About This Chapter
Mathematical Modeling for Precalculus - Chapter Summary and Learning Objectives
This chapter is designed to boost your knowledge of mathematical modeling for precalculus by providing you with various definitions, explanations and mathematical operations associated with the subject area. Make sure you know how to write and evaluate expressions and models, apply systems and solve problems effectively. Examples are available to ensure you fully understand these concepts.
Reviewing this chapter is fun, thanks to expert instructors who have created entertaining video lessons that keep you engaged. Feel free to review the lessons in any sequence you desire, and even access full transcripts with easily identifiable vocabulary words that can deepen your understanding of mathematical modeling. Self-assessment quizzes and a chapter exam are available to gauge your comprehension of the subject matter. After exploring the lessons in this chapter, you will understand the following:
- How to write and evaluate algebraic expressions for two-dimensional geometric figures and real-life linear models
- Questions about direct and inverse variation
- The process of applying systems of linear equations to breakeven point and market equilibrium
- Steps involved in using quadratic models to find minimum and maximum values
- Ways to use linear programming to solve problems
|Writing & Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures: Lesson & Quiz||Examine the process of writing and solving equations that relate the side lengths, perimeter and area of a two-dimensional figure.|
|Writing & Evaluating Real-Life Linear Models: Process & Examples||Learn how to write and solve real-life models, including d=rt and cost determination.|
|Direct and Inverse Variation Problems: Definition & Examples||Discover how to answer questions related to direct and inverse variation by exploring their definitions and learning to apply them to problems.|
|Applying Systems of Linear Equations to Breakeven Point: Steps & Example||Describe how to find the breakeven point by using systems of linear equations with revenue and cost functions.|
|Applying Systems of Linear Equations to Market Equilibrium: Steps & Example||Study how to use linear models to evaluate economic equilibrium and profit functions.|
|Using Quadratic Models to Find Minimum & Maximum Values: Definition, Steps & Example||Explain how to find maximum and minimum values of quadratic models.|
|Using Linear Programming to Solve Problems||Understand the meaning of linear programming, describe problems that require it, list linear program problem elements, and share the process of solving the linear program problem with two variables.|
1. Writing & Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures
Learning more about algebraic expressions and geometric figures will help you solve problems that occur in your life. In this lesson, you will use the perimeter of a two-dimensional geometric shape to solve a real-world problem.
2. Writing & Evaluating Real-Life Linear Models: Process & Examples
You make decisions about budgeting and other financial issues using linear models without even realizing it. Learn how to write and evaluate linear models.
3. Direct and Inverse Variation Problems: Definition & Examples
In this lesson, you'll learn how to approach questions about direct and inverse variation with a simple explanation of what the terms mean and how to apply them to problems.
4. Applying Systems of Linear Equations to Breakeven Point: Steps & Example
Businesses use breakeven points to determine price and sell products. Learn how to use systems of linear equations with revenue and cost functions to find the breakeven point.
5. Applying Systems of Linear Equations to Market Equilibrium: Steps & Example
Businesses use market equilibrium to determine price and sell products. Learn how to use systems of linear equations to find market equilibrium in this video lesson. Review what you know with a short quiz!
6. Using Quadratic Models to Find Minimum & Maximum Values: Definition, Steps & Example
Minimum and maximum values are found in parabolas that open up or down. In this lesson, learn how to find the minimum and maximum values algebraically and graphically.
7. Using Linear Programming to Solve Problems
This lesson describes the use of Linear Programming to search for the optimal solutions to problems with multiple, conflicting objectives, using linear equations to represent the decision problem.
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Other chapters within the Honors Precalculus Textbook course
- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Limits in Precalculus