COURSE DESCRIPTION:
The Pre-Calculus course is intended to provide a solid preparation for the student who intends to continue his study of mathematics at the college level. This full year course includes a thorough study of trigonometry plus extensive coverage of topics essential to the study of calculus, namely: limits of functions, limits of sequences, function, derived function (derivative), logarithmic functions, exponential functions, inverse functions, sequences, and curve sketching.

INSTRUCTIONAL MATERIALS:
TEXT: Precalculus with Limits A Graphing Approach , Larson, Hostetler and Edwards, Houghton Mifflin Company, 2005.

COURSE OBJECTIVES:
Upon completion of the course, the student should be able to:
1. Plot points in the Cartesian plane and sketch scatter plots
2. Use the Distance Formula to find the distance between two points
3. Use the Midpoint Formula to find the midpoint of a line segment
4. Find the equation of a circle
5. Translate points in the plane
6. Sketch graphs of equations by point plotting
7. Graph equations using a graphing utility
8. Use graphs of equations to solve real-life problems
9. Solve linear equations
10. Find x- and y-intercepts of graphs of equations
11. Find solutions of equations graphically
12. Find the points of intersection of two graphs
13. Solve polynomial equations
14. Solve equations involving radicals, fractions, or absolute values
15. Use properties of inequalities to solve linear inequalities
16. Solve inequalities involving absolute values
17. Solve polynomial inequalities
18. Solve rational inequalities
19. Use inequalities to model and solve real-life problems
20. Use line plots to order and analyze data
21. Use histograms to represent frequency distributions
22. Use bar graphs to represent and analyze data
23. Use line graphs to represent and analyze data
24. Find the slopes of lines
25. Write linear equations given points on lines and their slopes
26. Use slope-intercept forms of linear equations to sketch lines
27. Use slope to identify parallel and perpendicular lines
28. Decide whether relations between two variables represents a function
29. Use function notation and evaluate functions
30. Find the domains of functions
31. Use functions to model and solve real-life problems
32. Evaluate difference quotients
33. Find the domains and ranges of functions and use the Vertical Line Test for functions
34. Determine intervals on which functions are increasing, decreasing, or constant
35. Determine relative maximum and relative minimum values of functions
36. Identify and graph step functions and other piecewise-defined functions
37. Identify even and odd functions
38. Recognize graphs of common functions
39. Use vertical and horizontal shifts and reflections to graph functions
40. Use nonrigid transformations to graph functions
41. Add, subtract, multiply, and divide functions
42. Find compositions of one function with another function
43. Use combinations of functions to model and solve real-life problems
44. Find inverse functions informally and verify that two functions are inverse functions of each other
45. Use graphs of functions to decide whether functions have inverse functions
46. Determine if functions are one-to-one
47. Find inverse functions algebraically
48. Construct scatter plots and interpret correlation
49. Use scatter plots and a graphing utility to find linear models for data
50. Analyze graphs of quadratic functions
51. Write quadratic functions in standard form and use the results to sketch graphs of functions
52. Find minimum and maximum values of functions in real-life applications
53. Use transformations to sketch the graphs of polynomial functions
54. Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions
55. Find and use zeros of polynomial functions as sketching aids
56. Use the Intermediate Value Theorem to help locate zeros of polynomial functions
57. Use long division to divide polynomials by other polynomials
58. Use synthetic division to divide polynomials by binomials of the form (x-k)
59. Use the Remainder and Factor Theorems
60. Use the Rational Zero Test to determine possible rational zeros of polynomial functions
61. Use Descartes’s Rule of Signs and the Upper and Lower Bound Rules to find zeros of polynomials
62. Use the imaginary unit i to write complex numbers
63. Add, subtract and multiply complex numbers
64. Use complex conjugates to write the quotient of two complex numbers in standard form
65. Plot complex numbers in the complex plane
66. Use the Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function
67. Find all zeros of polynomial functions, including complex zeros
68. Find conjugate pairs of complex zeros
69. Find zeros of polynomials by factoring
70. Find the domain of rational functions
71. Find horizontal and vertical asymptotes of graphs of rational functions
72. Use rational functions to model and solve real-life problems
73. Analyze and sketch graphs of rational functions
74. Sketch graphs of rational functions that have slant asymptotes
75. Use rational functions to model and solve real-life problems
76. Recognize, evaluate, and graph exponential and logarithmic functions
77. Rewrite logarithmic functions with different bases
78. Use properties of logarithms to evaluate, rewrite, expand, or condense logarithmic expressions
79. Solve exponential and logarithmic equations
80. Use exponential growth models, exponential decay models, Gaussian models, logistic models, and logarithmic models to solve real-life problems
81. Fit exponential, logarithmic, power, and logistic models to sets of data
82. Describe an angle and convert between degree and radian measure
83. Identify a unit circle and describe its relationship to real numbers
84. Evaluate trigonometric identities
85. Sketch graphs of trigonometric functions
86. Evaluate inverse trigonometric functions
87. Evaluate the compositions of trigonometric functions
88. Use trigonometric functions to model and solve real-life problems
89. Use the fundamental trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions
90. Verify trigonometric identities
91. Use standard algebraic techniques and inverse trigonometric functions to solve trigonometric equations
92. Use sum and difference formulas, multiple-angle formulas, power-reducing formulas, half-angle formulas, and product-to-sum formulas to rewrite and evaluate trigonometric functions
93. Use the Law of Sines and the Law of Cosines to solve oblique triangles
94. Find the areas of oblique triangles
95. Represent vectors as directed line segments and perform mathematical operations on vectors
96. Find direction angles of vectors
97. Find the dot product of two vectors and use the properties of the dot product
98. Multiply and divide complex numbers written in trigonometric form
99. Find powers and nth roots of complex numbers
100. Solve systems of equations by Gaussian elimination, Gauss-Jordan elimination, by
using inverse matrices, by Cramer’s Rule, and graphically
101. Recognize a linear system in row-echelon form and use back-substitution to solve
the system
102. Solve nonsquare systems of equations
103. Use systems of equations to model and solve real-life problems
104. Write matrices, identify their order, and perform elementary row operations
105. Perform operations with matrices
106. Find inverses of matrices
107. Find the determinants of square matrices
108. Use the sequence, factorial, and summation notation to write the terms and sums of
sequences
109. Recognize, write, and use arithmetic sequences and geometric sequences
110. Use the Binomial Theorem and Pascal’s Triangle to calculate binomial coefficients
and write binomial expansions
111. Estimate limits and use properties and operations of limits
112. find limits by direct substitution and by using the dividing out and rationalizing
techniques
113. Approximate slopes of tangent lines, use the limit definition of slope, and use
derivatives to find slopes of graphs.

STUDENT RESPONSIBILITIES:
1. Be prepared for class every day. This means, not only bring yourself to class but your textbook, notebook, pencil, completed homework, etc. You WILL NOT be allowed to leave the classroom to get a book, homework, pencil, calculator, etc. So remember all necessary materials and have them on your desk ready to go at the start of class.

2. Your success is a direct result of your classroom attitude. If you believe in your ability and make a conscientious effort daily, your grades will reflect this. Do not miss classes. Missing even one class can put you behind the course by at least two classes. Do not schedule special conferences or guidance meetings for math class.

3. The only way to learn mathematics is to DO mathematics. Learning is an active process. Therefore, PRACTICE what you learn in class by doing all assignments.

4. ALWAYS take notes in class. You are responsible for ANYTHING that appears on the board. READ the notes given that day before you begin your homework. READ the notes AGAIN as you study for tests and quizzes.

5. HOMEWORK / ASSIGNMENTS: Homework will be assigned DAILY in the form of either readings or problems. Please make sure that all homework is done in PENCIL on loose leaf. WRITE on ONE SIDE of the page only and make sure to label each homework assignment according to the date and page number.
Homework will be collected DAILY and checked for completion. I will periodically grade random problems. Daily homework will be assigned a grade out of 4 points. If homework is turned in late the highest grade possible will be 2 points. Occasionally I will grade the homework more rigorously and the score will be out of 20 points. We will go over any questions on homework at the start of the class period that it is due. Homework will be collected after we have gone over any questions in class. Therefore, there is no reason why you should not receive a perfect score on homework if you have fulfilled your responsibilities by asking questions and copying down corrections.
Always do the homework. If homework questions are not able to be answered, put an asterisk besides those that gave you difficulty and ASK questions about those problems in the next class. YOU MUST DO THE WORK WHEN IT IS ASSIGNED! NEVER FALL BEHIND.

6. Work all homework problems with care and persistence. You may work with other students in class to pool your knowledge in completing the homework assignments. This does not mean that you can copy someone else’s homework.

CLASS RULES:
1. If you are going to be late to class get a note. If you do not have a note, go to the office and get a late pass.
2. Raise your hand to be recognized.
3. Be COURTEOUS and SHOW RESPECT for your teacher as well as your fellow classmates. DO NOT TALK WHILE SOMEONE ELSE IS SPEAKING. Disrespect to anyone at anytime will not be tolerated.
4. Please do not call out or get out of your seat without permission during class. NOTE: You WILL NOT be allowed to leave the classroom once the bell rings to get a book, homework, pencil, calculator, etc. that you forgot. Be aware of this rule. Do NOT disrupt the class by asking.
5. HONESTY IS THE ONLY POLICY. Copying others work is unacceptable.
6. During tests and quizzes, I will not answer any questions pertaining to material on the test or quiz that you should have studied. If you believe there is a typographical error on the paper, raise your hand and I will come to you and check.

MAKE UP POLICY:
If you do miss class due to illness or required activities, contact another student or check the website to learn what material was covered and what homework was assigned. IT IS YOUR RESPONSIBILITY.
- If you happen to miss a TEST as a result of your absence, you have 1 week from the day you return to make up the test. You must see me on the DAY YOU RETURN to schedule a make up time. Failure to see me to schedule a time will result in a ZERO for that test.
- If you happen to miss a QUIZ as a result of your absence, you must make up the quiz on the day you return. CLASS TIME IS NOT MAKE UP TIME!!!
- Missed homework (due to absence only) must be turned in to me on the day following your return unless a previous arrangement was scheduled with me.

GRADING:
The grading scale of this course follows the grading policy of Salesianum School ( 7 pt. scale with pluses as stated in the handbook ). Your marking period grade in this course will be determined on a percentage of total points earned in the following categories:
- chapter tests – 60%
- short quizzes – 20%
- individual/group projects – (point value varies, will count as part of tests)
- homework (daily and graded homework) – 20%
End of the year grades will be determined based on your final average made up of your 4 quarter grades as well as the final assessment.
(the above may change as situations merit)

USEFUL INFORMATION:
1. Absence: All students are responsible for making up missed work.
three Ways to Find out what you missed: 1.) call another student, 2.) look on netclassroom, or 3.) e-mail me at: tfleetman@salesianum.org

2. I am available in the mornings before school and after school until 3pm in room A208. Please see me or schedule an appointment with me if you are having difficulty.

3. Contact: easiest way is through e-mail or you can call (302)654-2495 Ext. 223.