Math 1050 (section 21)
College Algebra
Autumn 2014
Text:
Calculator:
Instructor:
A Streamlined approach to Pre-Calculus
Limited Use. TI 84 (any edition) is my choice.
Paul Christensen email: christen@math.utah.edu
Web page: http://www.math.utah.edu/~christen
Location:
U. of U. Bountiful Campus, Corner of 200 South and 100 East
Time:
Saturday mornings, 8:15 am to approx. 11:45 am
Pre-requisite Math 1010 or high school equivalent (Intermediate Algebra)
Credit Hours: 4.0
If you need to contact me, email is the best way to do it. I will respond to you as soon as possible.
Be patient.
Course Objectives
The essence of algebra is to use variables instead of just numbers. This enables us to
describe things in general rather than in particular, it helps us set up and solve
problems, and it is instrumental in constructing a link between formulas and
pictures which in turn much amplifies our problem solving ability. During this class
you will become used to the idea of having variables represent parameters and
unknowns, and will become competent at simple algebraic manipulations. You will
learn how to apply the basic techniques of solving linear and quadratic equations.
Your repertoire of functions will increase to include rational, exponential and
logarithmic functions. Throughout the course you will be using mathematics to
solve problems that originate in the world around us.
Support
Supplementary Notes available at www.math.utah.edu/online/1050
Videos available at http://www.math.utah.edu/lectures/index.html
Tutoring Lab: T.Benny Rushing Mathematics Student Center Rm. 155
M – H 8am – 8pm, F 8am – 6pm, closed weekends and holidays.
(The computer lab is Rm. 155C and has the same hours.)
If you are interested in group tutoring sessions, inquire at
www.math.utah.edu/ugrad/tutoring.html
The University Tutoring Center, 330 SSB, offers inexpensive ($6/hour) private
Tutoring. A list of private tutors is also available from the Math Dept. office.
Grading
15% on Attendance & Participation (2 absences allowed)
45% on Homework Midterms (3 of them)
40% on Final Exam Saturday December 07 (Not negotiable)
Tentative Schedule of discussion topics and tests.
Saturday August 31
1.
Basic Properties (Appendix 2)
Order of operations, simplifying by combining similar terms, simplifying polynomials,
(Pg. A 31 - 32 #’s 1 - 88) the Distributive Property, substitution, properties of radicals,
rules of exponents, and rational exponents (Pg. A20 - 22)
2.
A. Solving Linear Equations and Inequalities (Appendices 5 and 6)
Solving single variable Linear Equations by using inverse operations (Pg. A56)
Solving single variable Linear Inequalities by using inverse operations (Pg. A64)
Cross Multiplying and Clearing fractions (Pg. A56)
Solving Equations with Radicals (Pg. A57)
Solving Linear Equations with absolute value (Pg. A57)
Solving Linear inequalities and compound inequalities (Pg. A64)
Solving linear inequalities with absolute value (Pg. A64)
Saturday September 7
B. Graphing Linear Equations (Mostly Section 1.3)
Plotting points, especially x and y intercepts
Definition of slope and the slope formula
Graphing a line in slope-intercept form.
Changing Standard form into slope-intercept form.
Given two points find the equation of the line that goes through them
Equations and slopes of vertical and horizontal lines
The distance formula and the midpoint formula
Equations of circles (Pg. 17)
Change slope-intercept form into standard form
Find the equations of lines that are parallel/perpendicular to given lines and through
given points.
Saturday September 14
3.
Functions (Sections 1.4 – 1.9)
Definitions of relation and function, domain and range.
Vertical Line Test and function notation
Composite functions
Difference Quotient (Pg. 42)
Graphs of parent functions:
,
,
,
Symmetry, Even and Odd functions (Pg. 15, Pg. 55)
Horizontal and vertical translations of parent functions
,
,
Scale Transformations of parent functions
General graphing model
Restricted Domains and Piecewise functions
One – to – one Functions/Inverse Functions
Saturday September 21 First Midterm handed out at the end of class.
4.
Quadratic Functions (Appendix 5, and Section 2.1)
Extracting Roots
Factoring
Completing the Square as a solving tool
Quadratic Formula
Solving equations with radicals
Solving rational and radical equations that turn out to be quadratic
Completing the Square as a graphing tool
Other tips for graphing parabolas
Saturday September 28
5.
First Midterm DUE
Polynomial Functions (Sections 2.2 – 2.5)
Lead Coefficient Test and End Behavior
Define zeros of a polynomial
(x – a) is a factor of the polynomial function
“a” is a real zero of the polynomial
Long and Synthetic Division and The Remainder Theorem (Section 2.3)
Complex Numbers – definition and operations (Sections 2.4)
The Rational Zeros Test
Finding zeros and graphs of polynomial functions
Multiplicities of factors
Saturday October 5
6.
Rational Functions, Part I - The graphs (Section 2.6)
x and y intercepts of a rational function
Definition of asymptote
Domain of a rational function, vertical asymptotes
Horizontal Asymptotes
Oblique Asymptotes
Saturday October 12
7.
Second Midterm handed out at the end of class.
Exponential Functions (Sections 3.1, 3.5)
Graphs of exponential functions; asymptotes and “pivot points”. (Section 3.1)
The number “e” (3.1)
Compound Interest (3.1)
Exponential Growth and Decay (Section 3.5)
8.
Solving simple exponential equations (Section 3.1)
Logarithmic Functions (Sections 3.3 – 3.4)
Definition of a logarithm, the inverse of an exponential function
Changing back and forth between exponential form and logarithmic form of an equation
Graphs of logarithmic functions; asymptotes and “pivot points”.
Properties of Logarithms (Section 3.3)
Solving Logarithm Equations (Section 3.4)
Using Logarithms to Solve Exponential equations (Section 3.4)
Saturday October 19
No Class Fall Break
Saturday October 26
Second Midterm DUE
9.
Solving Systems Part 1 (Sections 7.1 – 7.3)
Solving 2 x 2 linear system by graphing, elimination, and substitution.
(Gaussian Elimination)
Solving a 2 x 2 non-linear system by substitution
Solving a 3 x 3 linear system by elimination and substitution
Intro to row-echelon form, back substitution, elementary row
Operations and Gaussian elimination (7.3)
10.
Matrices (Sections 8.1 – 8.4)
Definition and dimensions (order) of a matrix
Operations with matrices. (Section 8.2)
Determinant of a 2 x 2 matrix (8.3)
Inverse of a 2 x 2 matrix (8.3)
Solving a 2 x 2 system using the inverse-matrix method
Gauss-Jordan elimination and reduced row-echelon form (8.1)
Saturday November 02
11.
Solving Systems Part II (Sections 8.3 – 8.5)
Determinants of a 3 x 3 matrix by diagonals and cofactors. (8.4)
Inverse of a 3 x 3 matrix
Solving a 3 x 3 system by the inverse-matrix method
Cramer’s Rule (And other applications of determinants) (8.5)
Saturday November 09
12.
Third Midterm handed out at the end of class.
Rational Functions Part II (The equations)
A review of operations with rational expressions (Appendix 4)
Solving equations with rational expressions
Partial Fraction Decomposition (Section 7.4)
13.
Sequence and Series
Definition and notation (section 9.1)
Factorial and theFundamental Counting Principle (9.1, 9.6)
Explicit and Recursive Forumlas (9.1)
Arithmetic sequences and series (9.2)
Geometric sequences and series (9.3)
Saturday November 16
14.
Third Midterm DUE
Pascal’s Triangle (Section 9.5)
Binomial Expansion and the Binomial Theorem (Section 9.5)
Saturday November 23
Review and Practice Final
Saturday November 30
No Class Thanksgiving Break
Saturday December 07
Final Exam 9:00 – 11:00 a.m. (Bring an envelope!)
The final exam will about 20 questions long. You will have to
work independently without a calculator, notes, or help from
classmates. It will be important that you arrive at the correct
solution. Showing your work will still be necessary, but partial
credit will be given less liberally.
Note:
After you have taken the final exam, your grade is then final.
There is no “make-up” or “extra credit”. I tend to resent (and
generally ignore) any such solicitations. It is always disappointing
for me when a student has worked dutifully, and not attained the
level of success they were hoping for. However, my grading
responsibility is to keep track of your scores, and calculate your
final grade. I do not “give” you a grade. Your grade must reflect
your level of competence with the material, and not how much
effort you feel that may have put into the course. I have to trust
your exam scores to represent your level of comprehension. I do
not feel that a grade is negotiable.
Grading:
15% of your grade will come from attendance, and 15% from each of your
three midterms. The other 40% will come from your final exam. If your final
exam score exceeds any of your midterm scores, I will drop that midterm and
allow your final exam to count as 55% of your grade. The grading will be
precisely as follows:
A
AB+
B
92.5%
89.5%
86.5%
82.5%
BC+
C
C-
79.5%
76.5%
72.5%
69.5%
D+
D
D-
66.5%
62.5%
59.5%
Behavior:
All students are expected to maintain courteous behavior and respect for
other individual in the classroom. This includes no use of cell phones or
electronic/head phone devices. Students who, at the discretion of the
instructor, are unwilling to maintain appropriate behavior will be dismissed
from class for the day and, ultimately, if the problem persists, will be at risk
to receive a failing grade. Students are encouraged to read the Student Code
in the Student Handbook as many details are spelled out pertaining to
student classroom and conduct, and their rights and responsibilities.
Test Return:
If you would like your final exam to be returned to you after it has been
graded, then you must bring with you on the day of the final, an envelope
that is self-addressed and stamped. If you do not do this, your test will
be thrown away very shortly after it has been graded.
Policy Note:
The University of Utah seeks to provide equal access to its programs,
services, and activities for people with disabilities. If you need
accommodations in this class, reasonable prior notice needs to be given to
the instructor and to the Center for Disability Services, 162 Olpin Union
Bldg., 581 – 5020 (V/TDD). CDS will work with you and the instructor to
make arrangements for accommodations.