Praxis® Math Content Knowledge (5161) Practice Test & Study Guide

What Is the Praxis Math Content Knowledge (5161) Exam?

The Praxis Math Content Knowledge exam may go by several names, including the Praxis 2 Math or Praxis 5161. This Praxis exam is used in many states and is designed to test the knowledge and competencies of aspiring secondary education math teachers. Students are tested in various question types over a number of mathematical topics, including topics in geometry, algebra, functions, statistics, calculus, and discrete mathematics. The exam focuses on mathematical content knowledge and not teaching skills.

The content of the exam does not align with any specific mathematics curriculum but helps test concepts identified in national studies as important in mathematical education. An on-screen graphing calculator is provided for the exam. Below, we discuss in detail various aspects of the Praxis Math Content Knowledge exam and methods of Praxis exam preparation that would lead candidates to achieve the Praxis passing scores.

Praxis 5161 Exam Format and Length

The Praxis Math Content Knowledge exam consists of 60 questions. The Praxis test is delivered on the computer, and students answer different types of questions to test their problem-solving skills and math content knowledge. For example, students will answer selected-response questions, numeric entry questions, text completion questions, and drag-and-drop questions. The selected-response questions may have students select one answer or one or more answers, depending on the question type. Other question types may be included, and students will have an on-screen graphing calculator for their calculations.

Time Limit for Praxis Math Content Knowledge Exam

Students are allowed 150 minutes or 2.5 hours to complete the Praxis Math Content Knowledge exam on the computer. Some students may not need the entire allotted time, but others may choose to use the entire time to take the exam and check over their work.

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

What Is Covered on the Praxis Math Content Knowledge (5161) Exam?

The Praxis Math Content Knowledge (5161) exam tests students' knowledge and understanding of a wide range of areas within the field of mathematics. These mathematical concepts are tested in different types of questions that may require the use of a graphing calculator for calculations. The questions on this Praxis examination can be grouped into two main math categories. The first category includes number and quantity, algebra, functions, and calculus. The second category covers geometry, probability and statistics, and discrete mathematics. Here, we discuss these two categories of questions in greater detail.

Number and Quantity, Algebra, Functions, and Calculus

A majority of the questions on the Praxis Math Content Knowledge exam fall into the category of number and quantity, algebra, functions, and calculus. According to the ETS Praxis Study Companion for the exam, 68% of questions fall into this category. The guide also lists multiple competencies for each concept in the category. For example, in the number and quantity section, students should understand exponents, rational and irrational numbers, complex numbers, and more. In algebra, students should be able to write algebraic expressions, utilize polynomial identities, and create equations and inequalities to explain relationships. Under the function category, students must be able to use function notation, analyze function behavior, and understand differences between various models (i.e., linear, quadratic, etc.). Finally, the calculus section expects students to understand limits, derivatives, and foundational theorems of calculus.

Geometry, Probability and Statistics, and Discrete Mathematics

The other 32% of the Praxis Math Content Knowledge exam falls into the geometry, probability and statistics, and discrete mathematics category. Using the exam guide, students can check their familiarity with the required competencies in each section. For geometry, students need to understand concepts, such as transformations in a plane, geometric proofs, congruence, and trigonometric ratios. Under probability and statistics, students must understand how to summarize and interpret data with one or more variables, explain linear regression models, and apply probability to data. Some required concepts in discrete mathematics that students must know include understanding sequences, equivalence relations, and the terminology and symbols of logic.

How to Register for the Praxis Math Content Knowledge (5161) Exam

Students must register to take the Praxis Math Content Knowledge exam. There are several ways this can be done, including online, by mail, and by phone. Students wishing to complete Praxis registration online must:

  • Log into their ETS Praxis account with a valid address
  • Choose 'Register for a Test'
  • Select the Praxis Math Content Knowledge exam
  • Select a time and date for the exam upon viewing the Praxis test dates and locations available
  • Pay the required fee
  • Print the admission ticket if taking the exam at a Praxis testing center

Students who want to register by mail need to complete the Test Authorization Voucher Request Form, mail it to the ETS, and wait for a voucher form and instructions on how to register for Praxis exam, which can take up to 3 weeks. Students who choose to test at a test center will still need to print their admission ticket from their ETS account. Finally, those wishing to register via phone will need to pay a certain fee in addition to the Praxis test cost, call the ETS 4 days prior to their test date, and pay the required fee.

Registration Fees

The fee for taking the Praxis Math Content Knowledge exam is $130. There are also additional fees for different circumstances surrounding the Praxis exam. For example, if students register for the exam by phone, they will need to pay an additional $35 or $40 for changing Praxis test dates or test centers. Also, if students choose to have a score review after they have received their Praxis scores, they will need to pay a $65 fee.

Praxis 5161 Test Dates and Locations

Praxis 5161 test dates may vary depending on the chosen testing location. However, students can use the Praxis dates and locations page to select the Praxis Math Content Knowledge Exam and see the Praxis test dates available each month, which are highlighted in blue. The available dates are set by default for in-person testing at a testing center. Students can also use a checkbox to see the available at-home test dates, as students have the option to take Praxis at home.

Praxis testing centers are available around the globe at Prometric test centers and universities. Students can search for a test center near them by using the test center location tool on the ETS website. Students need to make sure they bring their admission ticket and a valid ID to their test center and leave behind most personal items. Students who choose to take Praxis test at home can opt to take the test 7 days a week from 10 am to 1 am Eastern Time.

How Is the Praxis Math Content Knowledge Exam Scored?

Students who take the Praxis Math Content Knowledge exam can usually expect to receive their Praxis scores 6 to 9 days after taking the exam. Usually, scores are reported after 5 pm Eastern Time on the following Tuesday after the exam for students who took the Praxis exam on Sunday through Tuesday and after 5 pm Eastern Time on the following Friday for students who took an exam Wednesday through Saturday.

The Praxis score report shows if the test taker passed the exam and the range of possible scores. The scores are also broken down into raw points for each content category, and students can see the middle 50% of scores for their exam. Students who have already taken the Praxis examination will also see their prior scores listed.

Praxis Math Content Knowledge Passing Score

The Praxis Math Content Knowledge passing score may vary across Praxis states. Students can use the state requirements page to see the Praxis II Math passing score for their state.

Several states, including Kentucky, Virginia, and New Mexico, only accept Praxis scores above 159. It should be noted that New Mexico is only accepting scores for the Praxis Math Content Knowledge exam through August 31, 2022. Kentucky is only accepting the 5161 until January 2022. These states are replacing the Praxis Math Content Knowledge (5161) exam with Mathematics (5165) in September 2021.

How to Prepare for the Praxis Math Content Knowledge Exam

Praxis 5161 test prep is available from a number of sources. Students can find Praxis 5161 practice tests online, but the ETS also provides a range of study materials, including a study companion and a study plan. Within the study companion, students can familiarize themselves with the Praxis content, as well as the types of questions that will be on the test. Students can explore Praxis test sample questions and read through several different study and preparation tips. For example, students should be sure to develop a study plan and ensure that they cover all of the different competencies for the exam. The day of the exam, students should eat well, do their best to stay calm, be well-rested, and be careful to monitor the time and check their answers if time allows.

Expert Contributor

Jenna Feldman

Jenna Feldman, M.Ed. has taught high school math for over 11 years. She has developed curricula for Algebra, Algebra 2, Precalculus, Geometry, Statistics, and Calculus. She passed the Praxis Core Academic Skills for Reading, Writing and Math, as well as the Praxis Mathematics Content Knowledge exam. Jenna earned her M.Ed. from Wesley College and her B.A. in Mathematics from the University of Delaware.

Frequently Asked Questions

  • Is the Praxis 5161 hard?

    The Praxis 5161 can be challenging; it covers a wide range of mathematical content. However, students can take advantage of study guides and practice exams to make sure they are familiar with the test, the types of questions that will be asked, and the mathematical content.

  • What do you need to pass Praxis 5161?

    The specific score that students need to pass the Praxis 5161 may vary by state, but some states require a 160 or above. To help increase the chances of passing, students should be sure to study and utilize a range of practice materials.


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  1. A chocolate bar manufacturing company is being audited. The auditing firm is checking if the weights of the chocolate bars are within a consistent range. Based on the chocolate manufacturing company's data, the mean weight of their chocolate bars is {eq}5.50~ounces {/eq} with a standard deviation of {eq}0.07~ounces {/eq}. If the data is accurate, what is the z-score of a chocolate bar in a production batch that has a weight of {eq}5.55~ounces {/eq}?

    • Correct Answer
  2. Sarah bought {eq}45~in {/eq} of blue ribbon, {eq}52~in {/eq} of red ribbon, and {eq}47~in {/eq} of green ribbon. What is the total length of the ribbons in yards?

    • Correct Answer
  3. A triangle has measured side lengths of 3.50 centimeters, 7.210 centimeters and 4.9 centimeters. What is the perimeter of this triangle rounded to the correct number of significant figures?

    • Correct Answer
  4. Which of the following choices represent non-linear functions?

  5. Which of the following graphs represents y = sin(x)?
    • Correct Answer
  6. Which of the following best describes the image below?

    A triangle in a circle

    A triangle in a circle where one vertex of the triangle touches the outline of the circle

    • Correct Answer
  7. There are 10 movies playing at the local movie theater. How many ways can you choose your top 3 movies to see in order of preference?

    • Correct Answer
  8. What is the limit of the function as x approaches -3?

    • Correct Answer
  9. Which of the following values contain 3 significant figures?

  10. James received a parcel put inside a rectangular-based box, which measures 40 cm by 56 cm. If its height is 80 cm, find the volume of the box?

    • Correct Answer
  11. Angeline will be happy if she gets a high score in math and if she gets a reservation to the broadway musical. She got a high score in math but failed to get a reservation in the broadway play. Therefore,
    • Correct Answer
  12. Determine the distance between the following points:

    {eq}A = (3, -1) \\ B = (9, 7) {/eq}

    • Correct Answer
  13. Which of the following is a local minimum?

    • Correct Answer
  14. Which of the following numbers are irrational?

  15. Multiply, then simplify:

    • Correct Answer