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. Solve .

2. If  when , what is the value of

3. A triangle with vertices and  is reflected across  to give , which is subsequently reflected across the -axis to give. Which of these statements is true?

A translation of  two units down gives A 90° rotation of  about  gives A reflection of  about the -axis gives A 270° rotation of  about gives .

4. A rainbow pattern is designed from semi-circles as shown below. Which of the following gives the area A of the shaded region as a function of ?

5. Which of these represents the equation of a sphere which is centered in the -space at the point (1, 0, -2) and which has a volume of 36π cubic units?

6. Find  when  and .

7. 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 sixteen 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.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 four times the length of Pendulum 2's string.

8. 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

–3311869

9. Which of the following expressions is equal to

10. What is the exact value of ?

1

11. 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?

12. A man looks out of a window of a tall building at a 45° angle of depression and sees his car in the parking lot. When he turns his gaze downward to a 60angle of depression, he sees his wife's car. If his car is parked 60 feet from his wife's car, about how far from the building did his wife park her car? 163 feet122 feet60 feet82 feet 13. If  is true, which of these is also necessarily true? None of these 14. A dress is marked down by 20% and placed on a clearance rack, on which is posted a sign reading, 'Take an extra 25% off already reduced merchandise.' What fraction of the original price is the final sales price of the dress? 15. Solve No solutionx = 2x = -5x = 1 16. Solve the system of equations: 17. For which of these does a rotation of 120° about the center of the polygon map the polygon onto itself? Regular decagonSquareRegular octagonRegular hexagon 18. Which of these statements is true for functions , , and ? None of these is true for functions  and .The degree of each polynomial function is 2.Each function has exactly one real zero at .The leading coefficient of each function is –2. 19. For functions , , and , determine the limit of the function as  approaches 2 and the continuity of the function at  given: 20. If  find the slope of the line tangent to graph of  at . 40–21 21. Calculate 22. Solve . 23. The path of a ball thrown into the air is modeled by the first quadrant graph of the equation h is the height of the ball in feet and t is time in seconds after the ball is thrown. What is the average rate of change in the ball's height with respect to time over the interval [1, 3]? 0 feet/second48 feet/second96 feet/second53 feet/second 24. Which of these functions includes 1 as an element of the domain and 2 as an element of the range? 25. In a town of 35,638 people, about a quarter of the population is under the age of 35. Of those, just over a third attend local K-12 schools. If the number of students in each grade is about the same, how many fourth graders likely reside in the town? Fewer than 100Between 300 and 400Between 200 and 300More than 400 ⚡ Recently practiced quizzes in this topic Live quiz activity HIT Terminology 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 | 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.