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Algebra with Trigonometry
Program Duration: Six weeks, Class meets fifteen
hrs/week, two elective High School credits
Instructor: Mr. Luis F. Villada
TAs: Luis Beyk
Lesson  Objectives 
1  Pretest to gauge students’ educational
background of subject material.**Review test** Divide students into Algebra and PreCalculus session. 
2  Exponents Properties of exponents . 
3  Polynomials Addition, subtraction, and multiplication of polynomials . 
4  Factoring Factoring techniques. 
5  Special factoring Perfect square trinomials, the difference of two squares , and the sum and difference of two cubes . 
6  Vectors Definition of vectors on a plane and geometric representations. Free vectors. Addition and subtraction of vectors. 
7  Decomposition of vectors. Coordinate components of a vector. Orthogonal projection components Coordinate components of a vector. 
8  Scalar components. Norm of a vector and its properties. Unit vector. 
9  Definition of angles between two vectors. Vector product. Parallel and orthogonal vectors 
10  Exam # 1 (one hour) Review exam and make sure students understand the material (theory and applications). 
11  Linear Equation in one variable Properties of equalities. 
12  Linear Inequalities in one variable Properties for inequalities. 
13  Rectangular Coordinate System Paired data and the rectangular coordinate system. Intercepts. 
14  The slope of a line Slopes of parallel and perpendicular lines. 
15  The Equation of a Line Study of the equations of a line. 
16  Linear Inequalities in Two Variables. 
17  Exam # 2 (one hour) Review exam and make sure students understand the material (theory and applications). 
18  Functions Introduction to functions. Graph of a function . Vertical line test. Notation of functions. 
19  Systems of Linear Equations in Two Variables The Addition and Substitution Method . Systems of Linear Equations in Three Variables 
20  Determinants Introduction to determinants. The Cramer’ s Rule . 
21  Rational Expressions and Rational Functions Properties of rational expressions. Rational functions Exam # 3 (one hour) Review the exam and make sure students understand the material (theory and applications). 
22  Addition and subtraction of rational expressions. Complex functions . Equations involving rational expressions. 
23  Rational Exponents Addition, subtraction, multiplication and division of rational exponents. Simplified form for radicals. Addition, subtraction, multiplication and division of radical exponents. 
24  Complex Numbers Complex number definition . Addition, subtraction, multiplication and division of complex numbers. 
25  Quadratic Functions Completing the square. The quadratic formula . Graphing parabolas. 
26  Exam # 3 (one hour) Review the exam and make sure students understand the material (theory and applications). 
27  Final Exam (2 hours) Review the exam and make sure students understand the material (theory and applications). 
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TEXT  ALGEBRA with TRIGONOMETRY for COLLEGE
STUDENTS, by Charles P. Mckeague, 5^{rd} Ed (Book Code ISBN 0534432956) 
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