# Math 100 - Beginning Algebra

Description: |
This course covers the fundamental concepts and operations of algebra and incorporates problem-solving skills. Topics include properties of real numbers, linear equations and inequalities, integer exponents, polynomials, and factoring polynomials. Other topics include rational and radical expressions, rational and radical equations, graphing and finding equations of lines, graphing and solving systems of linear equations, and graphing and solving quadratic equations. |

** Learning Outcomes and Objectives Upon completion of this course, the student will be able to:**

- simplify expressions using the basic operations and properties of real numbers.
- solve one-variable equations and inequalities.
- combine polynomials using the basic operations of polynomials.
- factor polynomials.
- simplify rational expressions.
- solve rational equations.
- solve linear equations.
- graph linear equations.
- find the equation of a line given (a) the slope and a point on the line, and (b) two points on the line.
- solve and graph systems of linear equations.
- simplify expressions containing integer exponents.
- simplify expressions containing second and third degree roots.
- solve quadratic equations.
- graph quadratic equations.
- develop an appropriate equation or system of equations and use the resulting equation(s) to solve application problems.

**Course Topics The topics for this course are typically allocated as follows:**

Lec |
Topic |

10 | Basic operations and properties of real numbers Fractions, symbols, and exponents Variables and equations Operations with real numbers Properties of addition and multiplication Note: students should be able to master all of the above topics without the use of a calculator |

10 | Equations and inequalities in one variable Simplifying expressions Solving equations, and inequalities Graphing inequalities on a number line Formulas, ratios, and proportions Applications |

10 | Exponents Degree of a single variable polynomial Properties of exponents Integer exponents Scientific notation Multiplication of polynomials Long division of polynomials: keep these problems at a basic level--no missing terms, fractions, etc. |

10 | Linear equations Graphing lines on the rectangular coordinate system Slope Finding equations of lines Parallel and perpendicular lines: determine if two linear equations are parallel or perpendicular Note: save the topic of finding equations for parallel and perpendicular lines for a higher level math course |

6 | Linear systems of equations Solving systems of linear equations by graphing, elimination/addition, and substitution methods Applications |

10 | Factoring Greatest common factor Grouping Trinomials Difference of two squares Solving quadratic equations by factoring Applications Note: factoring the sum and difference of two cubes, factoring by substitution, and problems that require more than two types of factoring should be saved as topics to be covered in a higher level math course |

7 | Rational expressions Multiplication, division, addition, and subtraction of rational expressions Complex rational expressions Note: the above topics should be taught at an introductory level; for example, save (a-b)/(b-a) = -1 for a higher level math course |

5 | Rational equations Applications Note: the above topics should be taught at an introductory level; for example, save (a-b)/(b-a) = -1 for a higher level math course |

10 | Roots and radicals Simplifying square roots and cube roots Products, quotients, and addition of radicals (square roots and cube roots) Rationalizing expressions with square roots Introduction to rationalizing expressions with square roots using the conjugate Solving equations with square roots, where repeated squaring is not necessary |

10 | Second degree equations Square root method Completing the square Quadratic formula Graphing quadratic equations using the x=-b/2a method to identify the vertex, and finding the x and y-intercepts (integer values only) Applications |

2 | Final exam |