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
- 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
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