ENGINEERING LEARNING CENTER

Pre Calculus – Module Syllabus

Resource Description /
Textbook required  PRECALCULUS, Mathematics for Calculus 
5th Edition, James Stewart, Lothar Redlin and Saleem Watson 
/
Other Resources  Companion website, Internet search of periodicals. /
Week Topic Chapters  
1Topic: Introduction to Algebra 
Content: 
Rules of Algebra 
Properties of Real Numbers (associative, commutative, distributive) 
Simplifying Algebraic Expressions 
 
1
2Topic: Equations and Inequalities 
Content: 
Solving Linear Equations 
Solving Linear Inequalities 
1
3Topic: Graphs of Equations 
 
Content: 
Cartesian Coordinate System 
Plotting Points and Graphing Lines 
Slope and Intercepts 
 
1
4Topic: Lines and Circles 
 
Content: 
Equation of a Line (Slope-Intercept and Point-Slope Form) 
Graphing Linear Equations 
Equation of a Circle and its Graph 
 
1
5Topic: Functions 
 
Content: 
Definition and Notation of Functions 
Domain and Range 
Evaluating Functions 
 
2
6Topic: Transformations of Functions 
 
Content: 
Vertical and Horizontal Shifts 
 
2
7Topic: One-to-One and Inverse Functions 
 
Content: 
Definition of One-to-One Functions 
Finding Inverse Functions 
Graphing Functions and Their Inverses 
 
2
8        MID TERM EXAM REVISION 
9Topic: Exponential Functions 
 
Content: 
Definition and Properties of Exponential Functions 
Graphing Exponential Functions 
Applications of Exponential Functions 
4
10Topic: Logarithmic Functions 
 
Content: 
Definition and Properties of Logarithms 
Laws of Logarithms 
Solving Logarithmic Equations 
4
11Topic: Trigonometric Functions 
Content: 
Definition of Trigonometric Functions (Sine, Cosine, Tangent) 
Graphing Trigonometric Functions 
5
12Topic: Trigonometric Identities 
 
Content: 
Fundamental Trigonometric Identities 
Pythagorean Identities 
Sum and Difference Formulas 
7
13Topic: Zeros of Polynomials 
 
Content: 
Finding Zeros of Polynomial Functions 
Polynomial Long Division  
10
14Topic: The Fundamental Theorem of Algebra 
 
Content: 
Statement and Implications of the Fundamental Theorem 
Factoring Polynomials 
Complex Conjugates and Polynomial Roots 
 
8-10
15Topic: Systems of Equations 
 
Content: 
Solving Systems of Linear Equations (Graphically, Substitution, Elimination) 
Applications of Systems of Equations 
10
16Topic:  FINAL EXAM REVIEW  
 
Content: 
Comprehensive Review of All Topics 
Sample Problems 
 
/