MAT 127 - College Algebra and Trigonometry
Course Department: Mathematics
Last Date of Approval: Fall 2017
5 Credits
Total Lecture Hours: 75
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0
Course Description:
This course is designed to prepare those students who are planning on taking all or part of the calculus sequence. Topics covered include algebraic, logarithmic, and exponential functions, inverse functions, sequences and series, conic sections, and the fundamentals of trigonometry. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving. This course satisfies a general education requirement in the Math/Science area.
Prerequisites: MAT 102 - Intermediate Algebra with C grade or better or the necessary score on the mandatory assessment and placement chart found in the course catalog.
Mode(s) of Instruction: Traditional/Face-to-Face
Credit for Prior Learning: This course offers an opportunity for students to earn Credit for Prior Learning for skills that they have brought with them to Iowa Central. For more information, please ask the instructor and see the Iowa Central Community College catalog.
Course Fees: ebook/Access Code: $90.00
Common Course Assessment(s): None
Student Learning Outcomes and Objectives:
Student Learning Outcomes:
- Outcome 1: Analyze algebraic functions and their operations.
- Outcome 2: Analyze logarithmic and exponential functions.
- Outcome 3: Analyze sequences and series.
- Outcome 4: Analyze conics.
- Outcome 5: Analyze and use trigonometry.
Unit Objectives:
Outcome 1: Analyze algebraic functions and their operations.
Task 1: Identify the domain and range of a function.
Task 2: Describe the basic properties of functions and be able to construct/interpret their graphs.
Task 3: Define even and odd functions and apply their properties.
Task 4: Find horizontal, vertical, and oblique asymptotes of a function.
Task 5: Apply the definition of the sum/difference/product/quotient of two functions.
Task 6: Be able to perform functional composition.
Task 7: Define the inverse of a function and use the definition to be able to find f -1(x).
Outcome 2: Analyze logarithmic and exponential functions.
Task 1: Evaluate logarithms using the definition of f (x) = logb(x).
Task 2: Use the product, quotient, and power rules to simplify logarithms.
Task 3: Explain the exponential function f (x) = bx and its properties.
Task 4: Use the properties of logarithms and/or exponential functions to solve application problems.
Task 5: Identify the key properties of the graphs of f (x) = logb(x) and f (x) = bx.
Task 6: Solve equations involving logarithmic and exponential functions.
Outcome 3: Analyze sequences and series.
Task 1: Calculate the nth term of arithmetic, geometric, and recursive sequences.
Task 2: Write the formula for the nth term of arithmetic and geometric sequences.
Task 3: Identify the definition of a series and how to use sigma notation.
Task 4: Test for convergence of an infinite geometric series.
Task 5: Calculate the sum of an infinite geometric series.
Outcome 4: Analyze conics.
Task 1: Calculate the vertex, focus, directrix, and intercepts of a parabola.
Task 2: Find the center and radius of a circle.
Task 3: Determine the foci, vertices, and endpoints of the major/minor axis of an ellipse.
Task 4: Create the fundamental rectangle of a hyperbola and use it to draw its graph
Outcome 5: Analyze and use trigonometry.
Task 1: Convert from degrees to radians and from radians to degrees.
Task 2: Apply the relationship between the sine and cosine functions and the unit circle.
Task 3: Define sine, cosine, tangent, cotangent, secant, and cosecant and be able to apply them.
Task 4: Identify the key features of the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions.
Task 5: Prove trigonometric identities.
Task 6: Solve applications using sine, cosine, and tangent.
Task 7: Solve trigonometric equations.
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