Math 20  Intermediate Algebra
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Course Details 


Description 

Topics include rational, irrational and complex numbers; fundamental operations on algebraic expressions and functions; introduction to polynomial, rational, exponential and logarithmic functions, equations and graphs; circles and parabolas; matrix row reduction. Emphasis is on advanced algebraic factoring and simplification. 

Prerequisite 

Math 31 





Textbook 

Dugopolski, Mark, Intermediate Algebra, 6^{th} ed., 2009, McGraw Hill
Mazorow et al, Math 20 Supplement, SMC 2010


Mathematics Skills Associated With This Course


Entry Level Skills 

Skills the instructor assumes you know prior to enrollment in this course
Simplify and perform basic operations on rational expressions.
Perform basic operations on polynomials.
Factor general trinomials at an elementary level.
Solve linear equations in a single variable over the rationals.
Solve second degree polynomial equations in a single variable over the rationals by factoring.
Simplify square roots.
Solve first degree linear inequalities in a single variable.
Solve applications involving equations in a single variable.
Solve linear systems of two equations in two variables.
Graph first degree equations/ inequalities in one and two variables.


Course Objectives 

Skills to be learned during this course
 Simplify advanced numerical and algebraic expressions involving multiple operations
 Solve linear, quadratic, rational and absolute value inequalities, graph their solution sets, and express the answer in interval notation.
 Solve literal equations for a designated variable
 Apply algorithms of completing the square, rationalizing the denominator, and long division and synthetic division of polynomials.
 Solve linear, quadratic form, simple cubic, radical, rational, absolute value, elementary exponential, and elementary logarithmic equations.
 Solve systems of linear equations in three variables using matrix row reduction
 Graph the solution sets of systems of linear and quadratic inequalities.
 Perform operations on complex numbers
 Perform operations on functions including composition of two functions and determine the domain of the resulting function
 Use proper mathematical notation to evaluate functions and obtain their inverses
 State and apply the fundamental properties of exponents and logarithms
 Demonstrate knowledge of standard vocabulary associated with graphing, including but not limited to slopes of lines, intercepts, vertex of parabola, asymptotes, and interplay between graph and functional notation.
 Given its graph, determine whether a relation is a function and whether it is onetoone, and determine its intercepts and domain and range
 Graph using horizontal and vertical translations and determine the domain and range of linear, quadratic, simple cubic, radical, reciprocal, absolute value, exponential and logarithmic functions.
 Graph circles and parabolas using horizontal and vertical translation
 Evaluate simple expressions involving summation notation.
 Set up and solve practical applications of the algebraic material.
