MAC 1147: Precalculus Algebra & Trigonometry
Summer 2007
Instructor:
S. Sippel
Office: DSSC 216
Office Phone: 253-7204
Office Hours: M-TH 7:15-7:45 am, 9:30-10:00
email: ssippel@hccfl.edu
Prerequisite: MAC 1105 with a "B" or better, or appropriate score on the Math Placement Exam.
Text:
Algebra and Trigonometry, 7th Edition by Sullivan
Calculators: A graphing calculator is required. A TI-83 will be used for classroom discussions and
demonstrations. Symbolic calculators (e.g.,TI-89,TI-92) are not allowed on exams.
Course
Major topics included polynomial, rational, and other algebraic functions, their
Description properties and graphs; polynomial and rational inequalities; exponential and logarithmic
functions; piece-wise defined functions; trigonometric functions of real numbers; radians and
angles; trigonometric identities; applications to right and oblique triangles; trigonometric
equations; polar form of complex numbers; conic sections; matrices and determinants;
vectors; sequences and series; mathematical induction; binomial theorem; applications.
Homework: The only way to learn math is to practice, so homework is required. All graded homework will
be completed online using MathXL software. The website for login is www.mathxl.com.
You MUST have access to a computer with internet access to complete the homework for this
course. Additional homework will be assigned from the text. (Although the textbook
homework is not graded, it is just as important to complete it as it covers problems not asked
in Mathxl and key objectives of the course that you will be tested on).
If you do not have a computer at home, the computer lab on the 3rd floor of the Social Science
building (DSSC 319) has Mathxl loaded. You can also print up to 10 pages per day in the lab,
so you could print your homework assignments, work on them elsewhere, and then return to
enter your answers.
MathXL homework is due on the day of the exam. There is one homework assignment for
each section we will be covering in the book.
Even though the homework answers are submitted online, all students are required to keep a
homework notebook showing all of the problems, work, and solutions from their MathXL
online homework. You can use the notebook to study for exams and make note of questions
you had difficulty with. The notebook must be neat and orderly. Use the following format:
1. Start each section on a new page. Label the top of the page with the section, e.g., Section
2.3.
2. Write down each question. Show an appropriate amount of work to support your answer.
Credit will not be given for writing only the answers when there is work to be shown.
3. The notebooks will be handed in on test days to support your Mathxl grade. Sections
missing the appropriate work will receive a corresponding deduction on the Mathxl grade.
Grading:
Besides homework, take-home quizzes will be given periodically and graded. Quizzes will be
announced and cannot be made up, however, the lowest quiz score will be dropped. There will
be 4 hourly exams, along with a comprehensive final exam. If a student scores higher on the
final exam than any of the previous hourly exams, then the percentage on the final will replace
the percentage of the lowest exam score. Cheating on any exam will result in an F for the
course. Overall, percentages and grading are as follows:
4 Exams:
Homework:
Quizzes:
Comprehensive Final Exam:
Attendance
/Make-ups:
50 %
15%
15 %
20 %
100 %
A: 90 - 100 %
B: 80 - 89 %
C: 70 - 79 %
D: 60 - 69 %
F: 0 - 59 %
Regular attendance is expected. If a student is absent, it is his/her responsibility
to obtain class notes and assignments. There are no make-up quizzes. If a student misses an
exam, they may be allowed to make up the exam, provided they have sufficient reason and/or
official documentation. Any make-up exam must be completed prior to the exams being
graded and returned. Only 1 make-up exam is allowed. If 1 exam is missed, the student's
percentage on the final will be used to replace the missing exam score, as discussed above.
Any further missed exams will result in a score of 0.
Withdrawal: The last day to withdraw without a grade is June 21st.
Tutoring:
Tutoring Center is located in DSSC 322.
The following is a tentative schedule for MAC 1147. Any changes will be announced in class.
DAY
DATE
SECTIONS
1
2
W 5/9
Th 5/10
Orientation, 3.1
3.1-3.2
3
4
5
6
M
T
W
Th
5/14
5/15
5/16
5/17
3.3-3.4
3.5-3.6
4.1-4.2
4.3-4.4
7
8
9
10
M
T
W
TH
5/21
5/22
5/23
5/24
4.5
Review, 4.6
Exam 1: Chap 3 & 4.1-4.4
4.7-5.1
11
12
13
M
T
W
TH
5/28
5/29
5/30
5/31
Memorial Day Holiday
5.2-5.3
5.4-5.5
5.6-5.8
14
15
16
17
M
T
W
TH
6/4
6/5
6/6
6/7
5.9 (opt)
Review, 6.1
Exam 2: 4.5-4.7, Chap 5
6.2-6.3
18
19
20
21
M
T
W
TH
6/11
6/12
6/13
6/14
6.4-6.5
6.6-6.7
6.8, 7.1
7.2-7.3
DAY
DATE
SECTIONS
22
23
24
25
M
T
W
TH
6/18
6/19
6/20
6/21
7.4-7.5
7.6, 7.7 (7.6 is self study)
7.8
Review, 8.1
26
27
28
29
M
T
W
TH
6/25
6/26
6/27
6/28
Exam 3: Chaps 6 & 7
8.2, 8.3
8.4, 9.1 (8.4 is self study)
9.2-9.3
30
31
32
M
T
W
TH
7.3
7/4
7/5
7/6
9.4-9.5
Independence Day Holiday
9.5
Review, 10.1
33
34
35
36
M
T
W
Th
7/9
7/10
7/11
7/12
Exam 4: Chaps 8 & 9
10.2-10.3
10.4-11.1,11.6
11.2-11.3
37
38
39
M
T
W
7/16
7/17
7/18
12.1-12.2
Review for Final
Final Exam
Special Accommodations: If, to participate in this course, you require an accommodation due to a
physical or learning impairment, you must contact the Office of Services to Students with Disabilities.
The office is located in the Student Services Building, Room 208. You may also reach the office by
phone, (813) 253-7031, TDD (813) 253-7035, or (813) 253-7336.
MAC 1147: MathXL and Text Assignment Sheet
Note: This is a tentative assignment sheet. Any changes will be announced in class.
The graded homework in Mathxl correlates to the following problems in the text. Problems listed from the text
cover additional material not asked in Mathxl. This homework is from textbook only, and will not be graded.
Chap 3: Functions and Their Graphs
3.1: Functions
3.2: Graphs of Functions
3.3: Properties of Functions
3.4: Library of Functions
3.5: Transformations
3.6: Mathematical Models
2.6: Linear Regression
Chap 4: Poly & Rational Functions
4.1: Quadratic Functions & Models
4.2: Polynomial Functions
4.3: Rational Functions I
4.4: Rational Functions II
4.5:
4.6:
4.7:
Polyn and Rational Inequalities
Real Zeros of a Poly Function
Complex Zeros
Chap 5: Exponential/Log Functions
5.1: Composite Functions
5.2: Inverse Functions
5.3: Exponential Functions
5.4: Logarithmic Functions
5.5:
Properties of Log Functions
5.6: Exponential and Log Equations
5.8: Growth and Decay
Chap 6: Trig Functions
6.1: Angles and their Measure
6.2:
6.3:
6.4:
Right Triangle Trig
Finding Values of Trig Functions
Trig Functions: General Angles
6.5:
Trig Functions: Unit Circle
6.6:
Graphs of Sine and Cosine
Note: All problems are odds unless otherwise indicated.
Mathxl: 15-19,25-27,33-41,47-51,55-57,61,65,69,73,75,83,85,91; Text: 31,53,67)
Mathxl: 9-17, 23-27, 35; Text: 31, 39, 41)
Mathxl: 11,13,15,17,19,21,27,29; Text: none)
Mathxl: 9,11,25,29,31,35,37,41,45,47; Text: Odds 13-23, 43, 51, 55a, 55b
MathXL: Odds 7-23, 27, 73; Text: Odds 35, 39-43, 49, 53, 65 (*Graph sketching)
Mathxl: 1, 5, 7, 9, 15, 17; Text: 18, 32. Also, do #68 from section 3.3.
Mathxl: none (doesn't graph); Text: 17, 19 (Use Mathxl’s Study plan if you need help).
Mathxl: 11,2,35,36,41,48,53,57,61,63,69,75,79; Text: 15,21,29,43,49,77,83,85,87,93
Mathxl: 11,15,25,37,43,45,47,59,67,69,81; Text: 13,17,19,21,23,53,61,85,95
Mathxl: 13,15,19,23,31,41-49 ; Text HW: 27
4.4 HW Mathxl: 45,49,55,59; Text: Odds 7-11,17,21-25,29,33,53
The majority of this section is assigned from the text. The mathxl hw requires you to
check for symmetry and where the function crosses the HA, which I consider optional.
(Use Mathxl’s Study plan if you need help).
Mathxl: 7,9,13,19,27,31,35,39,45,55; Text: 53,57
Mathxl: 33,39,45,51,57,69,77; Text: 49,61,67,71; (Ignore Descarte's Rule)
Mathxl: None; Text: 31,33,35,37
The Mathxl HW for these questions requires you to write the function in factored form
(including complex factors), along with listing all the complex zeros. I am only requiring
you to factor down to linear and quadratic factors (over reals). (Use Mathxl’s Study plan
if you need help).
Mathxl: 7,9,17,19,23,25,31,47,53,55,63; Text: 15,35,45,61,67
Mathxl: 9,13,17,19,51,55; Text: Odds 11,15,23-29,33,41-45,57
Mathxl: 11,17,23,53,55,57,71,75; Text: 21,25,27,29,35,37,39,47,49,74,79,80
Mathxl: 9,11,15,21,27,35,41,45,47,59,93,103
Text: Odds 17-19,23-25,29-33,39,43,49-61,67,71,75,77,85,95,87
MathXL: 9,19,31,33,41,43,45,51,55,59,61,63,65;
Text: 7,11,13,15,17,35,37,67,73*,75*,76*
* on 73, 75, 76: Graph by using domain and algebraically finding 2 pts. Don't use change
of base.
Mathxl: 1,3,5,9,11,17,21,23,25,27,29,33,45,55: Text: 7,19,51
Mathxl: 1,3,5,7,9,11,17,21,23 Text: 19; (If we do Newton's Law of Cooling:, add 13,15)
MathXL: 23,29,35,47,61,69,71,75,77,79,83,91,101
Text**: Odds 11-21, 25,31,37,41,43,49-59,63-67,73,93,95
Mathxl: 11,23,25,27,29,31,35,39,41 Text: 15; 55b,55c, 57a, 57b, 57d; 61a-e
Mathxl: Odds 17-29,33,37-51 Text: 5,6; Odds 7-15
Mathxl: 11,13,21,29,33,37,41,49,63,67,79,87,89,93,99,203
Text: Odds 25,31,39,43-47,51-61,65,.69-77
Mathxl: Odds 9,13,17,21-35,61,67
Text: 63,65,69,71
Note: Problems 21-31 state "use the fact that the trig functions are periodic to find the
exact values of each expression." What I want you to do is use the unit circle approach to
evaluate those functions.
Mathxl: 11,15,25,27,33,35,37,41,43,73,85: Text: Odds 9,13,17,61-67,71-81,89
Note: Where we used y=asin(bx-c)+d in class, the text (and mathxl) use different
symbols. They will use a = A, b="w", the period is T=2pi/b=2pi/w. Watch for prompts in
the online HW that ask for T and "w".
6.7:
6.8:
Other Trig Graphs
Phase Shift: Sinusoidal Curves
Chap 7: Analytic Trig
7.1: Inverse Trig Functions
7.2: Inverse Trig Functions (cont)
7.3: Trig Identities
7.4: Sum and Difference Formulas
7.5: Double and Half Angle Formulas
7.6: Product-Sum & Sum-Product
7.7: Trig Equations I
7.8: Trig Equations II
Chap 8: Apps of Trig Functions
8.1: Solving Right Triangles
8.2: Law of Sines
8.3: Law of Cosines
8.4: Area of a Triangle
Chap 9: Polar Coordinates; Vectors
9.1: Polar Coordinates
9.2:
Polar Equations & Graphs
9.4:
Vectors
9.5: The Dot Product
Chap 10: Analytic Geometry
10.2: Parabolas
10.3: Ellipses
10.4: Hyperbolas
Chap 11: System of Equations
11.1: Linear Systems: Subst & Elim.
11.6: Non-Linear Systems
11.2: Linear Systems: Matrices
11.3: Linear Systems: Determinants
Chap 12: Sequences
12.1: Sequences
12.2: Arithmetic Sequences
12.3: Geometric Sequences
Mathxl: 11,15 ; Text: All 7-16 (except 11,15)
Mathxl: None! The graphs are multiple choice, and mathxl is a bit picky as to how you
enter equations, so I am assigning this section from the text. (Use Mathxl’s Study plan if
you need help).
Text: All 4-7; Odds 15-19, 21d, 21e; HW Addendum to be handed out in class.
Mathxl: Odds 17,19,23-35; Text: 13,15,21
Mathxl: Odds 9-25; Text: None
Mathxl: Odds 9-17; Text: 19,23,27,35-45,49,53,67-71,75
Mathxl: 11,13,23,31,33,35,37; Text: 11,15,39,45,49,53,59,63
Mathxl: 7,9,17,19,21,23; Text: Odds 35-41,47,51,57,61
Mathxl: Odds 1-17; Text: None
Mathxl: 7-11,15-17,27-33,37,41,45-51; Text: 13,35,57a&b, 59a,b,d
Mathxl: 5,7,13,15,31,47,51; Text: 9,21,37,59,63a,65,67a,67b
Mathxl: Odds 9,19-21,25,29,33-41,47,49; Text: 13,17,31,51
Mathxl: Odds 21-25,29-33,41-43,47-49,55; Text: Odds 9,11,33-37,45,51
Mathxl: Odds 17,23-25,31-35,39; Text: Odds 9,13,37,41
This section is self-study and will not be covered in class. It offers alternatives to
finding the area of a triangle other than A = 1/2*bh. (using SAS or SSS.
Mathxl: Odds 13-19,23,27,33,35; Text: Odds 5-11
Mathxl:Odds 11,19,27,31,37,39,45,47,51-55,59,65,67-75,79
Text: Odds 13-17,21-25,33,35,41,43,49,57,61,77
There’s polar graph paper loaded on my HCC website under MAC 1147.
Mathxl: 13,17,19; Text: 15,21,29,35,37,45,49,53,55,69
For graphing the polar equations 37-69, just complete a table of values. I do not
expect you to recognize these in advance, test for symmetry, etc.
Mathxl: Odds 9,13,15,19,23,27-33,37-43,59-63;
Also, Section 9.5: 25,31,33 are assigned using methods of 9.4.
9.4 HW Text: 7,11,17,21,25,35,55,57,69
Mathxl: none; Text: Odds 7-15 (part a only)
Mathxl: Odds 11,17,19,23-29,35,37,43,47,49,55-59,63,69,73
Text: Odds 21,31,33,39,41,45,51,53
Mathxl: Odds 17,21,23,29-35,39-47,55,59-61,69,71,81
Text: Odds 13,15,19,25,37,51,57,77
Mathxl: Odds 17,19,23-27,31,39-43; Text: Odds 13,15,29,33,45-49,53
11.1 covers solving systems of equations by substitution and/or elimination. This is
review material, and I expect you to already know it in preparation for 11.6. If you
need a refresher, go to Study Plan, Chapter 11, Section 1, and look at exercises
9,17,19,23,25,29,35,67
Mathxl: 9,15,19,39,85; Text: 5,11,33,61,64,77,79
Mathxl: 7,15,17,21,37,39,47; Text: 5,11,25,43,49
Mathxl: 7,9,11,15,17,23; Text: 5,13,21,35
To be announced.
To be announced.
To be announced.
MAC 1147 Course Objectives
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Show extended knowledge of objectives presented in prerequisite courses including the use of
functional notations, finding function values, and evaluating derived functions and
compositions.
Recognize and graph functions (polynomial, rational, radical, absolute value, piecewise
defined, exponential, and logarithmic); determine their domain and range. Determine the
intervals on which the function is increasing, decreasing, or constant. Verify using a graphing
calculator.
Solve polynomial and rational inequalities. Express the solution as an inequality; write the
solution set in interval notation; graph the solution set. Verify, using a graphing calculator.
Solve radical equations, identifying those solutions which are extraneous.
Know and use the definition of absolute value; solve absolute value equations and inequalities.
Graph the solution set of inequalities. Verify using a graphing calculator.
Solve equations that are quadratic in form, identifying those solutions which are extraneous.
Verify using a graphing calculator.
Apply the translation of axes rule, the stretching/shrinking rule, and the x- and y-axis reflection
rules when graphing functions. Verify using a graphing calculator.
Determine which functions are one-to-one; find the inverse of those functions which are oneto-one; restrict the domain of those functions that are not one-to-one and find the inverse of
those restricted functions. Verify using a graphing calculator.
Solve problems involving direct, joint, and inverse variation with and without the words direct
or inverse.
Manipulate expressions involving rational and negative exponents. Solve exponential
equations. Verify using a graphing calculator.
Solve word problems that lead to polynomial, rational, or exponential functions as a
mathematical model. Where appropriate or necessary, use a graphing calculator.
Solve problems involving logarithms; change from logarithmic form to exponential form and
vice versa.
Solve exponential and logarithmic equations using the properties of logarithmic and
exponential functions.
Find complex zeros of polynomials of degree higher than two using theorems from the theory
of equations. Verify real zeros using a graphing calculator.
Find solutions of systems of equations which are nonlinear that require elimination and/or
substitution. Verify using a graphing calculator.
Find solutions of systems of at least three linear inequalities in two variables by graphing.
Identify arithmetic, geometric, and harmonic sequences and series; solve problems involving
them. Evaluate expressions involving summations notation.
Perform operations of multiplication and division with complex numbers in rectangular form.
Know and be able to use the Binomial Theorem. Find the rth term of a binomial expansion.
Use the algebra of matrices. Evaluate determinants of order two or three.
Understand the use of Mathematical Induction in proving that statements are true or not true
for positive integers.
Find a quadratic equation with real coefficients given an irrational or an imaginary root.
Solve a quadratic equation when “a”, “b”, and/or “c” are literal rather than numerical.
Define circle, parabola, ellipse, and hyperbola; recognize their equations, their properties, and
sketch their graphs.
Graph conic sections using translation of axes. Verify using a graphing calculator.
26. To use a calculator to convert decimal degrees to degrees, minutes, and seconds, and vice
versa.
27. To use the concepts of angle, degree, minute, second, radian, arc length, unit circle, terminal
point of an arc with a given arc length, and central angle.
28. To convert radian measure to degree measure and vice versa.
29. To find arc length and angular velocity.
30. To use the Pythagorean theorem with right triangles.
31. To find the six trigonometric functions of an acute angle of a right triangle using a calculator.
32. To identify missing angles or sides of right triangles.
33. To solve applications using right triangles.
34. To find the horizontal and vertical components of a vector in a plane.
35. To find the magnitude and direction of a vector.
36. To find the resultant of a sum of vectors.
37. To solve vector applications.
38. To find a vector given its magnitude and direction.
39. To identify all six trigonometric functions of any angle using the concept of co-terminal and
reference angles.
40. To apply the Law of Sines or Law of cosines to solve missing parts of an oblique triangle or an
application involving an oblique triangle.
41. To find the area of an oblique triangle.
42. To know the definitions of the six trigonometric functions of a real number using the unit
circle.
43. To identify the six trigonometric functions of the special angles or radians; 0 or 0,
30 or  6, 45 or  4, 60 or  3, 90 or  2, .
44. To use identities describing relationships among six trigonometric functions, addition
formulas, double angle formulas, half-angle formulas.
45. To prove identities, and verify with a graphing calculator.
46. To solve trigonometric equations algebraically and graphically.
47. To graph the six trigonometric functions and variations of these giving period, amplitude, and
phase shift. Verify using a graphing calculator.
48. To find the value of inverse trigonometric functions.
49. To identify characteristics of the inverse trigonometric functions.
50. To graph inverse trigonometric functions, specifying their domain and range. Verify with a
graphing calculator.
51. To convert the trigonometric form of a complex number to rectangular form and vice versa.
52. To use DeMoivres’ Theorem to find the positive integer powers of a complex number.
53. To find nth roots of a complex number.
54. To plot points in a polar coordinate system.
55. To convert polar coordinates and equations to rectangular and vice versa.
56. To graph polar curves.
57. To find dot product of vectors.
58. To recognize and graph the curve defined by a vector-valued function; determine the
corresponding parametric equation of the curve.
59. To solve word problems involving simple harmonic motion and other periodic phenomena.
60. To describe a vector in three dimensions and find the cross product of two vectors in three
dimensions.