# Ch 25: SAT Math: Equations and Expressions

### About This Chapter

## SAT Math: Equations and Expressions - Chapter Summary

The largest portion of the math SAT addresses algebra functions. Prepare by taking advantage of our user-friendly video lessons that cover essential topics:

- Linear equations
- Absolute value
- Systems of equations
- Direct and inverse variations
- Exponential equations
- Quadratics formula and equations
- Multiplication of binomials with FOIL and area methods
- Polynomials
- Complete the square

As you make your way through the short video lessons, make sure that you also complete the quick quizzes. Then you'll know if you're ready to go on to the next chapter or if there are topics you should review first.

### SAT Math Objectives

At least 35% of the math test, composed of 58 questions over 80 minutes, analyzes your algebra skills. The SAT topics tested in this area include the following:

- Exponents
- Simplifying and substituting
- Linear equations and inequalities
- Algebraic word problems
- Quadratic equations
- Radical and rational equations
- Absolute value
- Inverse and direct variation
- Equations of lines
- Algebraic functions concepts

By completing our review in this chapter, you'll address all of the topics listed above. Complete the accompanying exercises for additional practice in solving absolute value, using FOIL and the area method in multiplying binomials and in completing the square. By the time you take the quizzes, you should be ready for some positive feedback.

You may use an approved model of calculator on test day for the calculator section. There is also a no-calculator section. You don't lose any points for incorrect answers in responses, nor for questions you choose not to answer. Your raw score then converts into a scaled score ranging from 200-800. If you earn around 500, you'll know that your score was similar to the national average for SAT math test takers.

### 1. What is a Linear Equation?

A linear equation is a pattern of numbers with proportional increase or decrease that is used to represent a line graph. Learn how to plot a graph and build and solve a linear equation.

### 2. How to Write a Linear Equation

Rather than drawing a graph from an equation, graphs can be used to determine equations using common algebraic techniques. Learn how to write a linear equation using two points and the slope formula as well as using background information on parallel and perpendicular lines.

### 3. Linear Equations: Intercepts, Standard Form and Graphing

To solve a linear equation, begin by determining whether it is written in the standard form or the slope-intercept form. Explore the differences between the slope-intercept form and the standard form of a linear equation, and learn how to graph the point of intercept for each.

### 4. Problem-Solving using Linear Equations

Word problems can be solved after being translated into linear equations. Learn what a linear equation is and how to use it to solve simple problems, and take a look at some real-world practice problems.

### 5. Solving Linear Equations: Practice Problems

Linear equations are algebraic expressions of a line. Become familiar with recognizing and solving linear equations through examples and practice problems.

### 6. How to Solve a System of Linear Equations in Two Variables

A system of linear equations in two variables is an important concept that is used in many math disciplines. Review a detailed explanation of these systems and explore how to solve them using the substitution method.

### 7. How to Recognize Linear Functions vs Non-Linear Functions

There are only two ways to represent information on a graph and that is in linear or non-linear functions. Learn more about their application on graphs and how to interpret them when written as equations.

### 8. Identifying Linear & Nonlinear Functions Using Graphs & Tables

Linear and nonlinear functions can be identified using graphs and tables in different ways. Learn how lines on graphed functions and organized tables of inputs and outputs can identify linear and nonlinear equations.

### 9. Using Nonlinear Functions in Real Life Situations

Though it seems unlikely in a class setting, many math concepts are applicable to real life. Delve deeper into non-linear functions and learn how to select ones with real-life applications.

### 10. What is a System of Equations?

Math word problems often ask students to compare and contrast, which are types of problems that can be solved with a system of equations. Learn about solving word problems using systems of equations and how to graph them, as well as the algebraic method of substitution through an example.

### 11. How Do I Use a System of Equations?

Most word problems that appear on math tests require a system of two or more equations to solve. Through examples, learn how to solve a system of equations with substitution and elimination in three steps.

### 12. Direct and Inverse Variation Problems: Definition & Examples

With direct variation, numbers change proportionately in the same direction, while with inverse variation, they change in opposite directions. Learn how to solve direct and inverse variation problems, explore their definitions, and work examples to understand the equations and techniques for solving them.

### 13. How to Solve Exponential Equations

Exponential equations typically have a variable in the exponent that must be solved, which is done by using a logarithmic function. Learn how to use logarithmic functions, such as the natural logarithm with a base of e, or Euler's number, to solve exponential equations.

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### Other Chapters

Other chapters within the SAT Prep: Practice & Study Guide course

- SAT: About the Test
- SAT Writing: About the Writing Section
- SAT Writing: Text & Argument Analysis
- SAT Writing: Word Choice & Expression
- SAT Writing: Standard English Grammar
- SAT Writing: Writing & Language Test Practice
- SAT Writing: The Essay Portion
- SAT Writing: Planning and Writing Your Essay
- SAT Writing: Parts of an Essay
- SAT Writing: Sentence Clarity and Structure
- SAT Writing: Essay Writing Skills
- SAT Writing: How to Write An Argument
- SAT Writing: Supporting Your Writing
- SAT Writing: Revising Your Writing
- SAT Reading: About the Reading Section
- SAT Reading: Reading Passages
- SAT Reading: Understanding Reading Passages
- SAT Reading: Interpreting & Analyzing Text
- SAT Reading: Literary Terms
- SAT Reading: US Documents & Speeches
- SAT Vocabulary Practice
- SAT Math: About the Math Section
- SAT Math: Numbers and Operations
- SAT Math: Exponents
- SAT Math: Rational Equations and Expressions
- SAT Math: Inequalities
- SAT Math: Functions
- SAT Math: Quadratic Equations
- SAT Math: Ratios, Rates & Proportional Relationships
- SAT Math: Unit Rate & Measurement Conversions
- SAT Math: Geometry and Measurement
- SAT Math: Triangles & Trigonometric Ratios
- SAT Math: Data Analysis, Statistics and Probability
- SAT Prep Flashcards
- SAT Flashcards
- SAT Prep Essay Tips & Practice