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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. 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.
2. The set  forms a group under operation #. Which of these statements is (are) true about the group?

#

a

b

c

d

a

c

d

b

a

b

d

c

a

b

c

b

a

d

c

d

a

b

c

d


# I. The identity element of the group is d. II. The inverse of c is c. III. The operation # is commutative.
3. Which of the following is the truth table for logic circuit shown below?

4. If 1' on a map represents 60 ft, how many yards apart are two points if the distance between the points on the map is 10'?
5. 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?
6. Which of the following statements is true?
7. Which of these statements is true for functions , , and ?

8. Determine the number of diagonals of a dodecagon.
9. If  when , what is the value of
10. Solve
11. Find  if .
12. Solve the system of equations.

13. 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?
14. 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?

15. Identical rugs are offered for sale at two local shops and one online retailer, designated Stores A, B, and C, respectively. The rug's regular sales price is $296 at Store A, $220 at Store B, and $198.00 at Store C. Stores A and B collect 8% in sales tax on any after-discount price, while Store C collects no tax but charges a $35 shipping fee. A buyer has a 30% off coupon for Store A and a $10 off coupon for Store B. Which of these lists the stores in order of lowest to highest final sales price after all discounts, taxes, and fees are applied?
16. Given the figure and the following information, find  to the nearest tenth. is an altitude of  is an altitude of triangle  ;
17. Solve
18. Which of these statements is NOT necessarily true when?
19. 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 ?
20. 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]?
21. Which of the following expressions is equal to
22. Which of these describes the graph of the equation ?
23. 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?
24. Which of these forms a group?
25. 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?

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