# Sylabii for Calculus & Precalculus

**Honors Calculus**

Calculus is the study of how things change, and represents a college-level mathematics course and is the usual first-year mathematics course for those students who are pursuing careers in science, mathematics, and engineering fields. It provides a framework for modeling systems in which there is change, and a way to deduce the predictions of such models.

The subject of Calculus stands at the gateway to much of higher mathematics, and to applications in many different fields such as physics, biology, chemistry, economics, business, and statistics. In Arithmetic, *operations *are carried out on numbers; in Algebra, *operations* are carried out on symbols that stand for numbers; whereas in Calculus *operations* are carried out on functions that represent the relationships between two variable quantities. Some integration techniques of Calculus date back to the time of the ancient Greek world, but what we now know as Calculus was developed independently by Isaac Newton in 1666 and Gottfried Wilhelm Leibniz in 1675. Newton called his invention the method of *fluxions*, which he developed at the same time he was developing the foundations of the branch of Physics known as Mechanics. The symbolic notation of Calculus however is that introduced by the German Leibniz!

Students at Comfort High School must have successfully passed the Precalculus course. It is an honors-level class. Students enrolled are eligible to take the AP Exam in Calculus AB should they desire, but are responsible for the testing fee which last year wass $ 83.00.

Attached is a sample outline of topics used in our Calculus course.

**Major Assessments:**

Two to Three Tests each six weeks over the topics of that six-week period .

Five to Six Quizzes each six weeks which assess and reassess topics taught to that date since the beginning of the course.

**Study References:**

Students will be expected to maintain a notebook of the concepts, definitions, and examples discussed for each daily lesson. Additionally, students will be issued a textbook for referencing and additional examples. All assignments are returned to students after the teacher has checked for completion; and these assignments can serve as additional study guides, as most quiz and test problems are modeled after the exercises students have completed on the daily assignments.

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**Grading System:**

- Daily Work................ 50 % B. Tests........................ 50%

- Quizzes 40 %
- Homework 10 %

Note: Late homework in never accepted as the purpose of the assignment is to reinforce concepts taught daily. If a Six-Week Exam is given, the exam will comprise no more than 20% of the final grade for the six weeks. The Semester Exam will comprise 25% of the Semester Grade.

**Tutoring Time: **

This year the student will need to contact the teacher to set up a time for additional help and tutoring.

**Conference Period:** 4__ ^{th}__ Period

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**Discipline Plan:**

Students must come ready to work each day. All materials, including the assignment, must be brought to class each day. Each student has received a copy of the Class Rules and the various consequences for off-task behaviors -- warnings, parental letters, detentions, and principal referrals. Cheating will result in a zero for the test, quiz, or assignment in question; a “U” in conduct for that six-week period; and a principal referral.

**Miscellaneous:**

Students need a scientific calculator at least; graphing calculators are recommended and are required for the student taking the AP Examination. Students are expected to graph functions without the aid of a graphing calculator, and will be required to show proficiency in graphing functions without the aide of this device on some quizzes and tests throughout the school year.

**Contact Information:**

CHS Office Phone: 830-995-6430, Ext# 231

CHS Address: P.O. Box 280, Comfort, Texas 78013

e-mail address: real@comfortisd.net

Grade Levels: Honors & Regular Program Grades 11 and 12

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**Precalculus**

**Description:**

This course is designed to extend the student’s learning in reference to the analysis, use, and application of functional concepts in mathematics. There is a significantly large emphasis on the student’s understanding of trigonometric, polynomial, exponential, and logarithmic functions; sequences, series, and the introductory concepts of limits; and the general discussions as they relate to the fundamental properties of the locus of an equation.

**Learner Outcomes:**

The student will be able to:

- solve linear, higher degree polynomial, absolute value, radical, exponential, logarithmic, trigonometric, polar, and algebraic rational equations and inequalities.
- graph, analyze, and apply higher degree polynomial, absolute value, radical, exponential, logarithmic, trigonometric, polar, algebraic rational, and piecewise-defined functions.
- perform the arithmetic of the complex number system expressed in both the rectangular and trigonometric forms of the complex numbers.
- determine the inverse of a function and relate its graph to the original function.
- analyze and graph quadratic relations or functions traditionally identified as conic sections
- perform the arithmetic of two or more functions, and establish its domain and range.
- determine the composition of two functions, and establish its domain and range.
- solve stated problems requiring the application and representation of linear, quadratic, exponential, logarithmic, and rational algebraic functions.

**Topical Sequence:**

__[TEKS]__

**1 ^{st}**

**Six Weeks:**

Review of Functions

Mathematical Models & Periodic Functions

Fundamentals of Trigonometry

Definition, Application, and Graphs of the Sine Function

Solution of Right and Oblique Triangles

Solution of Trigonometric Equations

Definition, Application, and Graphs of the Cosine Function

**2 ^{nd} Six Weeks:**

Solution of Oblique Triangles and Trigonometric Equations

Problem Solving Using Trigonometry

Definition, Application, and Graphs of the Tangent Function

Definition, Application, and Graphs of the Secondary Trigonometric Functions

Fundamental Identities -- Simplification of Trigonometric Expressions and the

Proving of Trigonometric Identities

Sum and Difference of Two Angles Formulae

Double Angle and Half-Angle Formulae

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**3 ^{rd} Six Weeks:**

Solving Trigonometric Equations

Graphs of Trigonometric Functions with All Major Parameter Changes

Writing the Equations of Sinusoids

General Inverse Trigonometric Relations

Trigonometric Form and the Arithmetic of Complex Numbers

Inverse Trigonometric Functions

General Discussions of Relations and Functions

** [TEKS]{TAKS}**

**4 ^{th} Six Weeks:**

DeMoivre’s Theorems and the Roots of Numbers

Linear Equations and Inequalities

Polygonal Convex Sets and Linear Programming

Set Theory -- Conjunctions, Disjunctions, Negations

Theory of Conditionals and the Nature of Proof

Sinusoidal Functions as Mathematical Models

Absolute Value

The Arithmetic of Functions

The Theory of Polynomial Functions and Equations

**5 ^{th} Six Weeks:**

Curve Sketching & Continuity

Mathematical Induction

Sequences and Series

Binomial Theorem [

Limits and Sums of Infinite Series

Introductory Theory of the Derivative of a Function

e, the Natural Number, and Exponential Functions

Composition of Functions

The Inverse of a Function

**6 ^{th} Six Weeks: **

Logarithms and Logarithmic Functions

Polar Coordinates

Discussion of Loci

Analysis of Conic Sections

**Major Assessments:**

Two to Three Tests each six weeks over the topics of that six-week period .

Five to Six Quizzes each six weeks which assess and reassess topics taught to that date since the beginning of the course.

**Study References:**

Students will be expected to maintain a notebook of the concepts, definitions, and examples discussed for each daily lesson. Additionally, students will be issued a textbook for referencing and additional examples. All assignments are returned to students after the teacher has checked for completion; and these assignments can serve as additional study guides, as most quiz and test problems are modeled after the exercises students have completed on the daily assignments.

** **

**Grading System:**

- Daily Work............................... 50 % B. Tests....................................... 50%

- Quizzes 40 %
- Homework 10 %

Note: Late homework in never accepted as the purpose of the assignment is to reinforce concepts taught daily. If a Six-Week Exam is given, the exam will comprise no more than 20% of the final grade for the six weeks. The Semester Exam will comprise 25% of the Semester Grade.

**Tutoring Time: **

This year the student will need to contact the teacher to set up a time for additional help and tutoring.

**Conference Period:** 4^{th} Period

**Discipline Plan:**

Students must come ready to work each day. All materials, including the assignment, must be brought to class each day. Each student has received a copy of the Class Rules and the various consequences for off-task behaviors -- warnings, parental letters, detentions, and principal referrals. Cheating will result in a zero for the test, quiz, or assignment in question; a “U” in conduct for that six-week period; and a principal referral.

**Miscellaneous:**

Students need a scientific calculator at least; graphing calculators may be used, but students will be required to show proficiency in graphing functions without the aide of this device.

**Contact Information:**

CHS Office Phone: 830-995-6430, Ext# 231

CHS Address: P.O. Box 280, Comfort, Texas 78013

e-mail address: real@comfortisd.net