Feb 21, 2024  
2021-2022 Course Catalog 
    
2021-2022 Course Catalog [ARCHIVED CATALOG]

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MAT 129 - Precalculus

Credits: 5
Lecture Hours: 5
Lab Hours: 0
Practicum Hours: 0
Work Experience: 0
Course Type: Core


The central theme of this course is the concept of a function and its graph. Topics include: functions (linear, radical, exponential, logarithmic, polynomial, piecewise and trigonometric) and their graphs, and basic trigonometry.
Prerequisite: Minimum ALEKS scores of 61% or MAT 130  with a C- or better
Competencies
  1. Analyze mathematical functions
    1. Describe a function
    2. Determine if a relation is a function
    3. Analyze the function to determine the domain and range of a function
    4. Determine minimum and maximum values of a function
    5. Analyze a function to determine whether functions are increasing, decreasing or constant
    6. Categorize whether functions have even or odd properties
  2. Evaluate functions
    1. Examine and graph common functions (including piece-wise functions)
    2. Compare and contrast transformations
    3. Create functions using standard function operations
    4. Describe an inverse function
    5. Manipulate a one-to-one function to create an inverse function 
  3. Evaluate polynomial functions
    1. Analyze a polynomial function and relate it to a real-world application
    2. Rewrite a quadratic function in standard form
    3. Find the vertex and any x-intercepts of a graph of a quadratic function
    4. Determine real and complex zeros of a polynomial function
    5. Utilize the fundamental Theorem of Algebra
    6. Apply the intermediate value, remainder, factor, and rational root theorems to find polynomial roots
    7. Examine and graph polynomial functions
    8. Interpret inequalities involving polynomial functions
  4. Evaluate rational functions
    1. Analyze a rational function
    2. Determine horizontal/vertical/oblique asymptotes and any removable discontinuities
    3. Examine and graph a rational function
    4. Interpret inequalities involving rational functions 
  5. Evaluate exponential functions
    1. Analyze exponential functions
    2. Examine and graph exponential functions
    3. Solve exponential equations
  6. Evaluate logarithmic functions
    1. Analyze logarithmic functions
    2. Apply the properties of logarithms
    3. Examine and graph logarithmic functions
    4. Solve logarithmic equations
    5. Apply exponential and logarithmic functions to problems involving interest, growth and decay
  7. Solve systems of equations
    1. Calculate and interpret solutions of linear systems
    2. Perform partial fraction decomposition
  8. Utilize matrices and determinants
    1. Compute matrix solutions to linear systems using Gaussian elimination
    2. Perform matrix operations
    3. Calculate multiplicative inverses
    4. Identify and solve matrix equations 
  9. Interpret angles and their measure
    1. Draw angles whose measures are given in degrees and radians
    2. Determine a positive angle less than one revolution that is coterminal with a given angle
    3. Use radian measure of angles
    4. Convert degree measure to radian measure
    5. Convert radian measure to degree measure
  10. Establish the trigonometric functions on a unit circle
    1. Determine sine, cosine, and tangent using the unit circle
    2. Determine the reciprocal functions using the unit circle
    3. Make sense of the eight fundamental identities
    4. Use the fundamental identities to simplify trigonometric expressions
    5. Evaluate trigonometric functions using the fundamental identities
    6. Determine the values of trigonometric functions
    7. Identify the signs of the trigonometric functions by quadrant 
  11. Assess trigonometric functions
    1. Interpret the generalized definition of the trigonometric functions
    2. Evaluate the trigonometric functions given a point on the terminal side
    3. Find the reference angle for any given triangle
    4. Evaluate trigonometric functions of real numbers by table/calculator
    5. List the exact values for the trigonometric functions pi/6, pi/4, pi/3, pi/2, pi
    6. Analyze the trigonometric functions using a table/calculator
    7. Determine the domain and range
  12. Graph trigonometric functions
    1. Sketch the standard forms of the cosine, sine, tangent, secant, cosecant, and cotangent curves from memory
    2. Graph by plotting points
    3. Analyze and sketch trig functions using: amplitudes, periods, and phase shifts
  13. Investigate trigonometric identities.
    1. Apply half angle, double angle, and sum/difference trigonometric identities to write equivalent forms of expressions
    2. Find exact values by using half angle, double angle, and sum/difference trigonometric identities 
  14. Solve trigonometric equations
    1. Solve linear and quadratic trigonometric equations
    2. Solve quadratic trigonometric equations
  15. Assess inverse trigonometric functions
    1. Define inverse trigonometric relations and functions
    2. Evaluate inverse functions including domain and range
  16. Investigate the right triangle definition of the trigonometric function
    1. Use the right-triangle definition of the trigonometric functions
    2. Solve mathematical and real-life right triangle problems
    3. Apply the Law of Cosines to mathematical and real-life problems
    4. Apply the  Law of Sines to mathematical and real-life problems

 



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