# Ch 11: Compass Math: Substituting Values

### About This Chapter

## Compass Math: Substituting Values - Chapter Summary

Sit down with this chapter to remember the process involved in substituting mathematical values. To perform substitution correctly on equations on the ACT Compass Mathematics Test, be sure to go over the following key areas:

- The substitution method
- The substitution property of equality
- Solving regular and difficult integrals with substitution
- Trigonometric substitution
- Using substitution for quadratic equations

If you learned about substitution early on during your pre-algebra and algebra courses, you might need a quick refresher to get back on track. Our short video lessons can guide you through the process and remind you of all the intricacies involved. Read through the transcripts to develop a deeper understanding of the topic. Going through the lesson summaries at the bottom of the transcripts may prove to be a useful cram-session strategy. Other than brushing up on major topics, you may want some practice solving equations before you take the actual ACT Compass Mathematics Test. For some pre-test exercises, try tackling the questions on our lesson quizzes or the chapter exam.

### Compass Math: Substituting Values Objectives

Academic institutions use the ACT Compass Mathematics Test to evaluate the knowledge and skills of applicants. The test can include up to five different domain sections, but not all colleges include all five sections. This chapter on substituting values will strengthen your knowledge for answering related questions within the algebra and college algebra sections. Although all the questions are multiple-choice, the questions will measure your ability to do math in three different ways. For some questions, you will have to demonstrate your skills at analysis, whereas other questions may measure your understanding of basic mathematics concepts or your ability to apply mathematical principles to a problem.

### 1. Substitution Property of Equality: Definition & Examples

In this lesson, you will learn the definition of the substitution property of equality and why this property is so important in mathematics. You will be given examples to illustrate.

### 2. Solving Equations with the Substitution Method: Algebra Examples & Overview

What does the substitution method have to do with substitute teachers? Learn why you should love substitutes. Also learn how substitutes make your life easier when it comes to solving sets of equations.

### 3. How to Solve Integrals Using Substitution

Some integrals are as easy as riding a bike. But more often, integrals can look like deformed bikes from Mars in the year 3000. In this lesson, you will learn how to transform these scary-looking integrals into simpler ones that really are as easy as riding a bike.

### 4. Substitution Techniques for Difficult Integrals

Up, down. East, West. Opposites are everywhere. In this lesson, learn how you can think of substitution for integration as the opposite of the chain rule of differentiation.

### 5. How to Use Trigonometric Substitution to Solve Integrals

In this lesson, we use each of the common integration techniques to solve different integrals. It's not always obvious which technique will be the easiest, so being familiar with an arsenal of methods might save you a lot of work!

### 6. Understanding Trigonometric Substitution

Sometimes a simple substitution can make life a lot easier. Imagine how nice it would be if you could replace your federal tax form with a 'Hello, my name is...' name badge! In this lesson, we review how you can use trigonometry to make substitutions to simplify integrals.

### 7. Solving Quadratic Equations by Substitution

After watching this video lesson, you will be able to solve more complicated quadratic equations by the method of substitution. Learn how substitution makes your problem solving easier.

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### Other Chapters

Other chapters within the ACT Compass Math Test: Practice & Study Guide course

- Compass Math: Integers
- Compass Math: Decimals
- Compass Math: Fractions
- Compass Math: Exponents
- Compass Math: Roots & Radicals
- Compass Math: Percents
- Compass Math: Ratios, Rates & Proportions
- Compass Math: Median, Mean & Mode
- Compass Math: Algebraic Equations & Expressions
- Compass Math: Linear Equations
- Compass Math: Monomials & Polynomials
- Compass Math: Factoring Polynomials
- Compass Math: Matrices & Absolute Value
- Compass Math: Inequalities
- Compass Math: Complex Numbers
- Compass Math: Logarithms
- Compass Math: Basic Geometry
- Compass Math: Lines & Angles
- Compass Math: Polygons
- Compass Math: Triangles
- Compass Math: Quadrilaterals
- Compass Math: Circles
- Compass Math: Similar Figures
- Compass Math: Complex Figures
- Compass Math: Constructions
- Compass Math: Area, Circumference & Perimeter
- Compass Math: Mathematical Modeling
- Compass Math: Quadratics
- Compass Math: Quadratic Functions
- Compass Math: Trigonometric Functions
- Compass Math: Rational Functions
- Compass Math: Function Operations
- Compass Math: Trigonometric Identities
- Compass Math: Trigonometric Equations
- Compass Math: Trigonometric Applications
- Compass Math: Trigonometric Graphs
- Compass Math: Graph Symmetry
- Compass Math: Polar Coordinates & Parameterization