Las Positas College 3033 Collier Canyon Road Livermore CA 94551 7650 925 373 5800 925 443 0742 Fax Course Outline for Mathematics 55 INTERMEDIATE ALGEBRA I CATALOG DESCRIPTION MATH 55 INTERMEDIATE ALGEBRA 5 units Concepts involving complex numbers quadratic equations parabolas and circles functions and their graphs systems of equations rational exponents radical equations absolute value equations and inequalities exponential and logarithmic functions and equations Prerequisite Math 65 or 65B or 65Y completed with a grade of C or higher or an appropriate skill level demonstrated through the Mathematics assessment process May not receive credit if Mathematics 55B or 55Y has been completed 5 lecture hours 01 laboratory hour II NUMBER OF TIMES COURSE MAY BE TAKEN FOR CREDIT One III PREREQUISITE AND OR ADVISORY SKILLS Before entering this course the student should be able to A B C D E F G H I J K L M N O demonstrate ability to use set theory add subtract multiply and divide polynomials perform real number operations solve linear equations in one variable solve and graph linear inequalities in one variable develop and graph linear equations in two variables using various methods factor difference of two squares perfect squares and general trinomials add subtract multiply and divide and simplify rational expressions apply the laws of integer exponents use algebraic methods to solve word problems solve quadratic equations by factoring completing the square and using the quadratic formula solve systems of equations by the addition method and substitution solve literal linear equations for any given variable solve equations involving rational expressions add subtract multiply divide and simplify expressions involving square roots IV EXPECTED OUTCOMES FOR STUDENTS Upon completion of the course the student will be able to A B C D E F G perform basic operations on complex numbers find complex roots of a quadratic equation sketch graphs of conic sections sketch the graphs of functions and relations sketch the graph of algebraic functions using synthetic division sketch the graph of logarithmic and exponential functions solve exponential and logarithmic functions Course Outline for Mathematics 55 INTERMEDIATE ALGEBRA H I J K L M N Page 2 apply the concepts of logarithmic and exponential functions to other fields solve systems of linear equations in two and three unknowns using elimination and substitution solve systems of nonlinear equations in two unknowns using elimination and substitution understand the properties of and perform operations with rational and irrational exponents solve equations and inequalities involving absolute values solve equations involving radicals find rational roots of polynomials with integral coefficients V CONTENT Math 55X A L Math 55Y M V A Review solving linear equations and inequalities B Absolute value equations and inequalities C Review exponents operations with polynomials and factoring D Review operations with rational expressions E Synthetic division F Review simplifying and operations with radicals G Rational and irrational exponents H Solving equations with radicals I Complex numbers J Quadratic equations 1 The quadratic formula 2 The discriminant K Solving nonlinear and rational inequalities in two variables L Solving equations involving quadratic forms M Graphing linear equations and inequalities in two variables N Distance midpoint and the slope of a line O Variation P Introductions to functions 1 Types even and odd functions 2 Operations 3 Composite 4 Inverse Q Graphing polynomial and rational functions with synthetic division R Find rational roots of polynomials S Exponential and logarithmic functions 1 Definition 2 Equations 3 Graphing 4 Applications T Conic sections 1 Parabola 2 Ellipse 3 Hyperbola 4 Circles 5 Translation of axes U System of non linear equations and inequalities V Systems of linear equations VI METHODS OF INSTRUCTION A Lectures B Classroom discussion on line discussion C Collaborative learning where applicable D Individual assistance during lab hour E Math X self paced mastery learning Course Outline for Mathematics 55 INTERMEDIATE ALGEBRA Page 3 VII TYPICAL ASSIGNMENTS A Assigned homework problems are usually from the book At the end of each section there is a homework set The answers to the odd numbered problems are in the back of the book The homework exercises begin with easy problems and increase in difficulty Be careful not to assign too many difficult problems Homework should take an average student 1 to 2 hours for each hour in class For example topic is solving a linear system of equations in two variables Assignment Page 237 1 37 odd B If it is a difficult topic such as completing the square then maybe the lecture and homework needs to be over 2 days Assignment 1st Day Page 263 5 29 odd 2nd Day Page 263 30 63 every 3rd C If the assignment involves word problems then initially try to assign problems of the same type After covering all the different types then assign a set of review problems that covers all types D During lab hour this week spend time practicing factoring the sum and difference of two cubes VIII EVALUATION A Methods of evaluation 1 Examinations 2 Final Exam 3 Any or all of the following at the discretion of the instructor a homework b quizzes announced or unannounced in class take home or on line c collaborative group activities or labs B Frequency of evaluation 1 Recommended minimum of 5 exams plus the final C Types of problems 1 Most questions should be open ended a Factor y3 216 b Solve the equation 5m m 1 2 1 m c Simplify i35 d Carmen and Paul can clean the house together in 2 hours Working alone it takes Carmen hour longer than it takes Paul to do the job How long would it take Carmen alone 2 Use the multiple choice and true false questions at a minimum and only where appropriate a Find the degree of the following polynomial x 6 x 3 2x 1 a 10 b 9 c 3 d 6 e none of the answers b True or False In the expressions 4x 2 3x 2 4 is called the leading coefficient IX TYPICAL TEXTS A Lial Hornsby Miller Intermediate Algebra 6thEdition Boston Addison Wesley 1998 B Tussy Gustafson Intermediate Algebra 2nd Edition Pacific Grove Brooks Cole 2002 X OTHER MATERIALS REQUIRED OF STUDENTS A calculator may be required Creation Date 1 94 Revision Date 2 01 8 02 Approved by Curriculum Committee 10 09 02 Effective Date Spring 2003 Approved for Distance Education 10 09 02