Official Course Description: MCCCD Approval: 11-27-2012
MAT187  2013 Spring - 9999	LEC  5.0 Credit(s)  5.0 Period(s)  5.0 Load  Acad
Precalculus
A precalculus course combining topics from college algebra and trigonometry. Preparation for analytic geometry and calculus. Prerequisites: Grade of B or better in MAT120, or MAT121, or MAT122, or equivalent, or satisfactory score on a placement test.
Course Notes: Strongly recommended that students have some knowledge of trigonometry. Students may receive credit for only one of the following: MAT150, MAT151, MAT152, or MAT187.   Course Attribute(s): Arizona Shared Unique Number : MAT 1187 General Education Designation: Mathematics - [MA]

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MCCCD Official Course Competencies:
MAT187  2013 Spring - 9999	Precalculus

 

1.         Find real and complex zeros of polynomial functions. (I-II)

2.         Calculate and interpret average rate of change. (I-III)

3.         Determine the inverse of a relation when represented numerically, analytically, or graphically. (I-IV)

4.         Analyze and interpret the behavior of functions, including domain and range, end behavior, increasing and decreasing intervals, extrema, asymptotic behavior, and symmetry. (I-V)

5.         Determine whether a function is one-to-one when represented numerically, analytically, or graphically. (I-V)

6.         Determine whether a relation is a function when represented numerically, analytically, or graphically. (I-V)

7.         Graph polynomial, rational, exponential, logarithmic, power, absolute value, piecewise-defined, and trigonometric functions. (I-V)

8.         Perform operations, including compositions, on functions and state the domain of the resulting function. (I-V)

9.         Solve polynomial, rational, exponential, logarithmic, and trigonometric equations analytically and graphically. (I-V)

10.       Use transformations to graph functions. (I-V)

11.       Communicate process and results in written and verbal format. (I-IX)

12.       Compare alternative solution strategies. (I-IX)

13.       Justify and interpret solutions to application problems. (I-IX)

14.       Model and solve real-world problems. (I-IX)

15.       Read and interpret quantitative information when presented numerically, analytically, or graphically. (I-IX)

16.       Find and evaluate inverse trigonometric functions. (IV-V)

17.       Use the definition and properties of trigonometric functions and formulas to solve application problems. (IV-VII)

18.       Verify trigonometric identities. (VI)

 

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MCCCD Official Course Outline:
MAT187  2013 Spring - 9999	Precalculus

 

I           Behavior and Nature of Functions

            A         Graphic, numeric, and algebraic representations

            B         Characteristics of basic functions

            C         Properties, operations, transformations, and inverses of functions

II          Polynomial and Rational Functions

            A         Polynomial and rational equations

            B         Graphs of polynomial and rational functions

            C         Applications

III        Exponential and Logarithmic Functions

            A         Properties of logarithms

            B         Exponential and logarithmic equations

            C         Graphs of exponential and logarithmic functions

            D         Applications

IV        Definition and Properties of Trigonometric Functions

            A         Acute and general angles

            B         Right-triangle trigonometry

            C         Graphs of trigonometric functions

            D         Inverse trigonometric functions

            E          Applications

V         Circular Functions and The Unit Circle

            A         Radian measure

            B         Length of an arc

            C         Area of a sector

            D         Linear and angular velocity

VI        Trigonometric Identities

            A         Fundamental identities

            B         Sum and difference identities

            C         Double-angle identities

VII       Trigonometric Formulas

            A         Law of sines

            B         Law of cosines

            C         Applications

VIII      Departments must include one or more of the following topics in their courses

            A         Matrices, including solving systems of three linear equations in three variables.

            B         Combinatorics

            C         Sequences and series

            D         Conics

IX        Departments may include one or more of the following topics in their courses

            A         Complex Numbers (Trigonometric Form of Complex Numbers, DeMoivre's Theorem, Roots of Complex Numbers)

            B         Vectors (Definitions, Operations, and Applications)

            C         Polar Coordinates, Equations and Graphs

            D         Parametric Equations and Graphs

 

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