Precalculus Mathematics | Weatherford College

This course is an in-depth combined study of algebra, trigonometry, and other topics for calculus readiness. It includes the study and applications of algebraic and transcendental functions and their graphs, including rational, exponential, logarithmic, and trigonometric functions. It includes five contact hours per week.

Competencies

To demonstrate and apply knowledge of properties of functions, the student should be able to:
1. Determine the domain and range of a function.
2. Use interval and function notation.
3. Determine the inverse of a function.
4. Find x- and y-intercepts of rational functions.
5. Find the partial fraction decomposition of a rational function.
To recognize and apply algebraic and transcendental functions and solve related equations, the student should be able to:
1. Relate logarithmic and exponential functions.
2. Evaluate logarithmic and exponential expressions.
3. Expand and condense expressions using logarithmic properties.
4. Solve exponential and logarithmic equations and applications.
5. Find an arc length and central angle measure and solve applications.
6. Find the area of a sector of a circle and solve applications.
7. Solve applications using linear and angular velocity formulas.
8. Find inverse trigonometric values.
9. Solve trigonometric equations.
To apply graphing techniques to algebraic and transcendental functions, the student should be able to:
1. Find all vertical, horizontal, and oblique asymptotes for rational functions.
2. Sketch the graphs of rational, exponential, and logarithmic functions.
3. Identify graphs of trigonometric functions.
4. Identify amplitude, period, vertical translations and phase shifts for trigonometric functions.
5. Graph sine and cosine functions using amplitude, period, translations, and phase shifts.
6. Graph tangent and cotangent functions.
To compute the values of trigonometric functions for key angles in all quadrants of the unit circle measured in both degrees and radians, the student should be able to:
1. Determine the complement and the supplement of an angle.
2. Distinguish types of angles and angle pairs and use their properties to find angle measures.
3. Perform calculations with angles.
4. Relate degree measure and radian measure.
5. Sketch angles in standard position and determine coterminal angles.
6. Classify types of triangles and find the angle and side measures.
7. Use the definitions of trigonometric functions to find trigonometric values of angles in standard position.
8. Use reciprocal and Pythagorean Identities to find function values.
9. Compute exact function values using 30, 45, and 60 degree angles and their multiples.
To prove trigonometric identities, the student should be able to:
1. Find all trigonometric function values, given one value and the quadrant.
2. Write expressions in terms of sine and cosine.
3. Simplify trigonometric expressions using fundamental identities.
4. Use the fundamental trigonometric identities to find exact values and verify identities.
5. Use the sum and difference identities to find exact values and verify identities.
6. Use the double- and half-angle identities and the product-sum formulas to find exact values and verify identities.
To solve right and oblique triangles, the student should be able to:
1. Use trigonometric functions to solve application problems.
2. Solve oblique triangles using the law of sines and law of cosines.
3. Find the area of a triangle using and Heron’s formula.
4. Use the law of sines and law of cosines to solve applications.
To demonstrate and apply knowledge of vectors, the student should be able to:
1. Perform vector operations, including addition, scalar multiplication, and dot product.
2. Sketch vectors and the resultant.
3. Use vectors to solve applications.
To identify conic sections and solve related equations, the student should be able to:
1. Identify conic sections and express in standard form by completing the squares.
2. Find the equations of conic sections given specific information.
3. Solve related equations involving conic sections.
To apply knowledge of conic sections and demonstrate graphing techniques, the student should be able to:
1. Find the center and radius of a circle.
2. Find the focus, directrix, and focal diameter of a parabola.
3. Find the vertices, foci, eccentricity, and lengths of axes of an ellipse.
4. Find the vertices, foci, eccentricity, and asymptotes of a hyperbola.
5. Sketch the graphs of conic sections.

Campus Resources for Students

Weatherford:
The Academic Support Center is a free public tutoring service provided by the college, offered in LART- LL Room 2, 817-598-6278

Instructional videos

Computer assisted instruction

Instructor’s office hours

Course Learning Objectives

Upon successful completion of this course, students will:

Demonstrate and apply knowledge of properties of functions.
Recognize and apply algebraic and transcendental functions and solve related equations.
Apply graphing techniques to algebraic and transcendental functions.
Compute the values of trigonometric functions for key angles in all quadrants of the unit circle measured in both degrees and radians.
Prove trigonometric identities.
Solve right and oblique triangles.
Demonstrate and apply knowledge of vectors.
Identify conic sections and solve related equations.
Apply knowledge of conic sections and demonstrate graphing techniques.

Lab Fee

$24

Required Textbooks

Precalculus, 7th ed., by Lial, Hornsby, Schneider, and Daniels, Pearson Education, 2013. MyLabsPlus access code.

Required Supplies

Scientific calculator. See instructor information sheet for specific requirements.

ISBN-10

9780135924150

Evaluation Standards

These course objectives and student learning outcomes will be assessed through the administration of a minimum of 3 in-class exams (65%), quizzes and/or homework (15%), and a comprehensive, final exam (20%).

Grading Standards

A - Student’s work is exceptional and consistently above average.
B - Student’s work is above average. Required assignments were completed in a timely manner and have met at least the minimum required standards.
C - Student’s work is acceptable. Majority of assignments meet the minimum required standards.
D - Student’s work fails to meet the minimum requirements for a grade of "C." Overall performance was sub-standard in comparison to normal expectations for this class.
F - Student’s work is clearly unacceptable. Student either did not attempt the work or failed to meet any of the minimum required standards.

To enroll in the next higher mathematics course that has a prerequisite, a student must earn a grade of C or better. A student could take the Compass test to also indicate competency for placement in a higher mathematics course.

Required Institutional Core Learning Outcomes

Communication (COM), Critical Thinking (CT), Empirical & Quantitative Reasoning (EQR)

Disabilities

ADA Statement:

Any student with a documented disability (e.g. learning, psychiatric, vision, hearing, etc.) may contact the Office on the Weatherford College Weatherford Campus to request reasonable accommodations. Phone: 817-598-6350 Office Location: Office Number 118 in the Student Services Building, upper floor. Physical Address: Weatherford College 225 College Park Drive Weatherford, TX.

Academic Integrity

Academic Integrity is fundamental to the educational mission of Weatherford College, and the College expects its students to maintain high standards of personal and scholarly conduct. Academic dishonesty of any kind will not be tolerated. Academic dishonesty includes, but is not limited to, cheating on an examination or other academic work, plagiarism, collusion, and the abuse of resource materials including unauthorized use of Generative AI. Departments may adopt discipline specific guidelines on Generative AI usage approved by the instructional dean. Any student who is demonstrated to have engaged in any of these activities will be subject to immediate disciplinary action in accordance with institutional procedures.

Hope Statement

Any student who faces challenges securing basic resources such as food, clothing, or housing and believes this may affect their performance in their course of study is urged to contact the Director of Student Resources, Dr. Deborah Cregger, for support at (817) 598-6444. Her office is on the first floor of Student Services. If the student prefers, they may contact their instructor, who can reach out on their behalf. Weatherford College also provides the Coyote Pantry. The Pantry maintains boxed and canned foods for students in need. The location of the Coyote Pantry is two blocks west of the Weatherford campus at the Baptist Student Ministry (118 E. Park Ave., Weatherford). Pantry hours are Mon-Thurs. 8:30 am-4:30 pm and Fri. 8.30 am-12:00 pm (817-599-6586).

Grading Key

100-90 = A
89-80 = B
79-70 = C
69-60 = D
59-below = F

Revised

Fall 2021

Last Modified

Friday, September 10, 2021, 3:31 PM