# 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 | ExponentsProperties of exponents. |

3 | PolynomialsAddition, subtraction, and multiplication of polynomials . |

4 | FactoringFactoring techniques . |

5 | Special factoringPerfect square trinomials , the difference of two squares, and the sum and difference of two cubes . |

6 | VectorsDefinition 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 SystemPaired data and the rectangular coordinate system. Intercepts . |

14 | The slope of a line Slopes of parallel and perpendicular lines. |

15 | The Equation of a LineStudy 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 | FunctionsIntroduction to functions. Graph of a function . Vertical line test. Notation of functions. |

19 | Systems of Linear Equations in Two VariablesThe Addition and Substitution Method. Systems of Linear Equations in Three Variables |

20 | DeterminantsIntroduction to determinants. The Cramer’ s Rule . |

21 | Rational Expressions and Rational FunctionsProperties 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 ExponentsAddition, subtraction, multiplication and division of rational exponents. Simplified form for radicals. Addition, subtraction, multiplication and division of radical exponents. |

24 | Complex NumbersComplex number definition . Addition, subtraction, multiplication and division of complex numbers. |

25 | Quadratic FunctionsCompleting 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). |

28 | |

29 | |

30 | |

TEXT |
ALGEBRA with TRIGONOMETRY for COLLEGE
STUDENTS, by Charles P. Mckeague, 5 ^{rd} Ed (Book Code ISBN 0-53443295-6) |

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