# Certification Exam Assignment

Certification Exam Assignment

For this assignment, you will work on questions like those you will see on the certification assignment for EC-6 or 4-8. For each question, you must justify your answer with either mathematical work or by explanation. If give the answer only, you will not receive any credit for that problem. You should upload your work in one PDF file. Please do not submit individual JPEGs or PDFs. You can compile it into one PDF.

Directions: For each of the problems, you must show work or justify your response in order to receive full credit for the problem.

1. Which of the following expressions is equivalent to 3 + 5 − 4 − 9 = 0? a. = −4 b. − + 4 = 0 c. − 4 = 0 d. = 4

2. Which model best fits the following data set? Let n= the number of party guests and p = pieces of pizza.

n 10 20 30 40 p 15 30 45 60

a. p = n + 15 b. p = 2n -5 c. p = 10 + 0.5 n d. p = 1.5 n

3. Suppose a horse is galloping at 19mph toward a clown, and the clown is racing toward the horse on an ATV which can sustain a speed of 15mph. They are 50 miles apart from one another and start at the exact same moment in time. How much time will it take for the horse and clown to collide?

a. In 1.47 hours b. In 2.3 hours c. In 45.6 minutes d. In 1.12 hours

4. Use the figure below to answer the question that follows:

Town C is 2 miles east of Town A and 2 miles south of Town B, as in the figure above. Which of the following is the best estimate of the shortest distance from Town A to Town B?

a. 2 miles b. 2.8 miles c. 3.4 miles d. 4 miles

5. From the given boxplot, what is the value of the lower quartile?

a. 14 b. 4 c. 10 d. 7

6. If the rocket’s trail is modeled as a line, which algebraic expression could represent the line?

a. = −5 − 5 b. = −.25 + 4 c. = .25 + 4 d. = 5 − 5

7. If the volume of a prism is calculated by multiplying the area of the base by the prism’s height, what is the volume of a box with a square base whose side measures 5 centimeters and whose height is 12 centimeters? a. 720 cubic centimeters b. 300 cubic centimeters c. 34 cubic centimeters d. 60 cubic centimeters

8. Matteo is flipping two coins at the same time. What is the probability that his coins will have an outcome of 2 heads? a. ¾ b. ¼ c. 1/3 d. ½

9. The lines in the middle of the road could be described as:

a. Transverse b. Normal c. Perpendicular d. Parallel

10. When the pictured net is folded into a 3-D figure, the figure’s height is 6 inches. What is the volume of the 3-D figure?

a. 50 cubic inches b. 120 cubic inches c. 32 cubic inches d. 40 cubic inches

11. The table displays the top speeds of several historic vehicles. Which of these statements is true of the data?

Vehicle Top Speed A 160 km/hr B 137 km/hr C 90 km/hr D 122 km/hr E 204 km/hr

a. The median is less than the range b. The median is greater than the mean c. The range is greater than the mean d. The data set has no mode.

12. Joseph owns a distributing company that repackages cornmeal from bulk quantities into smaller packages. If Joseph wants to fill 100,000 bags that each hold 10 grams of cornmeal, how many kilograms of cornmeal should he buy?

a. 100 b. 1,000 c. 10,000 d. 100,000

13. The table below shows the results of a survey of 25 students:

Students who work at a part-time job.

Students who do not work at a part-time job.

Students who play a spring sport.

7 9

Students who do not play a spring sport.

6 3

What is the probability of randomly selecting, from all 25 students surveyed, a student who works a part-time job and plays a spring sport?

a. .54 b. .28 c. .64 d. .52

14. Each face of a number cube is numbered 1, 2, 3, 4, 5, or 6. When the cube is tossed, each number is equally likely to appear face up. The number cube is tossed twice, and the numbers that land are added together. What is the probability that the sum is a prime number?

a. ½ b. 8/21 c. 5/36 d. 15/3 e. None of these

15. The number of tennis shoes, t, in a dorm is 12 more than 5 times the number of dress shoes. Which of the following represents the number of dress shoes in the dorm in terms of t?

a. −12 5

b. 5 + 12 c.

5 − 12

d. 5 − 12

16. Use the figure below to answer the question that follows:

Toni is designing a new home. The floor of Room B is in the shape of a regular hexagon and will have a perimeter of 72 feet. The floor of Room A is in the shape of a square and will be sharing a wall with Room B as shown. How many square feet of carpet will Toni need to cover the floor of Room A?

a. 48 square feet b. 120 square feet c. 144 square feet d. 864 square feet e. None of the above

17. The scatterplot shows the sales, s, for a local ice cream store based on the daily high temperature, t.

There is a strong linear correlation between s and t. Based on the relationship, which of the following is the best estimate of the increase in sales for 1 degree Celsius increase in temperature?

a. $20 b. $60 c. $100 d. $30

18. For any point on the line, if x represents centuries, then y could equal the equivalent number of _____?

a. Weeks b. Decades c. Months d. Years

19. A circle with diameter d has an area of 60. What is the value of d?

a. 4�45

3

b. 15

c. 60

d. �240

20. If the pattern below is continued, how many blocks will be in the 7th term?

a. 36 b. 45 c. 28 d. 21

21.

a. 135 degrees b. 145 degrees c. 115 degrees d. 125 degrees

22. Which of the following geometric solids has five faces, eight edges, and five vertices? a. A pentagonal pyramid b. An octagonal prism c. A triangular prism d. A rectangular prism

23. Identical tables are offered for sale at two local shops and one online retailer, designated Stores A, B, and C, respectively. The table’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?

a. Store A, Store B, Store C b. Store B, Store C, Store A c. Store C, Store B, Store A d. Store C, Store A, Store B e. None of these

24. Use the table to answer the question that follows: College Graduate Annual Salary

A $36,000 B $35,250 C $71,555 D $34,7450 E $35,575

The table shows five college graduates and the annual salaries they earned during their first year in the workforce. Based on the data given in the table, which of the following statements is true?

a. The mean is less than the range of the data. b. The mean is less than the median of the data. c. The range is less than the mean of the data. d. The range is less than the median of the data.

25. A combination lock is opened by setting each of five barrels to the correct digit. If digits are randomly chosen from the digits 0 through 9, how many unique combinations can be generated? Repetition of numbers is allowed.

a. 10! b. (10)(9)(8)(7)(6) c. (10)(10)(10)(10)(10) d. 10!

5!4!

26. On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 30 cm2. What is the actual area of the room?

a. 30 square-meters b. 3,000 square-meters c. 3,000 square-centimeters d. 30,000 square-centimeters e. None of these

27. The graph of the function f is shown on the xy-plane. For which 2 values of x does f(x) = 3?

a. 5 and 6

b. 1.5 and 3.5

c. 6 and 8

d. 7 and 9

28. Mr. Sal’s after-school bird-watching club surveyed students in the school, asking them which of their favorite birds. The chart shows the results of the survey. If the survey results are representative of all the students in the school district, approximately how many of the 2,400 students in the district prefer either eagles or hawks?

a. 48 b. 100 c. 820 d. 1200

29. The side lengths of parallelogram X are 2 and 3. A similar parallelogram Y has side lengths 10 and 15. The area of parallelogram Y is how many times the area of parallelogram X?

a. 125 b. 5 c. 25 d. 3

30. The data table shown describes how students get to school each morning at Memorial Middle School. If a student is drawn at random from the walkers and bus riders, what is the probability they are a walker?

Transportation Number of Students Bus 148 Carpool 156 Walk 28 Bike 44

a. 7/37 b. 7/44 c. 7/11 d. 7/39

31. At the basketball game last night, all 12 players scored. The percentage of players that scored each point value is shown in the histogram.

Which table accurately shows the data as a list of the total points per player?

a. 12, 6, 6, 8, 2, 4, 6, 8, 10, 4, 2, 2 b. 12, 6, 8, 8, 2, 4, 6, 8, 10, 4, 2, 2 c. 12, 6, 6, 8, 2, 4, 6, 8, 10, 4, 4, 2 d. 12, 6, 6, 8, 2, 4, 6, 8, 12, 4, 2, 2

32. A student was selected as a captain of a cooking team in a consumer and family studies class. The student could pick 2 of 5 girls and 3 of 7 boys to be on their team. What is the total number of different teams that this captain could pick?

a. 17 b. 170 c. 280 d. 350

33. John made a circular garden in his backyard. The garden has a diameter of 20 feet. He used 1/3 of the garden for tomatoes. He enclosed the entire garden with a fence that was 12 inches high. Which of the following questions could not be answered with the information provided?

a. What is the volume of the dirt in the garden? b. What is the area of the tomato patch? c. What is the area of John’s garden? d. How many feet of fence does John need?

34. Five cards are randomly chosen without replacement from an ordinary deck of 26 black and 26 red cards. What expression shows the probability that all five cards are red?

a. � 1 26 �� 1

25 �� 1

24 �� 1

23 �� 1

22 �

b. � 1 52 �� 1

51 �� 1

50 �� 1

49 �� 1

48 �

c. �26 52 ��26

52 ��26

52 ��26

52 ��26

52 �

d. �26 52 ��25

51 ��24

50 ��23

49 ��22

48 �

35. This is a diagram of Leo’s backyard. The blue square is a recently installed pool. Her backyard has a total area of 1,800 square feet. Which equation can be used for A, the area of the backyard not taken up by the pool?

a. A = 1800 + (20 x 15) b. A = 1800 + 2 (20 + 15) c. A = 1800 – (20 x 15) d. A = 1800 – 2 (20 + 15)