MediaKit Contents:
eBook: Precalculus Enhanced with Graphing Utilities
Syllabus:
This course is designed to provide students with a thorough background in the mathematics of functions. This may be the last math course that some students take, while others will continue on to Precalculus: Trigonometry. At the conclusion of this course, all students will be prepared to take an introductory course in Calculus.
Because the use of graphing utilities is a key component of this course, all students will need access to a graphing calculator. While a scanner is not required, many students find it convenient to use one to submit assignments.
Each week contains an Are You Prepared? section which reviews the mathematics needed to master the week’s topics. Each student is assigned to a study group, which provides a forum to work cooperatively on problems, discuss solutions and become better acquainted with classmates.
Week 1: Welcome to Precalculus: Functions
- Read the course overview & syllabus
- Introduce yourself
- Understand teacher & student expectations
- Create a class social contract
- Meet your classmates
- Build a library of helpful websites
- Complete a survey
Week 2: Distance, Midpoint, Intercepts and Symmetry
- Access your ebook and learn some of its features
- Learn to use your graphing calculator
- Graph two-variable equations
- Review the distance and midpoint formulas
- Find intercepts, test for symmetry and solve equations
Week 3: Equations of Lines and Circles
- Meet your study group members
- Calculate & interpret slope
- Graph equations & circles
- Find equations given information
- Write the equation of a circle in 2 forms
- Discuss peoples’ math fears
- Take a group quiz and submit it next week
Week 4: Functions & Graphs
- Review for the Chapter 1 Test
- Distinguish between relations and functions
- Determine the domain of a function
- Evaluate a function
- Perform operations on functions
- Identify the graph of a function
- Obtain information from graphs
- Take a quiz as a team
- Start a Calculator Challenge called Caching Up
Week 5: Functions: Properties & Library of Functions
- Identify odd & even functions from graphs & equations
- Determine increasing, decreasing & constant functions
- Locate local and absolute max & min values
- Find the average rate of change
- Graph 9 basic functions
- Graph piecewise functions
- Prepare for and take the Chapter 1 Test
- Submit Caching Up Calculator Challenge
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Week 6: Transformations & Linear Functions
Graph functions using vertical & horizontal shifts, compressions & stretches & reflections
Graph linear functions
Determine if a linear function is increasing, decreasing or constant
Use average rate of change to identify linear functions
Review for the Chapter 2 test
Post to a discussion on the importance of Algebra
Week 7: Quadratic Functions & Inequalities
Graph quadratic functions using vertex, axis of symmetry, intercepts, transformations
Identify the vertex & axis of symmetry
Find max or min value of a quadratic
Find a quadratic function given vertex and one point
Solve inequalities involving a quadratic function
Prepare for and take the Chapter 2 test
Make a mid-course private journal entry giving feedback on the course
Week 8: Polynomial Functions & Real Zeros
· Identify polynomial functions & their degree
· Graph polynomial functions using transformations
· Identify the real zeros of polynomial functions and their multiplicity
· Analyze the graph of a polynomial function
· Use the Remainder & Factor theorems and the Rational Zeros Theorem
· Find the real zeros of a polynomial function
· Solve polynomial equations
· Review for the Chapter 3 test
· Start the Algebra Calculator Challenge
Week 9: Rational Functions: Properties & Graphs
- Determine the domain of a rational function
- Find the vertical, horizontal or oblique asymptotes of a rational function
- Analyze the graph of a rational function
- Solve applied problems involving rational functions
- Prepare for & take the Chapter 3 test
- Submit the Algebra Calculator Challenge
Week 10: Polynomial Inequalities & Composite Functions
Solve polynomial & rational inequalities algebraically & graphically
Form a composite function
Determine the domain of a composite function
Review for the Chapter 4 test
Analyze careers that use math and report on one of them
Week 11: One-to-one, Inverse & Exponential Functions
Determine if a function is one-to-one
Find the inverse of a function defined by a map, set of ordered pairs or an equation
Obtain the graph of the inverse function from the graph of the function
Define the number e
Evaluate, graph & solve exponential equations
Prepare for & take the Chapter 4 test
Start the Geometry Calculator Challenge
Week 12: Logarithmic Functions
Change exponential statements to logarithmic and logarithmic to exponential
Determine the domain of a logarithmic function
Evaluate logarithmic expressions
Graph logarithmic functions & solve logarithmic equations
Work with properties of logarithms
Write a logarithmic expression as a sum or difference of logarithms or as a single logarithm
Evaluate & graph a logarithm whose base is neither 10 nor e
Submit the Geometry Calculator Challenge
Week 13: Logarithmic & Exponential Equations, Growth & Decay
Solve logarithmic & exponential equations
Find equations that obey the law of uninhibited growth
Find equations that obey the law of decay
Start the Algebra 2 Calculator Challenge
Week 14: Introduction to Limits
Find a limit using a table & using a graph
Review for and take the Chapter 5 test
Submit the Algebra 2 Calculator Challenge
Week 15: Uses of Calculus & Wrapping Up Precalc
Analyze a graph using limits
Say goodbye to your classmates via a final project
Comment on your classmates’ presentations
Watch some videos: Uses of Calculus
Discuss: Uses of Calculus in Real Life
Course Objectives:
Course Objectives:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively and ask useful questions.
Construct viable arguments and critique the reasoning of others
Model with mathematics and use appropriate tools strategically.
Learn to communicate precisely to others.
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