MCCCD Program Description

Precalculus

Course: MAT187

First Term: 2024 Fall

Lecture 5.0 Credit(s) 5.0 Period(s) 5.0 Load
Subject Type: Academic
Load Formula: S - Standard Load

Description: Topics in algebra and trigonometry in preparation for calculus.

MCCCD Official Course Competencies
1. Demonstrate conceptual understanding of asymptotes, continuity, end-behavior, rates of change of polynomial, absolute value, rational, radical, exponential, logarithmic, logistic, power, composite, and piecewise functions and complex roots of polynomial functions in preparation for Calculus. (I) 2. Determine the length of an arc, area of a sector, and linear and angular velocity. (II) 3. Use the unit circle to determine angle and reference angle measures in radians and degrees and convert between them. (III) 4. Determine triangle measurements using trigonometric ratios and law of sines and law of cosines. (IV) 5. Analyze (graphically, numerically, algebraically, and verbally) the trigonometric functions and their inverses. (V) 6. Use inverse trigonometric functions in solving equations. (V) 7. Verify trigonometric identities. (VI) 8. Use identities in solving trigonometric equations. (VI) 9. Solve applications involving vectors, their components, and visual representations. (VII) 10. Model real world situations graphically, numerically, algebraically, verbally, and interpret solutions using a variety of mathematical techniques. (VIII)
MCCCD Official Course Competencies must be coordinated with the content outline so that each major point in the outline serves one or more competencies. MCCCD faculty retains authority in determining the pedagogical approach, methodology, content sequencing, and assessment metrics for student work. Please see individual course syllabi for additional information, including specific course requirements.

MCCCD Official Course Outline
I. Conceptual understanding of precalculus topics A. End behavior of functions (including horizontal asymptotes) 1. Polynomial 2. Absolute Value 3. Rational 4. Radical 5. Exponential 6. Logarithmic 7. Logistic 8. Power 9. Trigonometric B. Vertical asymptotes vs holes C. Continuous and discontinuous piecewise functions D. Difference quotient, average rate of change and approximation of instantaneous rate of change E. Complex roots of polynomial functions F. Operations on complex numbers II. Circular functions A. Length of an arc B. Area of a sector C. Linear and angular velocity III. Unit circle A. Definition B. Cosine function definition and characteristics C. Sine Function definition and characteristics D. Reference angles E. Exact values using reference angles F. Radian and degree measurements and conversions IV. Triangle measurements A. Right triangle trigonometry B. Oblique triangles 1. Law of Sines 2. Law of Cosines C. Area V. Trigonometric functions A. Sine, cosine, tangent, cosecant, secant, and cotangent B. Notation, definition, domain and range C. Arcsine, arccosine, arctangent, arccosecant, arcsecant and arccotangent D. Equations VI. Trigonometric identities A. Fundamental identities 1. Pythagorean 2. Even/Odd 3. Reciprocal 4. Quotient 5. Cofunction B. Identities verification C. Sum and difference formulas D. Double-angle and half-angle formulas E. Equations VII. Vectors A. Scalar and vector quantities 1. Visual 2. Component form B. Direction of vector C. Vector operations 1. Visual 2. Component form D. Applications VIII. Real world modeling and applications with functions A. Polynomial B. Power C. Exponential D. Logarithmic E. Rational F. Trigonometric G. Piecewise H. Absolute Value

MCCCD Governing Board Approval Date: June 27, 2023

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.