MATH 0000D - Intermediate Algebra
http://catalog.sierracollege.edu/course-outlines/math-0000d/
Catalog Description DESCRIPTION IS HERE: Units Lecture-Discussion 72-90 Laboratory By Arrangement Contact Hours 72-90 Outside of Class Hours Course Student Learning Outcomes Simplify expressions and solve equations of the following types: linear, quadratic (including some with complex solutions), rational, radical, absolute value, exponential, and logarithmic. Interpret and construct graphs of linear, quadratic, exponential, and logarithmic functions and their inverse functions. Translate, model, and solve applied problems using linear, quadratic, rational, radical, exponential, and logarithmic functions. Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. Course Content Outline 1.Introduction A.Sets of real numbers B.Simplify algebraic expressions C.Order of operations D.Properties of integral exponents E.Multiply and divide with scientific notation 2.Linear Equations in 1 variable A.Solving linear equations B.Solving applied problems C.Solving literal equations 3.Functions A.Define relations and functions B.Find domain and range C.Interval notation D.Operations on functions E.Graphing and vertical line test F.Function notation G.Composite and inverse functions 4.Linear Equations in 2 variables A.Slope of a line B.Parallel and perpendicular C.Equations of lines (point slope, slope intercept and standard form) D.Graph linear equations E.Graph linear inequalities F.Solve applied problems 5.Systems of equations A.Solve systems of linear equations in 2 variables B.Solve systems of linear equations in 3 variables C.Solve systems of non-linear equations D.Solve applied problems 6.Inequalities A.Solve linear inequalities including interval notation B.Solve compound inequalities C.Solve systems of linear inequalities in 2 variables 7.Absolute Value A.Solve absolute value equations B.Solve absolute value inequalities C.Graph and perform transformations of absolute value functions 8.Polynomials A.Add, subtract and multiply polynomials B.Divide polynomials by monomials and binomials C.Calculate degree of polynomials in several variables D.Solve polynomial equations E.Solve applied problems 9.Factor polynomials completely A.Greatest common factor B.Difference of squares, sum and difference of cubes C.Trinomial D.Grouping 10.Rational expressions, functions and equations A.Simplify using four basic operations B.Simplify complex rational expressions C.Solve rational equations D.Find domain of rational functions E.Solve applied problems 11.Radicals, radical functions and rational exponents A.Simplify radical expressions B.Add, subtract and multiply radical expressions C.Rationalize denominators D.Solve radical equations E.Find domain of radical functions F.Simplify expressions containing rational exponents G.Graph and perform transformations of square root functions H.Perform 4 basic operations on complex numbers 12.Quadratic functions A.Solve equations with real and non-real solutions using quadratic formula, completing the square, factoring and the square root methods B.Solve equations quadratic in form C.Graph and perform transformations of square root functions D.Solve applied problems 13.Inequalities A.Solve polynomial inequalities B.Solve rational inequalities 14.Exponential and Logarithmic Functions A.Properties of exponential and logarithmic functions B.Find domain of exponential and logarithmic functions C.Graph and perform transformations of exponential and logarithmic functions D.Know the relationship between exponential and logarithmic functions E.Solve exponential and logarithmic equations F.Solve applied problems Course Objectives Course Objectives 1. Solve equations including linear, quadratic, polynomial, rational and absolute value types, exponential, logarithmic, or radical types, and their associated applied problems. 2. Solve inequalities including linear, quadratic, polynomial, rational and absolute value. 3. Graph and perform transformations on the following: linear, quadratic, exponential, logarithmic, absolute value, cubic, and square root functions. 4. Find the equation of a line given sufficient information about the line. 5. Utilize function notation, perform operations on functions, determine if a function is invertible, and find the inverse of functions. 6. Simplify and perform computations with scientific notation. 7. Simplify and perform operations on complex numbers and solve equations with non-real solutions. 8. Simplify and perform operations on algebraic expressions including polynomials, rational expressions, complex fractions, radicals, rational and integral exponents, and logarithms. 9. Analyze polynomial expressions to determine the best approach to factoring and complete factorization using that technique. 10. Solve linear systems of equations and inequalities with two variables and applied problems associated with such systems. 11. Solve linear systems of equations with three variables and applied problems associated with such systems. 12. Analyze and determine the domain for polynomial, radical, rational, logarithmic and exponential functions. Methods of Evaluation Problem Solving Examinations Reading Assignments 1. Find and read an article about the Richter scale. Note how it relates to the logarithms that we have studied and be prepared to discuss in class. 2. Find and read an article that discusses very large or very small numbers in an applied setting. Note how these numbers are more easily represented in scientific notation versus decimal notation and be prepared to discuss in class. Writing, Problem Solving or Performance 1. Solve applied mathematical problems that use exponential models. Example: Assume that on the day you were born your uncle put $8000 into an account that grew at a rate of 3.7% annual interest compounded continuously. How much money would you have in the account on your 21st birthday? 2. Solve an applied mathematics problem using a system of equations. Example: A wine company needs to blend a California wine with a 5% alcohol content and a French wine with a 9% alcohol content to obtain 200 gallons of wine with 6.5% alcohol content. How many gallons of each kind of wine must be used? Other (Term projects, research papers, portfolios, etc.) Methods of Instruction Lecture/Discussion Distance Learning Other materials and-or supplies required of students that contribute to the cost of the course.
