations)
    • 9/8: 2.1, 2.2 (Techniques for solving equations continued, completing the square)
    Homework #1 (due 9/6):
    • 1.1: 12, 18, 46, 51
    • 1.2: 10, 25, 38
    • 1.3: 8, 22, 29
    • 1.4: 3, 8, 12
    • 1.5: 3, 6, 10, 18
    • 1.6: 4, 12, 15, 22, 26, 35
    • answers
  • Week 3: 9/11-9/15
    • 9/11: 1.7, 2.3, 2.4 (Equations of circles, solving inequalities)
    • 9/13: 2.4, 3.1 (More inequalities, definition and examples of functions)
    • 9/15: 3.1, 3.2, 3.3 (Domains, ranges, graphs of functions, piecewise functions, maximum, minimum, average rate of change)
    Homework #2 (due 9/11):
    • 1.7: 3, 10, 18, 24
    • 2.1: 8, 14, 36, 39
    • 2.2: 2, 26, 34, 50, 66
    • answers
  • Week 4: 9/18-9/22
    • 9/18: 3.4, 3.5 (Graphing techniques: reflections and translations, combining functions, function composition)
    • 9/20: 3.6 (Inverse functions)
    • 9/22: 4,1, 4.2, 4.4, 4.5 (Linear and quadratic functions, minimization/maximization, applications)
    Homework #3 (due 9/18)
    • 1.7: 40, 44, 47
    • 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
    • answers
  • Week 5: 9/25-9/29
    • 9/25: 4.6, 4.7 (Polynomial and rational functions)
    • 9/27: 5.1 (Exponential functions)
    • 9/29: Midterm 1
    Homework #4 (due 9/25)
    • 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
    • answers
  • Week 6: 10/2-10/6
    • 10/2: 5.2, 5.3, 5.4 (e^x, logarithmic functions)
    • 10/4: 5.5 (Solving equations with exponentials and logarithms)
    • 10/6: 5.3, 5.7 (Applications: logarithmic scales and exponential growth/decay laws)
    Homework #5 (due 10/2)
    • 4.2: 6, 16, 23, 36
    • 4.4: 2, 4, 5
    • 4.5: 8, 13, 16
    • 4.6: 12, 30, 39
    • 4.7: 10, 20, 29
  • Week 7: 10/9-10/13
    • 10/9: 6.1, 6.2 (Definition of trig functions, basic trig identities)
    • 10/11: 6.3, 6.4 (Applications, trig functions defined using the unit circle)
    • 10/13: 6.5 (Proving trig identities)
    Homework #6 (due 10/9)
    • 5.1: 6, 12, 19, 31
    • 5.2: 1-8, 18, 20
    • 5.3: 10, 15, 22, 27
    • 5.4: 4, 7, 16, 22, 48, 53
    • 5.5: 2, 4, 9, 17, 24, 32
  • Week 8: 10/16-10/20
    • 10/16: 7.1, 7.2, 7.3 (Radians, circle geometry, trig functions in radians)
    • 10/18: 7.4, 7.5 (Graphs of sin x and cos x)
    • 10/20: 7.5, 7.7 (Graphs of A sin (Bx - C), A cos (Bx - C), and tan (Bx - C))
    Homework #7 (due 10/16)
    • 5.3: 46, 47
    • 5.7: 2, 3, 4
    • 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 9: 10/23-10/27
    • 10/23: 8.1, 8.2 (Addition formulas for sine and cosine, double angle and half angle formulas)
    • 10/25: 8.4 (Solving trig equations)
    • 10/27: 8.5 (Inverse trig functions)
    Homework #8 (due 10/23)
    • 6.5: 4, 11, 16, 26
    • 7.1: 8, 11, 14, 33
    • 7.2: 2, 7, 10, 11
    • 7.3: 4, 7, 10, 30, 39
    • 7.4: 3, 6, 9-12, 22
  • Week 10: 10/30-11/3
    • 10/30: 9.1 (Law of sines and cosines)
    • 11/1: 9.5 (Polar coordinates)
    • 11/3: Midterm 2
    Homework #9 (due 10/30)
    • 7.5: 6, 25, 26, 41, 42
    • 7.7: 2, 3
    • 8.1: 4, 15, 28, 36
    • 8.2: 3, 10, 25, 31, 34
    • 8.4: 2, 8, 14, 17, 45
  • Week 11: 11/6-11/10
    • 11/6: 9.6 (Polar graphs)
    • 11/8: 10.1 (Linear equations in 2 unknowns)
    • 11/10: No class
    Homework #10
    • 8.5: 4, 7, 11, 14, 20, 25, 36, 44
    • 9.1: 1, 6, 8, 10, 12, 16
  • Week 12: 11/13-11/17
    • 11/13: 10.2 (Gaussian elimination)
    • 11/15: 10.3 (Augmented matrices)
    • 11/17: 10.6 (Nonlinear systems of equations)
    Homework #11 (due 11/13)
    • 9.5: 2, 4-6, 7, 19, 26
    • 9.6: 6, 15, 30
    • 10.1: 4, 14, 22, 25, 30
  • Week 13: 11/20-11/24
    • 11/20: 10.7 (Systems of inequalities)
    • 11/22: 12.1, 13.6 (Complex numbers)
    • 11/24: No class
    Homework #12 (due 11/20)
    • 10.2: 4, 9, 14, 17, 24, 31, 36
    • 10.3: 11, 16, 20, 22
  • Week 14: 11/27-12/1
    • 11/27: 12.2 (Polynomial division)
    • 11/29: 12.3 (Remainder theorem, factor theorem)
    • 12/1: 12.4, 12.5, 12.6 (Fundamental theorem of algebra, rational roots theorem, conjugate roots)
    Homework #13 (due 11/27)
    • 10.6: 4, 6, 13, 16, 18, 19, 21
    • 10.7: 4, 14, 16, 20, 24
  • Week 15: 12/4-12/8
    • 12/4: 13.2 (Binomial theorem)
    • 12/6: 13.1 (Mathematical induction)
    • 12/8
    Homework #14 (due 12/6)
    • 12.1: 2, 10, 17, 22, 40, 41, 52, 60
    • 12.2: 6, 15, 28, 33, 38
    • 12.3: 16, 21, 30, 35
    • 12.4: 1, 12, 20, 23
    • 12.5: 7, 17, 20
    • 12.6: 6, 15
  • Final exam: 12/13