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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
| Week | Chapter/Topic/Lab |
|---|---|
| 1 | Ch 2 Graphs and Functions• Symmetries of graphs & equation of a circle• Relations and functions• Properties of functions• A library of common functions• Transformations of functions |
| 2 | 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 |
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| Week | Chapter/Topic/Lab |
|---|---|
| Test: Chapter 2 | |
| 3 | 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 |
| 4 | 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 |
| 5 | 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 |
| 6 | Ch 10 The Conic Sections • The parabola and its applications • The ellipse and its applications • The Hyperbola and its applications • Test: Chapter 10 |
| 7 | Ch 11 Further Topics in Algebra • Sequences and series • Arithmetic and Geometric sequences and series |
| 8 | Ch 11 Sequences and Series • Test: Chapter 11 • Exam: Midterm |
| 9 | 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 |
| 10 | Ch 6 Analytic Trigonometry • Inverse trigonometric functions; Review • Trigonometric identities and equations |
| 11 | 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 |
| 12 | Ch 7 Applications of Trigonometric Functions • The Law of Sines |
| 13 | Ch 7 Applications of Trigonometric Functions |
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| Week | Chapter/Topic/Lab |
|---|---|
| • Matrices and systems of equations • The Law of Cosines • Vectors • Polar Coordinates | |
| 14 | Ch 8 Systems of Equations & Ch 9 Matrices • Systems of equations in three variables • Matrix Algebra • Test: Chapter 7 |
| 15 | Matrices/Determinants • The matrix inverse • Determinants and Cramer's Rule • Test: Chapters 8*/9 |
| 16 | Final Exam |
8 Week Calendar
| Week | Chapter/Topic/Lab |
|---|---|
| 1 | Ch 2 Graphs and Functions • Symmetries of graphs & 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 |
| 2 | 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. |
| Test: Chapter 3 |
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| Week | Chapter/Topic/Lab |
|---|---|
| 3 | 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 |
| 4 | Ch 11 Further Topics in Algebra ● Sequences and series ● Arithmetic and Geometric sequences and series Test: Chapter 11 Exam: Midterm |
| 5 | 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 |
| 6 | 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 |
| 7 | Ch 7 Applications of Trigonometric Functions ● Matrices and systems of equations ● The Law of Cosines ● Vectors ● Polar Coordinates |
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| Week | Chapter/Topic/Lab |
|---|---|
| Ch 8 Systems of Equations & Ch 9 Matrices• Systems of equations in three variables• Matrix AlgebraTest: Chapter 7Matrices/Determinants• The matrix inverse• Determinants and Cramer's RuleTest: Chapters 8*/9Final Exam | |
| 8 |