# TEAS Math Study Guide

## Math Basics

### Lesson 1: Operations Basics

- Integers, Decimals, and Fractions
- Addition and Subtraction
- Multiplication and Division
- Exponents and Roots
- Laws of Exponents
- Exponents and Roots
- Associative Property
- Distributive Property
- Order of Operations

### Lesson 2: Factors and Multiples

- Prime Numbers, Factoring, and Prime Factorization
- Multiples
- Greatest Common Factor
- Least Common Multiple

### Lesson 3: Unit Conversions

## Fractions

### Lesson 1: Fraction Basics

- Improper Fractions and Mixed Numbers
- Fractions of a Whole
- Converting Improper Fractions to Mixed Numbers
- Changing Mixed Numbers to Improper Fractions
- Ordering Fractions

### Lesson 2: Fraction Operations

- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions
- Converting Percentages to Decimals and Fractions
- Converting Mixed Numbers to Decimals and Improper Fractions
- Converting Improper Fractions to Mixed Numbers and Decimals

## Decimals

### Lesson 1: Decimal Basics

### Lesson 2: Decimal Operations

- Adding and Subtracting Decimals
- Multiplying Decimals
- Dividing Decimals
- Converting Decimals to Fractions and Percentages
- Converting Decimals to Improper Fractions and Mixed Numbers
- Scientific Notation
- Changing a Number from Standard Form to Scientific Notation

## Equations and Functions

### Lesson 1: Equation Basics

- Arithmetic Sequences and their Formulas
- Absolute Value
- Solving Equation using Addition and Subtraction
- Solving Equation Using Multiplication and Division
- Solving Equation with Absolute Value
- Solving an Equation Using Four Basic Operations

### Lesson 2: Inequalities

- Equations and Inequalities
- Linear Inequalities
- Solving Inequalities Using All four Basic Operations
- Graphing Solutions to Linear Inequalities
- Solving Absolute Value Inequalities

### Lesson 3: Linear System of Equations

- System of Equations Basics
- Linear Equations Basics
- Comparison of Methods for Solving System of Equations

### Lesson 4: Graphing of Linear Equations and Functions

- Using a Graph
- Graphing Linear Equations
- Graphing the Inverse of a Function
- Graphing Absolute Value Equations
- Graphs of Functions
- Solutions of a Quadratic Equation on a Graph Changing Constants in Graphs of Functions: Linear Functions
- Changing Constants in Graphs of Functions: Quadratic Equations

## Geometry

### Lesson 1: Angle Basics

### Lesson 2: Triangles

- Area and Perimeter of a Triangle
- Proof that a Triangle is 180 Degrees
- Similar Triangles
- Pythagorean Theorem
- Measurements for Similar Triangles
- Measurements for Similar Triangles
- Measurements for Similar Triangles Continued

### Lesson 3: Circles

- Area and Circumference of a Circle
- Unit Circles and Standard Position
- Finding Measurements for Parts of a Circle

### Lesson 4: Volume and Surface Area of 3D Shapes

- 3D Geometric Shapes
- Volume and Surface Area of a Cube
- Volume and Surface Area of a Pyramid
- Volume and Surface Area of a Rectangular Solid
- Volume and Surface Area of a Right Circular Cone
- Volume and Surface Area of a Right Circular Cylinder
- Volume and Surface Area of a Sphere

## Word Problems

- Word Problems and Subtraction
- Word Problems and Addition
- Word Problems and Multiplication
- Word Problems and Division
- Right Triangle Word Problem
- Linear Equation Word Problem

## Probability, Statistics, Percentages, Ratios, and Proportions

### Lesson 1: Probability & Statistics

### Lesson 2: Percentages, Ratios, and Proportions

- Percentages
- Ratios and Percentages
- Computation with Percentages
- Calculation of a Percentage
- Finding the Percentage Increase
- Finding the Percentage Decrease
- Proportions
- Proportions and Percents
- Proportions in the Real World

## TSI Mathematics Review

The TSI—otherwise known as the Texas Success Initiative—is meant to evaluate how prepared you are for the college learning environment before you sign up for your first course load. As it stands, this particular examination is required of every student preparing to start college in the state of Texas. There are a few points of exemption for this exam, however, especially for those who performed well on a national college readiness exam, such as the SAT or ACT. If you turn out to have to take this exam before you enroll in your first official college courses, don’t feel discouraged. We at Mometrix Test Preparation are here and willing to help you however we can.

As you more than likely realize, the TSI assesses your capabilities with three specific subjects: Writing, Reading, and Mathematics. These three subjects will prove to be the most prevalent parts of your academic career as you journey toward your undergraduate degree, hence their position as the main (and only) three subjects of the exam. This particular page is meant to serve as an overview of the Mathematics portion of the TSI exam.

Why is math still such an important aspect of your college readiness? For starters, you spent an ample period of time studying it before you entered college, whether this was through your high school classwork or an equivalency program. Mathematics forms a sizable portion of your general education curriculum as you pursue your degree, and is considered a core subject. Depending on the degree you plan to earn, you may take either a few simple mathematical courses or have semesters filled with the subject. Since college is “higher education”—literally a step or several above high school and similar environments—you are expected to possess a certain level of knowledge in order to thrive in this new and different academic environment. Thus, you will need to be well-versed in basic college-level subjects.

Whether you’re extremely proficient with everything math-related or struggle with the subject, we want to offer you every possible tool for success. This is why we have constructed this TSI Mathematics study guide—to help you learn how this particular section of the exam works and what you can do to prepare for it adequately. On this page, you will find an overview of the TSI Mathematics section. It is our hope that you will be able to use it to formulate a thorough study strategy. For further study, we also have TSI Mathematics flashcards and a TSI Mathematics practice test published on our website. Keep reading to learn how this exam section works and what you can do to prepare.

### What Is Featured on the TSI Mathematics Section?

Like its sister subtests, the Mathematics portion of the Texas Success Initiative Assessment is composed of multiple choice questions. It spans 20 questions in length, and evaluates four specific math-related subjects. The diagnostic exam, which will be administered to you prior to taking the full TSI exam, is half the length of the TSI at 10 questions.

Before we go over the TSI exam, it is vital that we first review the the TSI diagnostic exam’s significance. The diagnostic exam is known formally as the TSI Pre-Assessment Activity. You cannot take the official TSI assessment without first taking the Pre-Assessment Activity. Through this Activity, you will receive a full explanation of every resource at your disposal, from how your school of choice can aid in your success within the college environment, the next moves available to you if you fail to earn a passing score on one or more sections of the TSI, a mock exam to show you what the exam will be like and what elements you need to improve on, and how significant the TSI is to your academic career. Upon completing the TSI Pre-Assessment Activity, you will receive a certificate. This certificate is a highly important ticket of entry for the official TSI assessment.

That said, the Pre-Assessment Activity and formal TSI exam are very similar to one another in terms of subject matter and presentation. The entirety of the test will be taken digitally. It is also worth noting that you cannot bring a calculator with you for help on the Mathematics section of the TSI. You will be able to use a calculator only for very specific questions on the exam. Access to this calculator will come in the form of a small icon next to a designated question, which you can click to open the calculator tool on your testing PC.

Below we will go over which specific mathematical subjects you can expect to find on the TSI Mathematics section, and how you can best approach questions of these types.

### Data Analysis, Statistics, and Probability

This knowledge category’s explicit purpose is to evaluate your capabilities with probability, statistics, and analyzing data. All of these subjects are interrelated. Probability involves the prediction of how likely the occurrence of a specific event will be. Statistics is the measurement of correlation, of how likely an event is to happen and how it relates to other events surrounding it. Data Analysis involves taking data presented to you, be it quantitative or based on specific categories, and deciphering what it means.

For each of these question varieties, you will need to pay close attention to the information given to you. Examine every piece of data given to you, as the questions follow them will ultimately tie into that information. Additionally, be sure to carefully read each question so you know exactly what is being asked of you. This easiest way to make a mistake, especially with this question format, is to misread a question or the data being presented. Knowing how you should be interpreting the data given to you is instrumental to solving the problem.

### Elementary Algebra and Functions

With questions under this category, you will have to know only the fundamentals of algebra—or, basically, what you learned when you first started high school or its equivalent. You will have to solve word problems, algebraic equations, and linear equations. This means you will also have to know how to interpret line graphs and know about their properties; how to solve for exponentials, square roots, and more; and how to decipher word problems.

Again, questions of this variety will require careful attention from you. Examine the line graphs provided to you—and their accompanying questions—closely so you know exactly what you’re supposed to be solving for. Read over the word problems you receive so you can solve the question properly and don’t miss any information.

### Geometry and Measurement

Questions of this variety seek to evaluate your competency with shapes, lines, and their properties. You will have to demonstrate, for instance, how well you understand three-dimensional shapes and their properties. This may involve measuring their volume, area, angles, or other measurements. You will also have to evaluate symmetry and transformations, or how shapes can be equalized and rearranged. You may be given the details about a specific shape and asked to solve for measurement based on the information either through pre-existing knowledge of the formula involved or through a formula provided to you by the word problem. This knowledge category is not the only one where you will have to have some knowledge of mathematical formulas beforehand. As with the other categories, be sure to pay careful attention to what the questions are asking you to do. Through this information, you will be able to decipher which formula you are supposed to use to properly solve the problem.

### Intermediate Algebra and Functions

Questions under the Intermediate Algebra and Functions category cover more advanced algebraic operations which, again, are similar to what you may have learned back in high school. The principles covered by these questions include exponential and rational problems; polynomials; the properties of radicals, roots, and powers; and quadratics. All of these question varieties involve making judgments about numbers, meaning you will have to brush up on just what all of these algebraic principles are and how to solve for them. You will, again, have to also memorize formulas—such as the quadratic formula—to be able to solve for and answer problems to your best possible ability.

While this TSI Mathematics study guide isn’t 100 percent exhaustive in terms of what you will need to know and how you can prepare, we hope it will serve as a launching pad for your studies with this particular section of the exam. For any more extensive help you may need, feel free to turn to our other resources, which include a TSI Mathematics practice test and TSI Mathematics flashcards. We at Mometrix Test Preparation care about your success. This is why we do our best to provide you with excellent tools for any and every exam you may face throughout your academic career. Good luck, and study hard!

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Last updated: 12/13/2018