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Praxis Mathematics (5165 ) Exam Practice
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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. A small company is divided into three departments as shown. Two individuals are chosen at random to attend a conference. What is the approximate probability that two women from the same department will be chosen?

Department 1

Department 2

Department 3

Women

12

28

16

Men

18

14

15

2. Approximate the area  under the curve by using a Riemann sum with .
3. Which of these statements is true for functions , , and ?

4. Natasha designs a square pyramidal tent for her children. Each of the sides of the square base measures  ft, and the tent's height is  feet. If Natasha were to increase by 1 ft the length of each side of the base, how much more interior space would the tent have?
5. Evaluate .
6. 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?

7. On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30 .
What is the actual area of the room?
8. Calculate .
9. 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?
10. If , what is ?
11. For which of these does a rotation of 120° about the center of the polygon map the polygon onto itself?
12. In order to analyze the real estate market for two different zip codes within the city, a realtor examines the most recent 100 home sales in each zip code. She considered a house which sold within the first month of its listing to have a market time of one month; likewise, she considered a house to have a market time of two months if it sold after having been on the market for one month but by the end of the second month. Using this definition of market time, she determined the frequency of sales by number of months on the market. The results are displayed below. Which of the following is a true statement for these data?
13. If  and  are inverse functions, which of these is the value of  when ?
14. Complete the analogy:  is to  as …
15. Use this data to answer the question:
What is the probability that a student chosen at random from class 2 made above a 73 on this test?
16. Which of the following expressions is equal to
17. Zeke drove from his house to a furniture store in Atlanta and then back home along the same route. It took Zeke three hours to drive to the store. By driving an average of 20 mph faster on his return trip, Zeke was able to save an hour of driving time. What was Zeke's average driving speed on his round trip?
18. Given the figure and the following information, find  to the nearest tenth. is an altitude of  is an altitude of triangle  ;
19. As shown below, four congruent isosceles trapezoids are positioned such that they form an arch. Find  for the indicated angle.
20. If  find the slope of the line tangent to graph of  at .
21. Simplify .
22. Simplify .
23. Which of these statements is (are) true for function ?
I. II. The graph of  is discontinuous at . III. The range of  is all real numbers.
24. 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?
25. 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?