Foothill CollegeApproved Course Outlines

Physical Sciences, Mathematics & Engineering Division | |||||

MATH 48B | PRECALCULUS II | Summer 2014 | |||

5 hours lecture. | 5 Units | ||||

Total Quarter Learning Hours: 60
(Total of All Lecture, Lecture/Lab, and Lab hours X 12) | |||||

Lecture Hours: 5 |
Lab Hours: | Lecture/Lab: | |||

Note: If Lab hours are specified, see item 10. Lab Content below. | |||||

Repeatability - | |||||

Statement: | Not Repeatable. | ||||

Status - | |||||

Course Status: Active | Grading: Letter Grade with P/NP option | ||||

Degree Status: Applicable | Credit Status: Credit | ||||

Degree or Certificate Requirement: Certificate of Achievement, AS Degree, Foothill GE | |||||

GE Status: Communication & Analytical Thinking | |||||

Articulation Office Information - | |||||

Transferability: Both | Validation: 6/10; 11/27/12;11/16/13 | ||||

1. Description - | ||

This course is a continuation of topics from MATH 48A. Topics include rational, exponential and logarithmic functions, piecewise functions, combination and composition of functions and an introduction to trigonometry. | ||

Prerequisite: MATH 48A. | ||

Co-requisite: None | ||

Advisory: Demonstrated proficiency in English by placement into ENGL 1A as determined by score on the English placement test or through an equivalent placement process; UC credit for MATH 48A, B & C is limited to a maximum of 7.5 units for the combination or any portion of the series completed. | ||

2. Course Objectives - | ||

The student will be able to: - Graph and analyze rational functions and solve related equations and inequalities
- Graph and analyze exponential functions and solve related equations and inequalities
- Graph and analyze logarithmic functions and solve related equations and inequalities
- Analyze combinations of functions
- Analyze piecewise functions
- Investigate composition of functions
- Model data with linear, quadratic, power, exponential, logarithmic, polynomial and rational functions
- Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (G) above.
- Discuss mathematical problems and write solutions in accurate mathematical language and notation
- Interpret mathematical solutions
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3. Special Facilities and/or Equipment - | ||

- Graphing Calculator
- When taught hybrid: Four lecture hours per week in face-to-face contact and one hour per week using CCC Confer. Students need internet access.
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4. Course Content (Body of knowledge) - | ||

- Graph and analyze rational functions and solve related equations and inequalities
- Examine vertical, horizontal asymptotes and removable discontinuities
- Find limits of and at infinity
- Find the domain of rational functions
- Graph functions that contain vertical and horizontal asymptotes
- Solve equations and inequalities involving rational expressions
- Investigate applications involving rational functions
- Interpret the meaning of asymptotes in real-world applications
- Find the inverse of a rational function
- Graph and analyze exponential functions and solve related equations and inequalities
- Calculate change factors from tables and graphs
- Calculate percentage rates of change from tables, graphs and change factors
- Recognize the difference between functions with a constant percentage change and functions with a constant difference change
- Construct exponential models algebraically from tables or words
- Use exponential models to predict and interpret results
- Graph exponential functions given in equations, tables or words
- Use exponential regression to model real-world data sets
- Examine applications involving half-life and double time
- Investigate the relationship between growth factors and graphs of exponential functions
- Investigate exponential growth and decay problems
- Investigate the number e
- Solve equations and inequalities involving exponential functions
- Investigate applications involving exponential functions such as:
- Compound interest
- Exponential population models
- Radioactive decay
- Newton's law of cooling
- Find the inverse of an exponential function
- Graph and analyze logarithmic functions and solve related equations and inequalities
- Graph logarithmic and exponential functions from equations and tables
- State and use properties of logarithms
- Identify common and natural logarithms
- Solve exponential equations using logarithms and interpret the real-world meaning of the results
- Solve logarithmic equations and interpret the real-world meaning of the results
- Investigate applications involving logarithms such as:
- pH
- Intensity of sound
- Intensity of earthquakes
- Use logarithmic regression to model real-world data sets
- Use logarithms to linearize exponential data to find an exponential model
- Analyze combinations of functions
- Compute the sum, difference, product, or quotient of functions
- Use combination of functions to model real-world situations
- Determine the practical and theoretical domain and range of the combination of functions
- Analyze piecewise functions
- Define piecewise functions using equations, tables, graphs and words
- Determine function values of piecewise functions from a graph, equation, and table
- Construct piecewise functions to model real-world situations
- Investigate absolute value functions
- Solve inequalities involving absolute values
- Investigate composition of functions
- Compose two or more functions using tables, equations, or graphs
- Create, use and interpret function composition
- Model data with linear, quadratic, power, exponential, logarithmic, polynomial and rational functions
- Select the best function to model a real-world data set given a graph, table of data or verbal description
- Use the appropriate function to predict and interpret unknown results
- Use technology such as graphing calculators and/or computer software to assist in solving problems involving any of the topics in (A) through (G) above
- Calculator/computer utilities for evaluating problems involving optimization
- Calculator/computer utilities for determining mathematical models using regression
- Calculator/computer utilities for finding intersection points for graphs of two functions
- Calculator/computer utilities for finding zeros or roots of functions
- Discuss mathematical problems and write solutions in accurate mathematical language and notation.
- Application problems from other disciplines
- Proper notation
- Interpret mathematical solutions.
- Explain the significance of solutions to application problems.
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5. Repeatability - Moved to header area. | ||

6. Methods of Evaluation - | ||

- Homework
- Quizzes
- Exams
- Proctored Comprehensive Final Exam
- Class Participation
- Exploratory worksheets or labs
- Group projects
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7. Representative Text(s) - | ||

Wilson, Adamson, Cox and O'Bryan, Precalculus: A Make It Real Approach, 1st Edition, Cengage Learning, 2013. Stewart, Redlin, and Watson, Precalculus: Mathematics for Calculus, 6th Edition, Cengage Learning, 2012. | ||

8. Disciplines - | ||

Mathematics | ||

9. Method of Instruction - | ||

- Lecture
- Discussion
- Cooperative learning exercises
| ||

10. Lab Content - | ||

Not applicable. | ||

11. Honors Description - No longer used. Integrated into main description section. | ||

12. Types and/or Examples of Required Reading, Writing and Outside of Class Assignments - | ||

- Homework Problems: Homework problems covering subject matter from text and related material ranging from 30 - 60 problems per week. Students will need to employ critical thinking in order to complete assignments.
- Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.
- Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB.
- Worksheets: Problems and activities covering the subject matter.
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13. Need/Justification - | ||

This course is a required core course for the AS degree in General Studies Science, a restricted support course for the Certificate of Achievement in Transfer Studies: CSU GE and satisfies the Foothill GE Requirement for Area V, Communication and Analytical Thinking. |

Course status: | Active | |

Last updated: | 2014-03-21 20:27:22 |

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