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Math 117 - Precalculus for Scientists and Engineers
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Text Typically Used: |
Precalculus Understanding Functions |
Course Content: |
This course is designed to prepare you for Math 241 Analytical Geometry and Calculus A. The major topics include a review of algebraic skills, functions, linear functions, quadratic functions, graphing principles, composition, inverse functions, polynomial functions, radical functions, exponential and logarithmic functions and trigonometry. |
Final Exam |
Sample M117 Final Exam (requires the free Acrobat Reader software installed) |
Sections and Topics Covered: |
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Chapter 1 |
Algebra: The Fundamentals |
1.1 |
The Real Numbers (Review on own) |
1.2 |
Operations with Real Numbers (Review on own) |
1.3 |
Polynomials and Rational Expressions |
1.4 |
Exponents and Radicals |
1.5 |
Complex Numbers |
1.6 |
First Degree Equations and Inequalities in One Variable |
1.7 |
Absolute Value Equations and Inequalities |
1.8 |
Quadratic Equations and Equations in Quadratric Form |
1.9 |
Quadratic and Rational Inequalities |
1.10 |
Substitution |
Chapter 2 |
Functions and Graphs: Part I |
2.1 |
The Cartesian Coordinate System: Graphing Straight Lines and Equations of Circles |
2.2 |
Slope |
2.3 |
Equations of a Line |
2.4 |
Relations and Functions |
2.5 |
Function Notation |
2.6 |
Relating Functions to Their Graphs |
2.7 |
Introduction to Graph Sketching: Symetry |
Chapter 3 |
Functions and Graphs: Part II |
3.1 |
Basic Graphing Principles |
3.2 |
More Graphing Principles; Types of Functions |
3.3 |
Extracting Functions from Real Life Situations |
3.4 |
Quadratic Functions |
3.5 |
Operations On Functions |
3.6 |
Inverse Functions |
Chapter 4 |
Polynomial, Rational, and Radical Functions |
4.1 |
Polynomial Functions |
4.2 |
More Polynomial Functions and Mathematical Models |
4.3 |
Polynomial Division, Roots of Polynomial Equations: The Remainder and Factor Theorems |
4.4 |
Roots of Polynomial Equations: The Rational Root Theorem |
4.5 |
Rational Functions |
4.6 |
Radical Functions |
Chapter 5 |
Exponential Functions |
5.1 |
Exponential Functions |
5.2 |
Logarithmic Functions |
5.3 |
Properties of Logarithms; Logarithmic Equations |
5.4 |
Common and Natural Logarithms; Exponential Equations and Change of Base |
5.5 |
Applications |
Chapter 6 |
Trigonometry |
6.1 |
Angle Measurement and Two Special Triangles |
6.2 |
The Trigonometric Functions |
6.3 |
Right Triangle Trigonometry and Applications |
6.4 |
The Trigonometric Functions as Functions of Real Numbers |
Chapter 7 |
The Trigonometric Functions |
7.1 |
The Sine and Cosine Functions and Their Graphs |
7.2 |
The Tangent, Secant, Cosecant, and Cotangent Functions and Their Graphs |
7.3 |
Basic Identities |
7.4 |
Trigonometric Equations |
7.5 |
The Inverse Trigonometric Functions |
Chapter 8 |
More Trigonometry and Its Applications |
8.1 |
The Addition Formulas |
8.2 |
The Double-Angle and Half-Angle Formula |
8.3 |
The Law of Sines and the Law of Cosines |
Chapter 9 |
Systems of Equations and Inequalities |
9.1 |
Elimination and Substitution: 2 X 2 Linear Systems |
Chapter 10 |
The Conic Sections |
10.7 |
Non-Linear Systems of Equations and Inequalities |
Chapter 11 |
Sequences and Series and Related Topics |
11.1 |
Sequences |
11.2 |
Series and Sigma Notation |