MATH 1113 – Content Standards
Title: Precalculus
Catalog course description. Prerequisite: Math 1111, or departmental approval. Trigonometric functions, identities, inverses, and equations; vectors; polar coordinates, conic sections.
Goals. Prepare students for a course in calculus by consolidating their understanding of algebraic, trigonometric, exponential, and logarithmic functions, and the introduction of ideas leading to the concepts of limit and derivative.
Course Content Standards
The following standards are offered as guidelines for assessing student progress, judging the effectiveness of instructional programs, and developing curricular units. The subject matter outlined in these standards represents the minimum knowledge in which a student should demonstrate proficiency at the successful completion of the course.
CS1. Quantitative Reasoning
Students will use quantitative reasoning in problem solving situations including: geometric an symbolic representation and manipulation; pattern recognition; translating mathematics into words and words into mathematics; recognizing incorrect answers and arguments and knowing when an answer is reasonable; being able to write out a solution in a logical and clear form rather than presenting a collection of unidentified intermediate numbers that may end with the final numerical answer.
CS2. Algebraic Functions
Students will use functions and related concepts including: recognition of a function in either graphical, table, implicit, or explicit form; be able to find domains and ranges and determine if a function is one-to-one; perform operations of functions including composition, finding inverses, and finding difference quotients; graphically determine when a functions is increasing, decreasing, constant, one-to-one, continuous, and even or odd; apply basic graph transformations including af(x), f(x) + d, f(x – c), f(bx), 
, f( 
) to the parent functions; graph a function defined as piecewise.
CS3. Defining the Trigonometric Functions
Students will use circular and trigonometric functions and related concepts including: find exact values of the functions by using the unit circle, wrapping function, and special triangles; know the relationship between radian measure and degree measure and be able to convert from one unit to the other; know the definition of the six (6) trigonometric functions as related to the right triangle; distinguish between right angled and oblique triangles and recognize the appropriate method needed to solve the triangle (Law of Sines, Law of Cosines, Pythagorean Theorem)
CS4 Use of Trigonometric Functions
Students will demonstrate knowledge of and be able to use trigonometry. Specifically: (1) given one of the trig values of an angle in a certain quadrant, be able to find the other five trigonometric functions through identities not limited to Pythagorean, identity, reciprocal identities, even/odd identities and quotient identities, (2) solve oblique triangles using the Law of Sines, and Law of Cosines, and work related applied problems, (3) graph the basic six trigonometric functions, including sine and cosine functions with applied graph transformations; identify the domain, range, period, amplitude and phase shifts of the functions. (4) find the exact values of the inverse trig functions, (5) solve linear and quadratic trigonometric equations and equations with compound angles.
CS5. Mathematical Proofs
Students will demonstrate an understanding of mathematical proofs and related concepts by specifically developing: sum, difference, and co-function identities, double angle and half angle formulas, and sum to product and product to sum identities.
CS6. Analytic Geometry
Students will be demonstrate knowledge of and be able to use analytic geometry concepts and related techniques, including polar coordinates and conic sections including: convert polar to rectangular coordinates and vice versa; sketch graphs of polar functions including cardioids, roses, circles, and spirals; identify equations of parabolas, hyperbolas, and ellipses and sketch their graphs.
CS7. Vectors
Students will demonstrate an understanding of algebraic and geometric vectors and be able to use them to model situations and solve problems.
CS8 Applications and Technology
When applying analytic, algebraic, geometric and algorithmic techniques to solving applied problems, students should be able to use technology when appropriate. Care should be taken to ensure that use of technology is not accompanied by a decrease in mathematical or fundamental understanding.