Math 20 - Intermediate Algebra

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

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.

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 one-to-one, 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.