Southside High School
HONORS PRECALCULUS
Mr. Howard

Textbook: Precalculus with Limits by Larson Hostetler and Edwards

Units: 1

Purpose:
Precalculus is the study of mathematics that focuses on the development of the students’ ability to understand and apply the study of functions and advanced mathematical concepts to solve problems. The course will include an in-depth study of polynomial, exponential, rational, logarithmic and trigonometric functions. Other topics include sequences, series, vectors, conic sections, parametric equations and polar curves. The honors course includes two units past the regular level course. Therefore, the honors course will proceed at a faster pace and will include problems that require a greater depth of understanding. Emphasis is on active participation through modeling, technology lab activities, group activities and communication in mathematics.

Course Outline
Standard PC-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.
Indicators
PC-1.1 Communicate knowledge of algebraic and trigonometric relationships by using mathematical terminology appropriately.
PC-1.2 Connect algebra and trigonometry with other branches of mathematics.
PC-1.3 Apply algebraic methods to solve problems in real-world contexts.
PC-1.4 Judge the reasonableness of mathematical solutions.
PC-1.5 Demonstrate an understanding of algebraic and trigonometric relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic).
PC-1.6 Understand how algebraic and trigonometric relationships can be represented in concrete models, pictorial models, and diagrams.
PC-1.7 Understand how to represent algebraic and trigonometric relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs).

Standard PC-2: The student will demonstrate through the mathematical processes an understanding of the characteristics and behaviors of functions and the effect of operations on functions.
Indicators
PC-2.1 Carry out a procedure to graph parent functions (including y = xn, y = loga x, y = ln x, y = , y = ex, y = ax, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).
PC-2.2 Carry out a procedure to graph transformations (including –f(x), a • f(x), f(x) + d,
f(x - c), f(-x), f(b • x), f(x), and f(x)) of parent functions and combinations of transformations.
PC-2.3 Analyze a graph to describe the transformation (including –f(x), a • f(x), f(x) + d,
f(x - c), f(-x), f(b • x), f(x), and f(x)) of parent functions.
PC-2.4 Carry out procedures to algebraically solve equations involving parent functions or transformations of parent functions (including y = xn, y = loga x, y = ln x, y = ,
y = ex, y = ax, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).
PC-2.5 Analyze graphs, tables, and equations to determine the domain and range of parent functions or transformations of parent functions (including y = xn, y = loga x, y = ln x, y = , y = ex, y = ax, y = sin x, y = cos x, y = tan x, y = csc x, y = sec x, and y = cot x).
PC-2.6 Analyze a function or the symmetry of its graph to determine whether the function is even, odd, or neither.
PC-2.7 Recognize and use connections among significant points of a function (including roots, maximum points, and minimum points), the graph of a function, and the algebraic representation of a function.
PC-2.8 Carry out a procedure to determine whether the inverse of a function exists.
PC-2.9 Carry out a procedure to write a rule for the inverse of a function, if it exists.


Standard PC-3: The student will demonstrate through the mathematical processes an understanding of the behaviors of polynomial and rational functions.
Indicators
PC-3.1 Carry out a procedure to graph quadratic and higher-order polynomial functions by analyzing intercepts and end behavior.
PC-3.2 Apply the rational root theorem to determine a set of possible rational roots of a polynomial equation.
PC-3.3 Carry out a procedure to calculate the zeros of polynomial functions when given a set of possible zeros.
PC-3.4 Carry out procedures to determine characteristics of rational functions (including domain, range, intercepts, asymptotes, and discontinuities).
PC-3.5 Analyze given information to write a polynomial function that models a given problem situation.
PC-3.6 Carry out a procedure to solve polynomial equations algebraically.
PC-3.7 Carry out a procedure to solve polynomial equations graphically.
PC-3.8 Carry out a procedure to solve rational equations algebraically.
PC-3.9 Carry out a procedure to solve rational equations graphically.
PC-3.10 Carry out a procedure to solve polynomial inequalities algebraically.
PC-3.11 Carry out a procedure to solve polynomial inequalities graphically.

Standard PC-4: The student will demonstrate through the mathematical processes an understanding of the behaviors of exponential and logarithmic functions.
Indicators
PC-4.1 Carry out a procedure to graph exponential functions by analyzing intercepts and end behavior.
PC-4.2 Carry out a procedure to graph logarithmic functions by analyzing intercepts and end behavior.
PC-4.3 Carry out procedures to determine characteristics of exponential functions (including domain, range, intercepts, and asymptotes).
PC-4.4 Carry out procedures to determine characteristics of logarithmic functions (including domain, range, intercepts, and asymptotes).
PC-4.5 Apply the laws of exponents to solve problems involving rational exponents.
PC-4.6 Analyze given information to write an exponential function that models a given problem situation.
PC-4.7 Apply the laws of logarithms to solve problems.
PC-4.8 Carry out a procedure to solve exponential equations algebraically.
PC-4.9 Carry out a procedure to solve exponential equations graphically.
PC-4.10 Carry out a procedure to solve logarithmic equations algebraically.
PC-4.11 Carry out a procedure to solve logarithmic equations graphically.


Standard PC-5: The student will demonstrate through the mathematical processes an understanding of the behaviors of trigonometric functions.
Indicators
PC-5.1 Understand how angles are measured in either degrees or radians.
PC-5.2 Carry out a procedure to convert between degree and radian measures.
PC-5.3 Carry out a procedure to plot points in the polar coordinate system.
PC-5.4 Carry out a procedure to graph trigonometric functions by analyzing intercepts, periodic behavior, and graphs of reciprocal functions.
PC-5.5 Carry out procedures to determine the characteristics of trigonometric functions (including domain, range, intercepts, and asymptotes).
PC-5.6 Apply a procedure to evaluate trigonometric expressions.
PC-5.7 Analyze given information to write a trigonometric function that models a given problem situation involving periodic phenomena.
PC-5.8 Analyze given information to write a trigonometric equation that models a given problem situation involving right triangles.
PC-5.9 Carry out a procedure to calculate the area of a triangle when given the lengths of two sides and the measure of the included angle.
PC-5.10 Carry out a procedure to solve trigonometric equations algebraically.
PC-5.11 Carry out a procedure to solve trigonometric equations graphically.
PC-5.12 Apply the laws of sines and cosines to solve problems.
PC-5.13 Apply a procedure to graph the inverse functions of sine, cosine, and tangent.
PC-5.14 Apply trigonometric relationships (including reciprocal identities; Pythagorean identities; even and odd identities; addition and subtraction formulas of sine, cosine, and tangent; and double angle formulas) to verify other trigonometric identities.
PC-5.15 Carry out a procedure to compute the slope of a line when given the angle of inclination of the line.

Standard PC-6: The student will demonstrate through the mathematical processes an understanding of the behavior of conic sections both geometrically and algebraically.
Indicators
PC-6.1 Carry out a procedure to graph the circle whose equation is the form .
PC-6.2 Analyze given information about the center and the radius or the center and the diameter to write an equation of a circle.
PC-6.3 Apply a procedure to calculate the coordinates of points where a line intersects a circle.
PC-6.4 Carry out a procedure to graph the ellipse whose equation is the form .
PC-6.5 Carry out a procedure to graph the hyperbola whose equation is the form .
PC-6.6 Carry out a procedure to graph the parabola whose equation is the form .

Materials Needed:
• Notebook with plenty of loose leaf paper and graph paper.
• TI-83 or TI-83 plus graphing calculator (classroom set available).
• #2 pencils (colored pencils optional)

Classroom Expectations:
1. Bring all materials to class and use them accordingly.
2. Keep hands, feet, objects, and comments to yourself.
3. Obey all rules in the student Handbook.

If you choose to not do what is expected:
1st Offense: Warning
2nd Offense: Parent contact
3rd Offense: Referral and parent phone call
**** Severe disruptions will result in an immediate office referral ****

Attendance:
It is extremely important that you attend class each day! Missed discussions and explanations are almost impossible to make up. If you are absent, you are responsible for making up all work missed. If you know that you will be absent, please get assignments beforehand. State law mandates that any student exceeding 10 unexcused absences may be denied course credit.

Grading:
Homework will be given periodically on recently covered material. Though homework will not be checked extremely rigorously, an honest attempt at all problems assigned is expected and all work should be shown.
Classwork will be any work assigned and attempted during class, such as group work, labs, quizzes, and various other assignments. Classwork is expected to be correct since assistance will be provided before and/or during the assignment.
Major grades will usually occur at the end of each chapter or unit. Tests may be cumulative on what has been covered up to that point. Alternative assessments, such as presentations or reports, may be counted as major grades.
Participation in class is expected. Any activity that is not related to the lesson will result in a reduction of grade. Participation includes completing the Problem of the day and journal entries. A problem of the day will be assigned at the beginning of most classes as a review of a previous lesson.
A journal entry will be made at the end of most classes as a review of the day’s objectives.
The problem of the day and journal should be kept together and will be checked periodically.
Exams will be given on all material covered at the end of each semester. Exams will count as 20% of the semester grade as per the student parent handbook.

Unit Grading Weights:
Major grades ------------------------------------- 40%
Classwork/Homework -------------------------- 50%
Problem of the Day/Journal ------------------- 10%
Each Quarterly Grade will consist of the straight average of Unit grades during the quarter. There will be six to eight unit grades each quarter.

If you need extra help, do not hesitate to ask! I will be happy to arrange a time to help you. I am available after school on most Monday, Tuesday, and Thursday afternoons and during lunch on most days. If problems occur, do not wait to seek help.