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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 Pre-test to gauge students’ educational background of subject material.**Review test**
Divide students into Algebra and Pre-Calculus 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,
5rd Ed (Book Code ISBN 0-53443295-6)
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