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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:


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