# Praxis® Math Content Knowledge Practice Test

## What Is the Praxis Math Content Knowledge Exam?

If you have decided to take the journey to become an educator, the certification process can seem overwhelming, as each state institution and organization has unique requirements. Most states require one or more Praxis tests for teachers based on the grade level and subject you will be teaching. If you have decided to follow a mathematics route in secondary education, your state or institution may require you to take the Praxis Math Content Knowledge 5161 test. The average tester has completed a bachelor's degree with an emphasis in mathematics and possesses a general understanding and ability to apply mathematical concepts to solve problems.

Practice tests give you a better idea of the topics you have mastered and those you should keep studying.

## Praxis 5161 Exam Overview

The Praxis 2 math test (Praxis 5161) is composed of two content categories with a total of 60 questions. It is a computer-delivered exam with questions formatted as selected-response (multiple-choice, numeric entry, text completion and drag-and-drop). You will have 150 minutes to complete the Praxis math content knowledge exam. On some questions, you will have access to an on-screen graphing calculator. The table below will give you an overview of the sections on the test, the approximate number of questions, and the weight of the questions on your exam.

 Number and Quantity, Algebra, Functions, and Calculus Geometry, Probability, and Statistics Approximate Number of Questions 41 19 Approximate Percentage of Exam 68% 32%

### Content Category: Number and Quantity, Algebra, Functions, and Calculus

This section of the Praxis 5161 is grouped into 4 subcategories and represents the bulk of the test questions. Below you will find a list of concepts contained in the subcategories.

#### Number and Quantity

• Properties of exponents
• Properties of irrational and rational numbers, interactions between them
• Quantitative reasoning and problem solving
• Integers and basic order of operations
• Complex numbers and polynomial equations
• Matrices
• Ratios, proportions, rates, averages, percents

#### Algebra

• Algebraic expressions
• Arithmetic operations on polynomial and rational expressions
• Create equations and inequalities
• Justify reasoning
• Concept of intercepts (line, slope, rate of change)
• Zeros of functions
• Linear and nonlinear equations

#### Functions

• Function concept and notation
• Domain and range
• Compositions, transformations, inverses
• Linear, quadratic, and exponential models
• Trigonometric identities, functions, and measures

#### Calculus

• Limit and derivative of a function
• Relationship between continuity and differentiability
• Standard Differentiation and integration techniques
• Behavior of a function
• Foundational theorems of Calculus
• Limits of sequences
• Simple infinite series

### Content Category: Geometry, Probability, and Statistics, Discrete Mathematics

Similar to the first content category, the second is broken down into 3 subcategories listed below.

#### Geometry

• Transformations in a plane
• Geometric theorems
• Geometric constructions
• Congruence and similarity
• Trigonometric ratios
• Circles-length and area measurements
• Triangles-ratios in right triangles, trigonometry about triangles
• Perimeter, area, surface area, and volume
• Properties of parallel and perpendicular lines, triangles, quadrilaterals, polygons, and circles

#### Probability and Statistics

• Summarize, represent, and interpret data
• Linear regression models
• Statistical processes
• Make inferences and draw conclusions
• Independence and conditional probability
• Probabilities and simple, compound, and conditional events

#### Discrete Mathematics

• Sequences
• Recursion
• Equivalence relations
• Discrete and continuous representations
• Counting techniques
• Basic terminology and symbols of logic
• Basic set theory

## Taking the Praxis Math Content Knowledge Exam

Once you have determined that Praxis 5161 is the correct test for your certification, you can begin your Praxis test preparation and think about what happens after you have completed the Praxis test. The first step is to register for the Praxis 2 math content knowledge test, so you will have a timeline of studying and a set testing day. Then, you can begin exploring study materials, getting a baseline of what you already know and what you need to know. Finally, you will take your exam and wait to receive your scores/have your scores sent to the agency or institution (s) of your choice. We'll cover these steps in detail below.

### Registering for the Praxis 5161

You can begin the test registration process by ensuring you are signing up for the exam needed to meet your certification requirements, looking at the testing locations available, finding Praxis 5161 test dates, and familiarizing yourself with Praxis test fees. The Praxis 5161 fee is $130, and both in-person and at-home testing locations are available. If you would like to take Praxis at home, you must reside in the United States and meet equipment and environment requirements. You can search for an in-person testing center near you on the ETS website. After deciding where you would like to take your test, you can create a free account and proceed with Praxis online registration. Alternatively, you can register by mail or by phone. There is a$35 processing fee when registering by phone.

### Praxis 5161 Test Prep

Studying for a test, especially one that directly affects your certification, can be intimidating. Luckily there are several resources available to help you study and perform your best on the Praxis math content knowledge test. A step in the right direction is taking a 5161 practice test. Praxis practice exams measure your current knowledge and give you a baseline for what you need to study on. To optimize your time, you can strategically study first what you do not know, and closer to the test, refresh your memory on the things you already know.

#### Praxis Math Content Knowledge Test Prep Materials

A great resource and starting place is a study guide or study companion that provides in-depth information on what is included in the exam, question format, and even Praxis 5161 practice test questions. Another useful test prep resource is a practice test that models the testing environment and gives you an in-depth explanation of each answer. It is recommended to take this test closer to your Praxis test day in order to get a good representation of how you will do on the test.

### Praxis 5161 Test Day Preparation

You have made it to the day of the test! What to expect can vary based on whether or not you registered for an in-person or at-home examination.

#### In-Person Exams

If you are taking the exam in person, remember to bring your:

• Valid photo ID
• A calculator (if allowed and not provided on your test)

Do not bring personal items, as you will not be allowed to use them during the test or breaks. Avoid wearing jewelry, glasses, or other accessories that you do not need. Clothing is subject to be searched. It is recommended to arrive at the Praxis testing center 30 minutes prior to the exam. Once you arrive, the test administrator will check you in and show you your assigned seating. Most tests do not have scheduled breaks, although a 5-10 minute unscheduled bathroom break is permitted; the testing clock will not stop during an unscheduled break.

#### At-Home Exams

If you are taking the exam online, make sure your environment meets the requirements of a clear, well-lit, private space. Run a final equipment check and ensure all issues are fixed prior to the start time. Then, gather your:

• Valid photo ID
• Appropriate note-taking materials (erasable whiteboard or cellophane sheet)
• Cell phone or handheld mirror for check-in

Make sure your clothing is appropriate, your ears are visible, and you are not wearing jewelry/glasses/accessories that could be used to cheat. It is recommended that you log on 15 minutes prior to the start of the Praxis exam. You will check in by showing the proctor a 360-degree view of the room you are testing in and utilizing the cellphone or mirror to provide a view of your computer screen. The proctor will authenticate your identity, read you the rules, and begin your test. During the Praxis test, do not communicate with anyone except your proctor. Scheduled breaks are normally not included, but an unscheduled 5-10 minute restroom break is permitted, although your testing clock will not stop.

### Praxis Math Content Knowledge Passing Score

Praxis exams are graded by taking the raw points you earn on each question and transitioning them into a 100-200 point scale based on the difficulty of the test. On this scale, 100 is equal to 0% and 200 is equal to 100%.

Each state institution or agency has the ability to create the standards of certification, thus the passing Praxis score for your state may differ from someone in another state. The range of praxis 2 math passing scores is between 135-160 with 160 being the most common. On the ETS website, there is a helpful tool where you can input the test you took or your state/agency to see the passing score for your area.

## Expert Contributor

### Corey Sexton

Corey Sexton, M.Ed. has over 16 years of experience as a high school library media specialist. She holds teaching certificates for Pre-K, K-3, 1-8, and K-12 Library Media, as well as administrative licenses for 4-9 and 7-12. Corey graduated with an M.Ed. in Leadership from Concordia University and an M.Ed. in School Library Media & Information Technology from Mansfield University.

• ##### How many questions are on the Praxis 2?

The Praxis 2 Math test is composed of 60 questions divided into two sections, with approximately 41 questions in the first section and 19 questions in the second section. Some questions may be unscored, pretest questions that help introduce potential questions for future versions of the test. These questions can also help familiarize you with the exam.

• ##### What is on the Math Praxis 5161?

The Praxis 5161 includes two sections, 1. Number and Quantity, Algebra, Functions, and Calculus and 2. Geometry, Probability, and Statistics, Discrete Mathematics. The majority of the exam focuses on the first content section. Both categories ask specific questions about any of the subcategories. Questions can be formatted as multiple-choice or short-answer/essay questions.

• ##### What is a passing score for Praxis 5161?

Every state institution/agency has the ability to unique requirements for certification. To find your passing score you can access the ETS tool that shows each state requirements. The range of passing scores for the Praxis 5161 exam is 135-160 with the average passing score being 160.

## Take a Praxis Math Content Knowledge Practice Test Online

### Exam Instructions:

Complete the practice test below to test your knowledge of Praxis Math Content Knowledge.
Choose your answers below. Complete the 15 questions then click "See Results."

## You have answered 0 out of 15 correctly.

The correct answers are highlighted with green below.

1. Purity wants to demarcate her rectangular piece of land, which is next to a straight highway, using a 4500 m rope. Assuming she doesn't need to demarcate along the highway, what are the dimensions of the land that has the largest area?

2. Using the property of the logarithms, condense and simplify the following expression:

(4 log 3 + log (2x)) - log 18

3. Solve.; 102x - 2 (10x) + 1 = 0
4. What is the distance from point A to point B in the following graph?

5. Find the product for the following polynomial functions.

6. An arithmetic sequence follows the function defined by f(n) = 3n +5, for all integers n ≥ 1. What is the sum of the first five terms of the sequence?

7. The revenue of a company is represented by R(x) and their costs are represented by C(x). What is the profit function R(x) - C(x)?

8. A regular octagon has a side length of {eq}k + 2 {/eq}. What is its perimeter?

9. During the first four Summer Olympic games attended by the United States, these medal counts were awarded. Calculate the mean number of medals won during these Olympic Games. (Round it to the nearest whole number.)

10. The cost of a dozen of bottles of sherry is equal to \$120. What is the unit rate representing the cost of each bottle of sherry?

11. At which values of x is the following rational function undefined?

{eq}f(x) = \dfrac{x^2 - 4}{x^4 - 16} {/eq}

12. What is the discriminant for the following quadratic equation?

{eq}5x^2 - 3x - 2 = 0 {/eq}

13. Evaluate the following limit, if it exists:

{eq}lim_{x \rightarrow -1} \dfrac{\sqrt{x + 1}(x+1)}{(3x^2 - x + 4)} {/eq}