Math 115 syllabus
Precalculus Algebra and Trigonometry
Study of elementary functions, their graphs and applications, including polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions. This fast-paced course is designed as a review of the algebra and trigonometry needed in calculus.
Sufficient mathematics placement test score, or sufficient ACT or SAT Mathematics Subscore.
J. Douglas Faires and James DeFranza, Precalculus, Brooks/Cole, Florence, 5th edition, (2007). ISBN 9781133851608
Topics & Time Distribution
Chapters 1-6 (omitting 1.5 and 6.7), with the end of 4.5 by the middle of the term.
Chapter 1: Functions 2.5 weeks
Chapter 2: New Functions from Old 1.5 weeks
Chapter 3: Algebraic Functions 2.5 weeks
Chapter 4: Trigonometric Functions 3.5 weeks
Chapter 5: Exponential and Logarithmic Functions 1.5 weeks Chapter 6: Conic Sect., Polar Coordinates, Eq. 1.5 weeks
Detailed Coverage Below are the essential sections that should be covered by all instructors.
Chapter 1: 1.1, 1.2, 1.3, 1.4, 1.6, 1.7, 1.8.
Chapter 2: 2.1, 2.2, 2.3, 2.4, 2.5.
Chapter 3: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6.
Chapter 4: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9.
Chapter 5: 5.1, 5.2, 5.3, 5.4.
Chapter 6: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6.
- Recognition of function model groups by name, equation, and general graph shape: linear, quadratic, cubic, general polynomial, rational, trigonometric, inverse trigonometric, exponential, and logarithmic.
- Recognition of conic sections by their equations, both Cartesian and polar. Use of completion of the square for Cartesian and equivalent fractions for polar coordinates to put the equation in standard form. Use of the standard form to sketch the graph of the conic.
- Vocabulary used to describe graphs including, but not limited to: domain, range, increasing, decreasing, x-intercept, function zero, y-intercept, maximum, minimum, asymptote, vertical, horizontal, axis, scale, coordinates, vertex, axis of symmetry, center, foci, period, amplitude, phase shift, vertical shift, and end behavior.
- Real number line and solving inequalities to describe number sets on that line.
- Complex number arithmetic and application of the fundamental theorem of algebra to factor polynomials.
- Algebraic techniques for problem solving together with reasoning and argumentation skills needed to present mathematical arguments and proofs.
Method of Evaluation Grading Scale
Final grade = 85% of test average (four tests) and 15% quiz average. There will be a short quiz given every class period to check on homework.
Students must have a TI-89, or TI-83, or TI-84 graphing calculator and bring it to every class session. If you plan to go on to a higher math course, a TI is the best choice. The TI-83 Plus may be purchased on EBay for around $40.
Makeup tests will be left up to the instructor. Usually, if a test is missed, the Final Exam grade will be substituted for the missed test. You will receive a grade of zero on your second missed test.
Attendance ensures that you get notes which will help you learn the material being covered and allows you to learn from questions being asked and answered in class. Five or more absences could result in a lower or even failing grade.
Updated January 31, 2014