MAT 129 - Precalculus

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

Precalculus is a course that bridges together advanced algebra and trigonometry with a focus on functions and mathematical modeling to solve real-world problems. The intent of this course is to prepare students for the study of calculus. The course helps students make connections between numeric, graphical, and algebraic relations and various types of functions. The functions covered in this course include polynomials, rational functions, exponentials, logarithmic, piecewise, and trigonometric.
Prerequisite: Minimum ALEKS scores of 61% or MAT 130 with a C- or better
Competencies

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, decreasting, or contstant
6. Categorize whether functions have even or odd properties
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
Evaluate polynomial functions
1. Analyze a polynomial function in relation 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. Graph polynomial functions
8. Interpret inequalities involving polynomial functions
Evaluate rational functions
1. Analyze a rational function
2. Determine horizontal/vertical/oblique asymptotes and any removable discontinuities
3. Graph rational functions
4. Interpret inequalities involving rational functions
Evaluate exponential functions
1. Analyze exponential functions
2. Graph exponential functions
3. Solve exponential equations
Evaluate logarithmic functions
1. Analyze logarithmic functions
2. Apply the properties of logarithms
3. Graph logarithmic functions
4. Solve logarithmic equations
5. Apply exponential and logarithmic functions to problems involving interest, growth, and decay
Solve systems of equations
1. Interpret solutions of linear systems
2. Perform partial fraction decomposition
Create mathematical models
1. Determine the appropriate mathematical model based on given information (e.g., shape, behaviors, domain/range)
2. Build linear and higher order models (including trigonometric) for applied situation
3. Utilize technology to create mathematical models
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 and vice versa
5. Determine arc length and the area of a sector
Evaluate circular functions on a unit circle
1. Determine sine, cosine, and tangent of angles 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. Identify the signs of the trigonometric functions by quadrant

11. Evaluate 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. Graph trigonometric 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

Competencies Revised Date: AY2027