The Praxis Mathematics (5165 ) Exam is a test required by many states for credential candidates planning to teach mathematics at the high school level. It is a single, computer-delivered test that includes questions from two content categories.

The first content category includes Number and Quantity, Algebra, Functions and Calculus. The second content category includes Geometry, Probability and Statistics, and Discrete Mathematics.

The test consists of various question types including selected-response, numeric entry, drag-and-drop and text completion.

Praxis Mathematics (5165 ) Exam Practice

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25 Questions

1. Simplify .

10

2. A developer decides to build a fence around a neighborhood park, which is positioned on a rectangular lot. Rather than fencing along the lot line, he fences  feet from each of the lot's boundaries. By fencing a rectangular space  smaller than the lot, the developer saves $432 in fencing materials, which cost $12 per linear foot. How much does he spend?

$160$3,168The answer cannot be determined from the given information.$456

3. Use the following proof:

	Statement	Reason
1.	Given
2.
3.	Given
4.	Given
5.
6.
7.
Given: Prove:

Which of the following justifies step 5 in the proof?

SSSAASASASAS

4. Calculate .

5. Which of these could be the equation of the function graphed below?

6. For the right triangle below, where , which of the following is a true statement of equality?

7. Which of these demonstrates the relationship between the sets of prime numbers, real numbers, natural numbers, complex numbers, rational numbers, and integers?

None of these

8. Solve  for .

 or or There is no solution to the equation. or

9. Which mathematician is responsible for what is often called the most remarkable and beautiful mathematical formula, ?

FermatPythagorasEuclidEuler

10. Given the partial table of values for  and , find . (Assume that  and  are the simplest polynomials that fit the data.)

-2	8	1
-1	2	3
0	0	5
1	2	7
2	8	9

18–36931

11. If  and  are inverse functions, which of these is the value of  when ?

4–42

12. Which of these describes the graph of the equation ?

EllipticalHyperbolicParabolicCircular

13. What is the radius of the circle defined by the equation ?

12

14. Which of these can be modeled by a quadratic function?

Radioactive decayThe path of a sound waveThe distance an object travels over time when the rate is constantThe path of a bullet

15. Which of these would best illustrate change over time?

Line graphVenn diagramBox-and-whisker plotPie chart

16. A school is selling tickets to its production of Annie Get Your Gun. Student tickets cost $3 each, and non-student tickets are $5 each. In order to offset the costs of the production, the school must earn at least $300 in ticket sales. Which graph shows the number of tickets the school must sell to offset production costs?

17. In the 1600s, Galileo Galilei studied the motion of pendulums and discovered that the period of a pendulum, the time it takes to complete one full swing, is a function of the square root of the length of its string: , where  is the length of the string and  is the acceleration due to gravity. Consider two pendulums released from the same pivot point and at the same angle, °. Pendulum 1 has a mass of 100 g, while Pendulum 2 has a mass of 200 g. If Pendulum 1 has a period four times the period of Pendulum 2, what is true of the lengths of the pendulums' strings? The length of Pendulum 1's string is less than the length of Pendulum 2's string.The length of Pendulum 1's string is sixteen times the length of Pendulum 2's string.The length of Pendulum 1's string is four times the length of Pendulum 2's string.The length of Pendulum 1's string is eight times the length of Pendulum 2's string. 18. Which of these equations is represented by the graph below? "None of these 19. Which of these is the least biased sampling technique? To determine the average intelligence quotient (IQ) of students in her school of 2,000 students, a principal uses a random number generator to select 300 students by student identification number and has them participate in a standardized IQ test.Sixty percent of students at the school have a parent who is a member of the Parent-Teacher Association (PTA). To determine parent opinions regarding school improvement programs, the Parent-Teacher Association (PTA) requires submission of a survey responsTo determine which video game is most popular among his fellow eleventh graders at school, a student surveys all of the students in his English class.To assess his effectiveness in the classroom, a teacher distributes a teacher evaluation to all of his students. Responses are anonymous and voluntary. 20. Approximate the area  under the curve by using a Riemann sum with . 21. Find the derivative of 22. Solve  for  and . 23. As shown below, four congruent isosceles trapezoids are positioned such that they form an arch. Find  for the indicated angle. The value of  cannot be determined from the information given. 24. To which of the following sets of numbers does  NOT belong? The set of whole numbersThe set of real numbersThe set of rational numbersThe set of integers 25. Solve x = 2x = -5No solutionx = 1 ⚡ Recently practiced quizzes in this topic Live quiz activity Praxis II Technology Education (5051) Praxis II Elementary Education: Multiple Subjects (5001) Exam - Social Studies Praxis II Music Education Vocab Praxis II English Language Arts Content Knowledge (5038) Exam: Reading 7 Praxis Animal Science Praxis II Elementary Education: Multiple Subjects (5001) Exam - Science Praxis II Elementary Education: Multiple Subjects (5001) Exam - Reading and Language Arts Praxis II Library Media Specialist (5311) Exam Practice Test Praxis 5081 - Social Studies Praxis II Elementary Education: Multiple Subjects (5001) Exam - Mathematics Welcome to Fatskills Join 4M+ learners. Unlock unlimited quizzes, wrong-answer tracking, flashcards + reminders, study guides, and 1-on-1 challenges. Create a free account Sign in 900+ exams • Millions of questions • No spam   ❤ If you liked Fatskills, consider supporting us by checking out The Life Manuals You Never Got. 🌈  Our mission is to help improve your scores in any subject and exam withonline quizzes, practice tests, study guides, & advice for students. Since 2018. About | Explore | User Guide | Topics | Subjects | Doubt Solver | Career Aptitude Test | Answers | Free Tools | OSHA Basics Quiz | What Should We Know? Privacy | Terms | Without work one finishes nothing. - Ralph Waldo Emerson © 2026 Fatskills.com All trademarks, logos and brand names are the property of their respective owners. All company, product and service names used in this website are for identification purposes only. Use of these names, trademarks and brands does not imply endorsement.