Mac 2147 Precalculus Algebra/Trigonometry

MAC 2147 PRECALCULUS ALGEBRA/TRIGONOMETRY

MAC 2147 Precalculus Algebra/Trigonometry (4) (A.A.) Four hours lecture per week. Prerequisite: Grade of A or B in MAC 1105 or equivalent. This course meets Area II requirements for both AA General Education Requirements and AS General Education Requirements. This course is a one-semester course encompassing the topics of MAC 1140 Precalculus Algebra and MAC 1114 Trigonometry. Topics include the study of the following functions: polynomial, rational, radical, absolute value, exponential and logarithmic. Other topics include matrices and systems of equations and inequalities, trigonometric functions and applications, analytic trigonometry, vectors, trigonometric form of complex numbers, parametric equations, polar coordinates and equations, and conic sections. An emphasis will be placed on solving applications by mathematical modeling. This course is intended for students whose major requires the calculus sequence. Use of graphing calculator is integrated throughout this course.

STUDENT LEARNING OUTCOMES:

Upon successful completion of this course the student should be able to:

1. Understand functions, including concepts of one-to-one, odd and even, domain, range, composition, and combinations. 2. Graph linear, quadratic, polynomial, rational, exponential, and logarithmic functions. Graph transformations of these and test for symmetry. 3. Graph systems of equations and systems of inequalities, linear and non-linear. 4. Classify and determine real and complex zeros of polynomial functions to completely factor and graph polynomials. 5. Graph and evaluate piecewise-defined functions. 6. Determine horizontal and vertical asymptotes, intercepts, symmetry, and domain for rational functions. 7. Know the properties of exponents and logarithms, solve exponential and logarithmic equations and applications and understand common and natural logarithms. 8. Solve systems of two and three variables by substitution, elimination and using matrices and determinants. These include cases of independent, dependent, consistent and inconsistent solutions, as well as applications of systems. 9. Understand and use the basic properties of matrices, perform basic matrix operations, calculate determinants and inverses of matrices, and applications of matrices. 10. Understand sequence, series, and summation notation, calculate the nth term and sum of arithmetic, geometric, and infinite geometric sequences and series. Determine binomial coefficients, Pascal’s Triangle and the Binomial Theorem. 11. Determine the measurements of angles around the unit circle, conversions between degree to radian units. 12. Know the six trigonometric functions and their properties for right triangle and the unit circle; and work with right triangles and their applications. 13. Graph trigonometric and inverse trigonometric functions, as well as their combinations and transformations. 14. Simplify and apply trigonometric identities and solve trigonometric equations. 15. Know and apply the Laws of Sines and Cosines. 16. Find areas of triangles using trigonometric functions. 17. Graph in polar coordinates and polar equations and conic sections centered at (h,k). 18. Write complex numbers in polar form, compute multiplications, divisions and powers of complex numbers in polar form, and apply DeMoivre’s Theorem to find complex roots. 19. Know and use basic properties of vectors. 20. Prove a statement using mathematical induction.

Date of Original Submission: 1/9/98 Date of Last Review: MAC 2147 2 Date of Last Revision: 10/16/13