Modesto Junior College Course Outline of Record MATH 90

Transcription

1 Modesto Junior College Course Outline of Record MATH 90 I. OVERVIEW The following information will appear in the catalog MATH 90 Intermediate Algebra 5 Units Equivalent to second year high school algebr Topics include linear, quadratic, exponential and logarithmic functions and equations; complex numbers; solving systems of equations using substitution, matrices and determinants; conic sections; sequences, series and combinatorics. Prerequisite: Satisfactory completion of MATH 70 or MATH 71 and MATH 7 or equivalent placement by MJC assessment process Field trips are not require Units/Hours: 5.00 Units: Lecture hours Grading: A-F or P/NP - Student choice General Education: D.2 ) II. LEARNING CONTEXT Given the following learning context, the student who satisfactorily completes this course should be able to achieve the goals specified in Section III, Desired Learning: A. COURSE CONTENT Required Content: Graphing and functions i ii Review of the rectangular coordinate system Graphing of lines Introduction to functions Developing a library of functions Linear Quadratic Absolute value Cubic Transformations of graphs Systems of equations i ii Graphing method Substitution method Addition method Matrices and Gauss Jordan Elimination Division: Science, Math & Engineering 1 of 6

2 v Determinants and Cramer's Rule Applications Inequalities i ii Linear Compound Quadratic Absolute value Rational Quadratic equations and functions i ii Completing the square Quadratic formula Combining functions Graphing quadratic functions Applications e. f. g. Rational expression operations Radical and rational exponents Exponential and logarithmic functions i ii Applications Operations Inverse functions Properties of logarithms Exponential and logarithmic equations h. Conic sections i ii Parabolas Circles Ellipses Hyperbolas Sequences and Series i Arithmetic Geometric Division: Science, Math & Engineering 2 of 6

3 ii Summation notation j. k. Binomial Theorem Combinatorics B. ENROLLMENT RESTRICTIONS Prerequisites Satisfactory completion of MATH 70 or MATH 71 and MATH 72 or equivalent placement by MJC assessment process. Requisite Skills Before entering the course, the student will be able to: e. f. g. h. j. k. l. m. n. o. p. q. r. s. t. u. Simplify arithmetic expressions using the correct order of operations. Simplify algebraic expressions by combining like terms. Solve linear equations in one variable. Solve and graph linear inequalities in one variable. Graph linear equations and inequalities in two variables. Determine the slope of a line from either the graph or the equation and explain its meaning. Write the equation of a line describing the relationship between two variables. Solve systems of linear equations in two variables by the graphing method, the substitution method, or the addition metho Solve systems of linear inequalities by graphing and shading. Add, subtract, multiply and divide polynomials. Convert numbers to and from scientific notation and apply rules of exponents to these numbers. Factor polynomials by greatest common factor (GCF), grouping, special factorizations, and guess and check. Solve quadratic equations by factoring, completing the square, or using the quadratic formul Multiply and divide rational expressions. Add and subtract rational expressions with linear and simple quadratic denominators. Simplify complex fractions. Solve equations involving rational expressions by clearing fractions. Simplify radicals and expressions involving radicals, including fractional exponents. Solve equations involving radical expressions. Sketch the graph of simple parabolas from their equations. Create mathematical models of applications described in words, including those involving linear, quadratic, rational, and radical expressions. Division: Science, Math & Engineering 3 of 6

4 C. HOURS AND UNITS 5 Units INST METHOD TERM HOURS UNITS Lect Lab Disc D. METHODS OF INSTRUCTION (TYPICAL) Instructors of the course might conduct the course using the following method: Lecture Discussion Demonstration of mathematical techniques Guided practice Homework assignments Discussion of concepts with instructor and other students in class E. ASSIGNMENTS (TYPICAL) EVIDENCE OF APPROPRIATE WORKLOAD FOR COURSE UNITS Time spent on coursework in addition to hours of instruction (lecture hours) Daily homework assignments requiring on the average two hours per class hour Daily review of class notes 3. Ongoing review of flashcards or study sheets 4. Preparation for examinations, several times during term 5. Preparation for final examination EVIDENCE OF CRITICAL THINKING Assignments require the appropriate level of critical thinking Joe received $25,500 from an inheritance. He wishes to use the money in five years for the down payment on a house. If he deposits the money in a savings account paying 5% compounded quarterly, then how much will his investment be worth in five years? what will be the maximum purchase price of the house Joe can afford if the down payment will be 10% of the purchase price (ignore other costs associated with the purchase)? In 1989, an earthquake in San Francisco had a Richter scale reading of 6.9 The 1906 San Francisco earthquake had a Richter scale value of 8.3. To the nearest whole number, how many times more intense was the 1906 earthquake than the 1989 earthquake? Why do you think the Richter scale is based on logarithms? F. TEXTS AND OTHER READINGS (TYPICAL) Book: Kaufman, Schwitters (2007). Algebra for College Students (8th/e). Brooks Cole. III. DESIRED LEARNING Division: Science, Math & Engineering 4 of 6

5 A. COURSE GOAL As a result of satisfactory completion of this course, the student should be prepared to: develop facility with many aspects of functions while perfecting and extending their knowledge of algebr This course acts as a gateway to many different educational paths including the study of calculus, statistics, business mathematics and other general transferable mathematics courses. B. STUDENT LEARNING GOALS Mastery of the following learning goals will enable the student to achieve the overall course goal. Required Learning Goals Upon satisfactory completion of this course, the student will be able to: e. f. g. h. j. k. l. m. n. o. p. q. r. s. t. u. graph lines and find the equation of a line, given sufficient information. effectively use function notation to describe mathematical relationships. determine the domain and range of a given function. given a relation between two variables, determine if the relation is a function. graph linear, quadratic, absolute value, and simple cubic functions using transformations. solve systems of linear equations in two or three variables by choosing the most effective method for the given problem. solve linear, quadratic, absolute value, and rational inequalities. solve quadratic equations with real and complex solutions by completing the square and using the quadratic formul graph quadratic functions by determining and using the vertex and stretching constant. add, subtract, multiply, and divide complex numbers. convert radicals to rational exponents and vice vers add, subtract, multiply, divide, or compose two given functions. find the inverse of a given function. graph exponential and logarithmic functions using transformations. solve exponential and logarithmic equations. simplify expressions using the properties of logarithms. identify the equations for and sketch the graphs of conic sections. list a requisite number of terms of a given arithmetic, geometric, or recursive sequence. determine the general term of a given arithmetic or geometric sequence. determine the sum of a fixed number of terms of an arithmetic or geometric series, and determine the sum of an infinite geometric series when it exists. solve problems involving permutations, combinations, and probability. IV. METHODS OF ASSESSMENT (TYPICAL) A. FORMATIVE ASSESSMENT Division: Science, Math & Engineering 5 of 6

6 3. Midterm exams (excluding the following formats: multiple choice, open book, take home). Quizzes. Homework assignments. B. SUMMATIVE ASSESSMENT Required: Comprehensive 2 to 3 hour Final Exam (excluding the following formats: multiple choice, open book, take home). Division: Science, Math & Engineering 6 of 6