# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 12: Precalculus
Approved: 2011-09-01 (revised 2013-12-01, )

This course requires the Math Placement Exam. Read More.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Precalculus, 7th edition (Custom Version) by Cohen/Lee/Sklar; Cengage Publishing; Approximate cost - \$49.00-67.00
Search by ISBN on Amazon: 978-1133271130

Prerequisites:

Two years of High School algebra, plane geometry, plane trigonometry, and satisfying the Mathematics Placement Exam.

Suggested Schedule:

 Lecture(s) Sections Comments/Topics 1 1.1-1.4, 2.1-2.2, App. B.4 interval notation, absolute value, factoring, completing the square, quadratic formula, distance formula, midpoint formula 1 1.6, 1.7 lines, symmetry, circles 1 2.3, 2.4 solving inequalities 1 3.1, 3.3 functions, difference quotients; Emphasize finding domains and simplifying difference quotients 1 3.2, 3.3 graphs of functions, shapes of graphs, average rate of change 1 3.4, 3.5 translations, reflections, composition of functions 0.5 3.6 inverse functions 0.5 4.2 quadratic functions 1 4.4 setting up functions in applications 1.5 4.5 max-min problems 0.5 4.6 graphing polynomials 1.5 4.7 graphing rational functions, Give examples of polynomial division when covering slanted asymptotes. 1 5.1, 5.2 exponential functions, Assign Appendix B.3 to read 0.5 5.3 logarithmic functions 1 5.4 properties of logarithms 1 5.5 solving equations with logarithms and exponentials, Omit inequalities, or cover them only briefly. 0.5 6.1 trig functions of acute angles, Assign pp. 437-439. 0.5 6.2 right-triangle applications 1 6.3 trig functions of angles 0.5 7.1 radian measure and geometry 1 8.1 trig functions of real numbers 1 8.2, 8.3 graphs of sine and cosine, Omit phase shift, and assign pp. 585-590. 1.5 9.1, 9.2 addition formulas, double-angle formulas 1 9.4 trig equations 1 9.5 inverse trig functions, Omit the inverse cosine. 0.5 14.2 Pascal's triangle, Binomial Theorem, (Instructors can refer to Sec. 14.2 in the 7th edition for this material.) 0.5 13.2, 13.4 Factor Theorem, Rational Roots Theorem, (Instructors can refer to Sec. 13.2 and 13.4 in the 7th edition for these topics.) 1 5.7 exponential growth and decay, (if time permits)

Throughout the quarter, assign unsimplified derivative expressions to simplify.

The material from Ch. 13 and 14 is included to satisfy the requirements for the Single Subject Teaching Credential Waiver, and is not contained in the custom version of the text.

Learning Goals:

This course is designed to prepare students for our calculus classes. Students are expected to learn how to solve inequalities and how to simplify algebraic expressions encountered in calculus. They are also expected to learn how to graph functions, and to gain familiarity with translations, reflections, and compressions and expansions of graphs. The course also emphasizes mastery of the properties of logarithmic and exponential functions, and the trigonometric and inverse trigonometric functions.

In addition to these topics, the course emphasizes problem-solving skills and practice setting up functions for typical optimization problems presented in calculus courses.

Assessment:

Students' progress in the course is typically assessed by 2-3 tests during the quarter as well as a comprehensive final examination, and in some cases by homework problems and quizzes in addition.