# Math 138 Precalculus I: Algebra Spring 2018

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1 Math 138 Precalculus I: Algebra Spring 2018 Dept. of Mathematics Instructor's Name: Office Location: Office Hours: Office Phone: Course Description Precalculus I is a study of those topics on algebra which are essential in calculus. Topics included are functions, graphs of functions, linear, quadratic polynomial, rational, exponential and logarithmic functions, conic sections, sequences, and the binomial theorem. Illinois Articulation Initiative (IAI) number: N/A Credit and Contact Hours: Lecture 4 Lab 0 Credit Hours 4 Prerequisites: Satisfactory placement test score or Math 098 and Math 095 with a grade of C or equivalent. Books, Supplies, and Supplementary Materials A. Textbooks Required: Precalculus: Concepts Through Functions w/o Access Code), 3rd Ed., 2015, Sullivan. Publisher: Pearson Education ISBN: Pearson MyMathLab Stand Alone Student Access Kit (Optional), ISBN: , Pearson Education Publisher: Pearson Education or Precalculus: Concepts Through Functions w/access Code), 3rd Ed., 2015, Sullivan. ISBN: , Pearson Education B. Other Required Materials TI-83+ or TI-84+ graphing calculator Joliet Junior College Math 138 Precalculus I: Algebra Course Syllabus Page 1

2 Methods of Instruction: Lecture Online Student Learning Outcomes: General Education Student Learning Outcomes: Students will demonstrate the ability to accurately apply correct mathematical methods and techniques in various applications such as applied sciences, theoretical mathematics, physics, natural sciences and other applied sciences. Objectives Upon completion of this course, the student will be able to: 1. Find the distance between two points. 2. Find the midpoint of a line segment. 3. Graph relations on a calculator using appropriate window settings. 4. Determine symmetries of graphs. 5. Find intercepts of graphs. 6. Find slope and equations for a given line. 7. Determine whether two lines are parallel or perpendicular. 8. Find the standard form for the equation of a given circle. 9. (Optional) Use the graphing calculator to draw scatter diagrams, find equation of least squares regression line, find the correlation coefficient, and interpret these results. 10. Work applied variation (proportionality) problems. 11. Determine whether a given relation is a function. 12. Use function notation. 13. Determine the domain of a given function. 14. Recognize graphs of prototypical functions. 15. Use the calculator to determine intervals on which a function is increasing or decreasing. 16. Find the slope of a secant line to a graph by writing and reducing the difference quotient. 17. Recognize the graph of a function, which was obtained from that of a prototypical function by shifting, stretching, or reflection. 18. Find the sum, product, difference, quotient, and composition of two functions. 19. Determine whether a given function is one-to-one, and if so, determine its inverse. 20. Graph the inverse of a relation, given the graph of the relation. 21. Construct a function to model an applied optimization problem and use the graphing calculator to solve it. 22. State the Intermediate Value Theorem and use it to show the existence of a zero of a function on a given interval. 23. Solve quadratic equations graphically and algebraically. 24. Solve literal equations. 25. Solve applied problems using an equation in one variable. 26. Perform computations with complex numbers. 27. Solve polynomial and rational inequalities (algebraically and graphically). 28. Solve absolute value equations and inequalities (algebraically and graphically). 29. Find intercepts and vertex of the graph of a quadratic function. 30. Recognize the graph of a polynomial function given its zeroes with their multiplicities. 31. Find intercepts and equations of asymptotes to the graph of a rational function. 32. Determine a possible formula for a rational function given its graph. Joliet Junior College Math 138 Precalculus I: Algebra Course Syllabus Page 2

3 33. Factor a polynomial given its zeroes. 34. List the possible rational zeroes of a polynomial function using the Rational Zero Theorem. 35. Recognize irrational zeroes (which the calculator approximates) of a polynomial. 36. Use the complex conjugate pairs theorem to find zeroes of a polynomial function with real coefficients. 37. Use synthetic division to find zeroes of a polynomial and factor it. 38. Define exponential function. 39. Define e. 40. Graph exponential functions using transformations. 41. Define logarithmic function. 42. Convert between log and exponential expressions. 43. Find domains and ranges of log and exponential functions. 44. Find the asymptotes of log and exponential functions. 45. Graph logarithmic functions using transformations. 46. Use properties of logarithms to write equivalent expressions and solve equations. 47. Work applied problems involving exponential growth and decay. 48. (Optional) Use the graphing calculator to determine the best-fitting log and exponential functions to a set of data points, and determine which is most appropriate. 49. Define parabola using directrix and focus. 50. Define ellipse and hyperbola using foci. 51. Find an equation for a conic section given foci, vertices, asymptotes, etc. (graphically or numerically presented). 52. Given an equation of a conic section determine foci, vertices, and asymptotes, if any. 53. Find terms of a sequence, including those defined recursively. Use appropriate notation. 54. Recognize when a sequence is arithmetic or geometric. 55. Find terms and finite sums of arithmetic and geometric sequences. 56. Use mathematical induction to prove statements about sums of sequences and about divisibility. 57. Expand powers of binomials using the Binomial Theorem. 58. (Optional) Solve systems of nonlinear equations. 59. (Optional) Solve systems of inequalities. TOPICAL OUTLINE Days Topic or Class Activity 3 days Distance and Midpoint Formula; Graphs of Equations; Lines and Circles 6 days Functions and Their Graphs 7 days Linear and Quadratic Functions 6 days Polynomial and Rational Functions 4 days Zeroes of Polynomials 8 days Exponential and Logarithmic Functions 6 days Analytic Geometry Joliet Junior College Math 138 Precalculus I: Algebra Course Syllabus Page 3

6 Prepared by: Reviewed by: Prof. Elena Catoiu Prof. Jean McArthur Department Chair Date Revised 04/15 Developed 4/09 Joliet Junior College Math 138 Precalculus I: Algebra Course Syllabus Page 6

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