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# STARK STATE COLLEGE GENERAL SYLLABUS

## Course Information

Course Name: Precalculus

Course Number: MTH135

## Required Materials

Textbook(s): Precalculus- A Right Triangle Approach, 5th edition; Ratti, McWaters, Skrzypek, Bernards, & Fresh; Pearson, 2023

ISBN (Instant Access): 9780137519217

Required Readings: None

Additional Materials: A graphing calculator is required. The math department supports the TI 83 or 84. The instructor reserves the right to limit use of the graphing calculator for specific topics on tests and quizzes. Specific models prohibited: Casio CFX-9970G, Casio Algebra fx 2.0, Hewlett-Packard HP40G, TI-89/92 and NSpire

## Course Outline/Calendar

The date of coverage and order of coverage may be modified based on the faculty member and events beyond the control of faculty members that interfere with class times and teaching.

## 16 Week Calendar


<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>1</td><td style='text-align: center; word-wrap: break-word;'>Ch 2 Graphs and Functions• Symmetries of graphs &amp; equation of a circle• Relations and functions• Properties of functions• A library of common functions• Transformations of functions</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>2</td><td style='text-align: center; word-wrap: break-word;'>Ch 2 Graphs and Functions• Combining functions; composite functions• Inverse functionsCh 3 Polynomial and Rational Functions• Polynomial/Power functions and end behavior• Zeros and turning points• Graphing polynomial functions</td></tr></table>

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<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'></td><td style='text-align: center; word-wrap: break-word;'>Test: Chapter 2</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>3</td><td style='text-align: center; word-wrap: break-word;'>Ch 3 Long division and synthetic division
• Remainder and Factor Theorems
• Descartes’ Rule of Signs
• Zeros of polynomials: Bounds on real zeros
• Zeros of polynomials: Conjugate pairs theorem</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>4</td><td style='text-align: center; word-wrap: break-word;'>Ch 3 Polynomial and Rational Functions
• Find the domain of a rational function.
• Analyze graphs of rational functions.
• Find horizontal and vertical asymptotes.
• Graph rational functions
• Solve quadratic and polynomial inequalities.
• Solve rational inequalities.
• Test: Chapter 3</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>5</td><td style='text-align: center; word-wrap: break-word;'>Ch 4 Exponential and Logarithmic Functions
• Exponential and Logarithmic functions
• The natural exponential function
• Properties of logarithms
• Exponential and logarithmic equations
• Rules of Logarithms
• Test: Chapter 4</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>6</td><td style='text-align: center; word-wrap: break-word;'>Ch 10 The Conic Sections
• The parabola and its applications
• The ellipse and its applications
• The Hyperbola and its applications
• Test: Chapter 10</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>7</td><td style='text-align: center; word-wrap: break-word;'>Ch 11 Further Topics in Algebra
• Sequences and series
• Arithmetic and Geometric sequences and series</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>8</td><td style='text-align: center; word-wrap: break-word;'>Ch 11 Sequences and Series
• Test: Chapter 11
• Exam: Midterm</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>9</td><td style='text-align: center; word-wrap: break-word;'>Ch 5 Trig Functions
• Angles and angle measure
• Right angle trigonometry
• Trigonometric functions; the unit circle
• Trigonometric functions of any angle;
• The unit circle
• Graphs of the trigonometric functions
• Test: Chapter 5</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>10</td><td style='text-align: center; word-wrap: break-word;'>Ch 6 Analytic Trigonometry
• Inverse trigonometric functions; Review
• Trigonometric identities and equations</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>11</td><td style='text-align: center; word-wrap: break-word;'>Ch 6 Analytic Trigonometry
• Sum and difference formulas
• Double and half-angle formulas
• Product to sum and sum to product formulas
• Trigonometry equations
• Test: Chapter 6</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>12</td><td style='text-align: center; word-wrap: break-word;'>Ch 7 Applications of Trigonometric Functions
• The Law of Sines</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>13</td><td style='text-align: center; word-wrap: break-word;'>Ch 7 Applications of Trigonometric Functions</td></tr></table>

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<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'></td><td style='text-align: center; word-wrap: break-word;'>• Matrices and systems of equations
• The Law of Cosines
• Vectors
• Polar Coordinates</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>14</td><td style='text-align: center; word-wrap: break-word;'>Ch 8 Systems of Equations &amp; Ch 9 Matrices
• Systems of equations in three variables
• Matrix Algebra
• Test: Chapter 7</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>15</td><td style='text-align: center; word-wrap: break-word;'>Matrices/Determinants
• The matrix inverse
• Determinants and Cramer&#x27;s Rule
• Test: Chapters 8*/9</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>16</td><td style='text-align: center; word-wrap: break-word;'>Final Exam</td></tr></table>

<div style="text-align: center;">8 Week Calendar</div>



<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>1</td><td style='text-align: center; word-wrap: break-word;'>Ch 2 Graphs and Functions
• Symmetries of graphs &amp; equation of a circle
• Relations and functions
• Properties of functions
• A library of common functions
• Transformations of functions
• Combining functions; composite functions
• Inverse functions

Ch 3 Polynomial and Rational Functions
• Polynomial/Power functions and end behavior
• Zeros and turning points
• Graphing polynomial functions

Test: Chapter 2</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>2</td><td style='text-align: center; word-wrap: break-word;'>Ch 3 Long division and synthetic division
• Remainder and Factor Theorems
• Descartes’ Rule of Signs
• Zeros of polynomials: Bounds on real zeros
• Zeros of polynomials: Conjugate pairs theorem
• Find the domain of a rational function.
• Analyze graphs of rational functions.
• Find horizontal and vertical asymptotes.
• Graph rational functions
• Solve quadratic and polynomial inequalities.
• Solve rational inequalities.</td></tr><tr><td style='text-align: center; word-wrap: break-word;'></td><td style='text-align: center; word-wrap: break-word;'>Test: Chapter 3</td></tr></table>

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<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>3</td><td style='text-align: center; word-wrap: break-word;'>Ch 4 Exponential and Logarithmic Functions
● Exponential and Logarithmic functions
● The natural exponential function
● Properties of logarithms
● Exponential and logarithmic equations
● Rules of Logarithms
Test: Chapter 4
Ch 10 The Conic Sections
● The parabola and its applications
● The ellipse and its applications
● The Hyperbola and its applications
Test: Chapter 10</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>4</td><td style='text-align: center; word-wrap: break-word;'>Ch 11 Further Topics in Algebra
● Sequences and series
● Arithmetic and Geometric sequences and series
Test: Chapter 11
Exam: Midterm</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>5</td><td style='text-align: center; word-wrap: break-word;'>Ch 5 Trig Functions
● Angles and angle measure
● Right angle trigonometry
● Trigonometric functions; the unit circle
● Trigonometric functions of any angle;
● The unit circle
● Graphs of the trigonometric functions
Test: Chapter 5
Ch 6 Analytic Trigonometry
● Inverse trigonometric functions; Review
● Trigonometric identities and equations</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>6</td><td style='text-align: center; word-wrap: break-word;'>Ch 6 Analytic Trigonometry
● Sum and difference formulas
● Double and half-angle formulas
● Product to sum and sum to product formulas
● Trigonometry equations
Test: Chapter 6
Ch 7 Applications of Trigonometric Functions
● The Law of Sines</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>7</td><td style='text-align: center; word-wrap: break-word;'>Ch 7 Applications of Trigonometric Functions
● Matrices and systems of equations
● The Law of Cosines
● Vectors
● Polar Coordinates</td></tr></table>

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<table border=1 style='margin: auto; word-wrap: break-word;'><tr><td style='text-align: center; word-wrap: break-word;'>Week</td><td style='text-align: center; word-wrap: break-word;'>Chapter/Topic/Lab</td></tr><tr><td style='text-align: center; word-wrap: break-word;'></td><td rowspan="2">Ch 8 Systems of Equations &amp; Ch 9 Matrices• Systems of equations in three variables• Matrix AlgebraTest: Chapter 7Matrices/Determinants• The matrix inverse• Determinants and Cramer&#x27;s RuleTest: Chapters 8*/9Final Exam</td></tr><tr><td style='text-align: center; word-wrap: break-word;'>8</td></tr></table>