Math 112: College Algebra
Division: Science, Mathematics, and Technology
Credit Hours:Three (3) credits
Prerequisites: Intermediate Algebra skills/ Math 095 or two years of high school
algebra
Textbook: College Algebra: A Graphing Approach, Fourth Edition, plus free HMmathSpace Tutorial CD-Rom + free SMARTHINKING, by Ron Larson, Robert Hosteller, and Bruce Edwards, 2005, Houghton Mifflin Company, ISBN: 0-618-51551-8
Course Description: This course is designed to prepare students for the upper level college mathematics courses. Topics include graphs and transformations of functions, inverse and combinations of functions, solving linear and absolute value equations and inequalities, quadratic equations, polynomial equations, polynomial, rational, exponential, and logarithmic functions and their graphs.
Required Materials Textbook, as listed above.
for Instruction:
Calculator: a graphing calculator may only be used in classroom discussions. Its use is NOT permitted on any test or final.
Course Syllabus (in the college store)
Optional Materials: Study and Solutions Guide by Bruce H. Edwards
Instructional Videotapes/DVDs by Dana Mosely (located in both
the Pemberton and TEC libraries)
HMmathSpace Tutorial CD-Rom
SMARTHINKING.com Live, On-Line Tutoring
Attendance: Attendance is taken at all class meetings. Please refer to the
Burlington County College catalog for details of the college’s
policy and specifically your instructor for his/her policy.
Course Content: Unit I – Chapter 1: Functions and their Graphs
· Review Graphs of Equations and Lines in the Plane
· Functions
· Graphs of Functions
· Shifting, Reflecting, and Stretching Graphs
· Combinations of Functions
· Inverse Functions
Unit II – Chapter 2: Solving Equations and Inequalities
· Linear Equations and Problem Solving
· Solving Equations Graphically
· Complex Numbers
· Solving Equations Algebraically
· Solving Inequalities Algebraically and Graphically
Unit III – Chapter 3: Polynomial and Rational Functions
· Review Quadratic Functions
· Polynomial Functions of Higher Degree
· Real Zeros of Polynomial Functions
· The Fundamental Theorem of Algebra
· Rational Functions and Asymptotes
· Graphs of Rational Functions
Unit IV – Chapter 4: Exponential and Logarithmic Functions
· Exponential Functions and their Graphs
· Logarithmic Functions and their Graphs
· Properties of Logarithms
· Solving Exponential and Logarithmic Equations
Evaluation: There are four (4) tests – one each on Units I, II, III, and IV.
Each test will be graded using the following scale:
|
Percent Correct |
Letter Grade |
|
100 - 90 |
A |
|
89 - 80 |
B |
|
79 - 70 |
C |
|
69 - 60 |
D |
|
below 60 |
F |
The final exam, to be administered during exam week, is comprehensive and multiple choice.
The course grade will be determined from the final test average. Adding the percent grades for each test, along with the score for the final exam, and dividing this sum by five will compute the final test average. The letter grades listed in the above scale will be used to determine the course grade.
Grades of “I” or “X” are assigned at the discretion of the instructor.
Unit I: – Chapter 1: Functions and Their Graphs
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
|
relation |
function |
range/domain |
|
input/output |
independent variable |
dependent variable |
|
function notation |
piecewise-defined function |
|
|
implied domain |
graph of a function |
vertical line test |
|
increasing and decreasing functions |
|
|
|
relative minimum and maximum values |
even and odd functions |
|
|
shifting, reflecting, and stretching graphs |
rigid transformations |
|
|
nonrigid transformations |
|
composition of functions |
|
sum, difference, product, and quotient of functions |
inverse functions |
one-to-one functions |
Upon completion of this unit, the student should be able to:
1. Decide whether relations between two variables represent a function
2. Use function notation and evaluate functions
3. Find the domains of functions
4. Evaluate difference quotients
5. Find the domains and ranges of functions and use the Vertical Line Test for functions
6. Determine intervals on which functions are increasing, decreasing, or constant
7. Determine relative maximum and relative minimum values of functions
8. Identify and graph step functions and other piecewise-defined functions
9. Identify even and odd functions
10. Recognize graphs of common functions
a. Constant function d. Square Root function
b. Identity function e. Quadratic function
c. Absolute Value function f. Cubic function
11. Use vertical and horizontal shifts and reflections to graph functions
12. Use nonrigid transformations to graph functions
13. Add, subtract, multiply, and divide functions
14. Find compositions of one function with another function
15. Find inverse functions informally and verify that two functions are inverse functions of each other
16. Use graphs of functions to decide whether functions have inverse functions
17. Determine if functions are one-to-one
18. Find inverse functions algebraically
Unit II: – Chapter 2: Solving Equations and Inequalities
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
|
equation |
solution |
identity |
|
conditional equation |
|
linear equation in one variable x |
|
extraneous solution |
x-intercept |
y-intercept |
|
zero of a function |
point of intersection |
complex numbers |
|
imaginary unit, i |
standard form, a + bi |
additive identity |
|
additive inverse |
complex conjugates |
complex plane |
|
imaginary axis |
real axis |
fractals |
|
quadratic equation in x |
|
second-degree polynomial equation |
|
polynomial equations of higher degree |
|
|
|
equations involving radicals or rational exponents or absolute values |
|
|
|
solution set of an inequality |
graph of an inequality |
|
|
equivalent inequalities |
linear inequalities |
|
|
solving polynomial inequalities |
solving rational inequalities |
|
Upon completion of this unit, the student should be able to:
1. Solve equations involving fractional expressions
2. Write and use common mathematical formulas to solve real-life problems
3. Find x- and y-intercepts of graphs of equations
4. Find solutions of graphs graphically
5. Find the points of intersection of two graphs
6. Use the imaginary unit i to write complex numbers
7. Add, subtract, and multiply complex numbers
8. Use complex conjugates to write the quotient of two complex numbers in
standard form
9. Plot complex numbers in the complex plane
10. Solve quadratic equations by factoring, extracting square roots,
completing the square, and using the Quadratic Formula
11. Solve polynomial equations of degree three or greater
12. Solve equations involving radicals
13. Solve equations involving fractions or absolute values
14. Use properties of inequalities to solve linear inequalities
15. Solve polynomial inequalities, rational inequalities, and inequalities involving absolute values
________________________________________________________________________
Unit III: – Chapter 3: Polynomial and Rational Functions
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
|
polynomial function of x with degree n |
axis of symmetry |
|
parabola |
vertex of parabola |
|
standard form of quadratic equation |
|
|
minimum and maximum values of quadratic functions |
|
|
continuous graphs |
The Leading Coefficient Test |
|
Real Zeros of Polynomial Functions |
multiplicity of a zero |
|
Long Division of Polynomials |
Synthetic Division |
|
Remainder Theorem |
Factor Theorem |
|
Rational Zero Test |
complex zeros |
|
Fundamental Theorem of Algebra |
conjugate pairs of complex zeros |
|
Graph of a Rational Function |
Domain of Rational Functions |
|
Vertical and Horizontal Asymptotes |
Slant aymptote |
Upon completion of this unit, the student should be able to:
1. Use transformations to sketch graphs of polynomial functions
2. Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions
3. Find and use zeros of polynomial functions as sketching aids
4. Use long division to divide polynomials by other polynomials
5. Use synthetic division to divide polynomials by binomials of the form
(x – k)
6. Use the Remainder and Factor Theorems
7. Use the Rational Zero Test to determine possible rational zeros of polynomial functions
8. Use the Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function
9. Find all zeros of polynomial functions, including complex zeros
10. Find conjugate pairs of complex zeros
11. Find zeros of polynomials by factoring
12. Find the domains of rational functions
13. Find horizontal and vertical asymptotes of graphs of rational functions
14. Sketch graphs of rational functions, as well as those having slant asymptotes
________________________________________________________________________
Unit IV: – Chapter 4: Exponential and Logarithmic Functions
Objectives: Upon completion of this unit, the student should be able to define, explain,
symbolize, and/or illustrate the following:
|
transcendental functions |
exponential function f with base a |
|
natural base (base e) |
natural exponential function |
|
logarithmic function with base a |
common logarithmic function |
|
properties of logarithms |
natural logarithmic function |
|
properties of natural logarithms |
domains of logarithmic functions |
|
change-of-base formula |
solving exponential equations |
|
solving logarithmic equations |
|
Upon completion of this unit, the student should be able to:
1. Recognize and evaluate exponential functions with base a
2. Graph exponential functions
3. Recognize, evaluate, and graph exponential functions with base e
4. Recognize and evaluate logarithmic functions with base a
5. Graph logarithmic functions
6. Recognize, evaluate, and graph natural logarithmic functions
7. Rewrite logarithms with different bases
8. Use properties of logarithms to evaluate or rewrite logarithmic expressions
9. Use properties of logarithms to expand or condense logarithmic expressions
10. Solve simple exponential and logarithmic equations
11. Solve more complicated exponential and logarithmic equations
________________________________________________________________________
Week # 1: Introduction to the Course/Chapter 1: Functions and their Graphs
2. Review Section 1.1 - Graphs of Equations
Recommended assignment: P. 82, 83 # 1, 3, 5, 7-10 all, 19-29 odd
3. Review Section 1.2 - Lines in the Plane
Recommended assignment: P. 94, 95 # 1-10 all, 19-31 odd,
# 51, 53, 55
Week # 2: 1. Section 1.3 - Functions
Recommended assignment: P.107-109 # 1-9 odd, 13-31 odd,
# 49-58 all
2. Section 1.4 - Graphs of Functions
Recommended assignment: P. 121-123 # 1-4, 5, 7, 9, 11-20,
# 29-37 odd, 41-53 odd, 63-71 odd
Week #3: 1. Section 1.5 - Shifting, Reflecting, and Stretching Graphs
Recommended assignment: P. 131-133 # 1-11 odd, 15-43 odd,
# 51, 55, 59, 63
2. Section 1.6 - Combinations of Functions
Recommended assignment: P. 141, 142 # 5-19 odd, # 35-49 odd,
# 55-71 odd
Week # 4: 1. Section 1.7 - Inverse Functions
# 25-47 odd
2. Review Unit I (Chapter 1)
Recommended assignment: P. 156-159 # 3, 7, 11, 17, 33, 41,45,
# 47-50, 51, 53, 55, 57, 59,
#63-93 odd, 101-109 odd, 113-125 odd
P. 160: Chapter Test and/or Practice Test 1 - P. 10
3. TEST # 1 – Chapter 1
Week #5: 1. Unit II: Chapter 2, Section 2.1 - Linear Equations and Problem Solving
Recommended assignment: P. 168 # 1-11 odd, 15-23 odd
2. Section 2.2 - Solving Equations Graphically
Recommended assignment: P. 179, 180 # 1-21 odd, 53-59 odd
3. Section 2.3 - Complex Numbers
Recommended assignment: P. 189, 190 # 1-61 odd, 65-71 odd
Week # 6: 1. Section 2.4 - Solving Equations Algebraically
Recommended assignment: P. 205, 206 # 5-11 odd, 15, 17, 19,
# 23-31 odd, 45-55 odd, 61-69 odd,
# 83-93 odd, 99-107 odd
2. Section 2.5 - Solving Inequalities Algebraically and Graphically
Recommended assignment: P. 219, 220 # 5-17 odd, 27-33 all,
# 43-49 odd, 53-56 all, 59, 61, 63
Week # 7: 1. Review Unit II (Chapter 2):
Recommended assignment: P.232-234 # 1-7 odd, 17-83 odd,
# 89-109 odd
P. 236: Chapter Test and/or Practice Test 2 - P. 11
2. TEST # 2 – Chapter 2
Week # 8: 1. Section 3.2 - Polynomial Functions of Higher Degree
Recommended assignment: P. 260, 261 # 1-8 all, 17-31 odd, # 35-43 odd, 61- 69 odd
2. Section 3.3 - Real Zeros of Polynomial Functions
Recommended assignment: P. 275, 276 # 1-7 all, 13-19 all, 25, 31,
# 35, 37
Week # 9: 1. Section 3.4 - The Fundamentals Theorem of Algebra
Recommended assignment: P. 284 # 1-8 all, 9-15 odd, 27-33 odd
Recommended assignment: P. 292, 293 # 7-12 all. 13-19 odd
Week # 10: 1. Section 3.6 - Graphs of Rational Functions
Recommended assignment: P. 301, 302 # 9-17 odd, 27, 29, 31,
# 43, 45
2. Review Unit III (Chapter 3):
Recommended assignment: P. 313-316 # 3, 5, 7, 9, 19, 21, 23, 25,
P. 318: Chapter Test, # 1-3, 5, 6, 8, 14-16 and/or Practice Test 3 -
P. 12
Week # 11: 1. TEST # 3 - Chapter 3
2. Unit IV - Chapter 4: Section 4.1
Exponential Functions and Their Graphs
Recommended assignment: P. 329, 330 # 1-13 odd, 15-18 all,
# 19-37 odd
Week # 12: 1. Section 4.2 - Logarithmic Functions and Their Graphs
Recommended assignment: P. 339, 340 # 1-29 odd, 35, 37, 39
# 45-48, 49, 51
2. Section 4.3 - Properties of Logarithms
Recommended assignment: P. 347 # 1-31 odd, 45- 53 odd
Week # 13: 1. Section 4.4 - Solving Exponential and Logarithmic Equations
Recommended assignment: P. 357 # 1-7 odd, 17-49 odd,
# 73-83 odd
2. Review Unit IV (Chapter 4)
Recommended assignment: P. 383-385 # 5-8 all, 9, 33, 35,
# 43, 57, 65, 69, 71, 73, 79, 83, 87, 91, 97, 107
P. 388: Chapter Test, # 6-20 and/or Practice Test 4 - P. 13
Week # 14: 1. TEST # 4 - Chapter 4
2. Final Exam Review – Cumulative Tests: P. 237, 238 # 12-29, 35, 37
and on P. 493 # 1-6, 8, 15, 17, 19, 23, 24-26
Week # 15: FINAL EXAM (comprehensive)