CliffsNotes CBEST - BTPS TESTING Ph.D., Jerry Bobrow Ph.D. & 8 more 2021

Section II: Mathematics
Practice Test 2

50 Questions

80 Minutes

Directions: In the following questions, select the one best answer of the five choices given. Mark your answers on a sheet of paper.

1. Joel shoots 80 arrows at a target, but only 15% of them actually hit the target. How many arrows actually hit the target?

A. 11

B. 12

C. 15

D. 16

E. 18

2. After a 40% discount, the price of a pair of shoes is $25.50. What was the price of the shoes before the discount?

A. $35.70

B. $40.80

C. $42.50

D. $102.00

E. $153.00

3. Sean knows that a geometric figure is a rectangle and that it has sides of 18 and 22. In the context of math reasoning, which of the following steps should Sean use to calculate the area of a square that has the same perimeter as this rectangle?

A. Add 18 and 22, double this sum, divide by 4, then multiply by 2.

B. Add 18 and 22, double this sum, divide by 4, then multiply by 4.

C. Add 18 and 22, double this sum, divide by 4, then square the quotient.

D. Add 18 and 22, double this sum, then multiply by 4.

E. Add twice 18 to twice 22, divide by 2, then square the quotient.

4. Five loads of clothes need to be laundered. If each load takes a total of 15 minutes to be washed, and the laundry person begins washing at 3:20 p.m. and washes continually, at what time will all the loads be finished?

A. 1:15 p.m.

B. 3:35 p.m.

C. 4:35 p.m.

D. 5:35 p.m.

E. 6:15 p.m.

5. On six tests, Zach averaged 85%. Although he failed to achieve a passing score on one test (on which he received a 56%), he also scored 100% twice. Which of the following can be determined from this information?

A. His two lowest percentage scores

B. His three highest percentage scores

C. The sum of all six percentage scores

D. The sum of the three lowest percentage scores

E. The average of the three highest percentage scores

Question 6 refers to the following table.

6. From the preceding chart, what is the total number of tons shipped on a given workday?

A. 33

B. 330

C. 33,000

D. 330,000

E. 33,000,000

7. Which of the following fractions is the largest in value?

A.

B.

C.

D.

E.

8. If 7 pounds of bananas cost $4.69, how much do 9 pounds of bananas at the same rate cost?

A. $3.65

B. $6.03

C. $6.69

D. $6.70

E. $13.43

Question 9 refers to the following diagram.

9. Based on the diagram, if spinning the spinner only once, what is the probability of spinning red, yellow, or blue?

A.

B.

C.

D.

E.

10. If feet equals one rod, how many inches are there in four rods?

A. 22

B.

C. 66

D. 792

E. 2,376

11. The total cost of a meal is $47.93 and Alex wants to leave a 15% tip. Which of the following is the best approximation of the tip that Alex should leave for the waiter?

A. $5.50

B. $6.00

C. $7.00

D. $8.00

E. $55.00

Question 12 refers to the following diagram.

12. Sarah is wrapping a birthday present and wants to know how much ribbon to buy. Based on the diagram, what is the total length of ribbon needed to wrap the present?

A. 32 inches

B. 64 inches

C. 128 inches

D. 448 square inches

E. 512 square inches

13. On average, a taxi travels 40 miles per hour while taking passengers from one location to another. The fare is $7.50 for each passenger and 6 cents for each quarter of a mile traveled. How much will the fare be for three passengers over a 1 hour and 45 minute time period?

A. Less than $30

B. At least $30, but less than $35

C. At least $35, but less than $40

D. At least $40

E. At least $40, but less than $50

14. Marco took a standardized math test, and his grade report showed that his score was in the 85th percentile. Which of the following is the best interpretation of the meaning of this percentile?

A. Marco got 85% of the problems correct.

B. Eighty-five percent of all those taking the exam had scores below Marco’s score.

C. Eighty-five percent of all those taking the exam had scores above Marco’s score.

D. Only 85% of those taking the exam received passing scores.

E. There was an 85% probability that Marco’s score was above the mean on the exam.

Question 15 refers to the following diagram.

15. Which of the following is a conclusion that can be drawn from the preceding diagram of circles A, B, C, and D?

A. A and B have something in common.

B. B and C have something in common.

C. A and D have nothing in common.

D. C and D have nothing in common.

E. D has something in common with A, B, and C.

16. Juan works 8 hours and receives $19.75 per hour. Mary works 24 hours and receives a total of $444. Which of the following cannot be derived from the preceding statements?

A. Juan’s total wages

B. Mary’s wage per hour

C. The difference between the wages that Juan and Mary each receives

D. The average total wages received by Juan and Mary

E. The hours Mary works each day

Question 17 refers to the following chart.

Providence High School State

Testing Score Averages

17. According to the chart, what is the mean (average) of the verbal state testing scores for the 5-year period?

A. 512

B. 514

C. 521

D. 527

E. 528

18. If the length of a rectangle is doubled and its width is decreased by 25%, how many times greater is the area of the new rectangle than the area of the original rectangle?

A. 1.5

B. 2

C. 2.5

D. 3

E. 3.5

19. On a map, 1 centimeter represents 35 kilometers. Two cities that are 245 kilometers apart would be separated on the map by how many centimeters?

A. 5

B. 7

C. 9

D. 210

E. 280

Question 20 refers to the following graph.

20. The bar graph shows the average quarterly profits for EcoSystems Technology Company. According to the graph, what is the approximate percent change in profits from the 3rd quarter to the 4th quarter?

A. 20%

B. 33%

C. 43%

D. 50%

E. 75%

21. A fair die is rolled three times. What is the probability that all three rolls will result in different numbers?

A. 0.50

B. 0.56

C. 0.58

D. 0.60

E. 0.61

22. The fraction is between the numbers listed in which of the following pairs?

A.

B. 0.1 and 0.12

C. 0.08 and 0.1

D. 1 and 2

E.

Question 23 refers to the following table.

23. Use the frequency table to determine the mean for the set of data.

A. 3.5

B. 4

C. 5

D. 5.6

E. 6

Question 24 refers to the following graph.

24. The circle graph represents the Belmont High School senior prom budget, distributed across five expense categories. If the total budget is $4,000, how many of the expense categories are budgeted for under $500?

A. 1

B. 2

C. 3

D. 4

E. 5

25. Which of the following must be true if a class of 30 students has a total of 60 pencils?

A. Each student has 2 pencils.

B. Every student has a pencil.

C. Some students have only 1 pencil.

D. Some students have more pencils than other students.

E. The class averages 2 pencils per student.

26. Mr. DiPietro is doing a project with his class of 19 students. If each student needs 8 inches of string, how much string will be left over from a spool of 5 yards?

A. 2 feet, 4 inches

B. 2 feet, 8 inches

C. 3 feet

D. 4 feet, 4 inches

E. 28 feet

27. There are 25 students enrolled in an English class. If 15 students average 80% on an English exam and 10 students average 90% on the same exam, which of the following represents the average percent for all 25 students?

A. 83%

B.

C. 84%

D. 85%

E.

28. John’s age is 4 years greater than four times Alex’s age. Alex’s age is 2 years less than half of Tony’s age. If Tony is y years old, what is John’s age in terms of y?

A. y + 6

B. 2y + 6

C. 4y + 2

D. 4y — 2

E. 2y — 4

29. If the edges of a 4-inch by 6-inch photograph are each enlarged by 20%, what is the perimeter of the new photograph?

A. 12 inches

B. 16 inches

C. 24 inches

D. 28 inches

E. 34.5 inches

30. Ramon tries to construct a pie graph representing his classmates’ eye colors. In his class of 24 students, 6 students have blue eyes, 12 students have brown eyes, 5 students have hazel eyes, and 1 student has green eyes. His teacher tells him that his graph (shown below) is not correct.

In order to fix the graph, Ramon should

A. increase the amount of green and decrease the amount of blue.

B. increase the amount of blue and decrease the amount of hazel.

C. decrease the amount of blue and increase the amount of brown.

D. decrease the amount of hazel and increase the amount of brown.

E. increase the amount of hazel and increase the amount of blue.

31. Nadine can fit 36 history textbooks into one carton. How many of the same textbooks can she fit into cartons?

A. 432

B. 414

C. 396

D. 360

E. 240

Questions 32—33 refer to the following graphs,

32. How much more money did the average college student spend on medical expenses in 2020 than in 2010?

A. $800—$900

B. $900—$1,000

C. $1,000—$1,100

D. $1,100—$1,200

E. $1,200—$1,300

33. What was the approximate increase from 2010 to 2020 in the percentage spent on food and drink?

A. 4%

B. 18%

C. 22%

D. 40%

E. 50%

34. Teachers will be assigned special camp duty one day of the week during a 7-day camping trip. If all the days of the week (Monday through Sunday) are tossed into a cap and each teacher chooses one day of the week, what is the probability that the first teacher will randomly select a weekday (Monday through Friday)?

A.

B.

C.

D.

E.

35. In a senior class of 800, only 240 decide to attend the homecoming game. What percentage of the senior class attended the homecoming game?

A. 8%

B. 24%

C. 30%

D. 33%

E. 80%

36. Which of the following is equal to of 0.02 percent?

A. 0.4

B. 0.04

C. 0.004

D. 0.0004

E. 0.00004

37. What is the probability of tossing a penny twice so that both times it lands heads up?

A.

B.

C.

D.

E.

38. Which of the following statements is true?

A.

B.

C.

D.

E.

39. A men’s suit that originally sold for $120 is on sale for $90. Which of the following represents the discount rate?

A. 20%

B. 25%

C. 30%

D.

E. 75%

40. Alicia hiked miles, and Melanie hiked miles. Which of the following is the total number of miles that they hiked together?

A.

B.

C.

D.

E.

41. Elisa is having trouble changing units of measure, but her teacher has given her a practice problem that requires her to change 3 miles to inches. In order to calculate the correct answer, Elisa should

A. multiply 3 by 5,280.

B. multiply 3 by 5,280 and then divide by 12.

C. multiply 3 by 5,280 and then multiply by 12.

D. divide 3 into 5,280 and then multiply by 12.

E. divide 3 into 12 and then multiply by 5,280.

42. A basketball is fully inflated to 9 pounds per square inch. A football is fully inflated to 10 pounds per square inch. The air pressure in the football is approximately what percent of the air pressure in the basketball?

A. 33%

B. 54%

C. 79%

D. 90%

E. 111%

43. Today is Lucy’s fourteenth birthday. Last year, she was 3 years older than twice Charlie’s age at that time. Using c for Charlie’s age now, which of the following can be used to determine Charlie’s age now?

A. 13 — 3 = 2(c — 1)

B. 14 — 3 = 2c

C. 13 — 3 = 2c

D. 13 + 3 = 2c

E. 13 + 3 = 2(c — 1)

Question 44 refers to the following information.

Eagle Savings and Loan pays 3% annual interest.

Firefighters Federal Credit Union pays 4% annual interest.

Simple interest is calculated as interest = principal × rate × time, or I = Prt.

44. What would be the difference in the amount of simple interest earned over 3 years on $1,200 if it were invested in the Firefighters Federal Credit Union instead of in the Eagle Savings and Loan?

A. $12

B. $36

C. $300

D. $360

E. $432

Question 45 refers to the following table.

45. The table above gives Dillan’s test results for the 10 tests given in his mathematics class. Find the mean, median, mode, and range for these values. Use them to calculate the following:

(mean — median) × (mode — range)

A. —62.5

B. —37.5

C. 37.5

D. 62.5

E. None of the above

46. If the value of x is between 0.0036 and 0.052, which of the following could be x?

A. 0.0028

B. 0.0481

C. 0.0529

D. 0.053

E. 0.07

47. Four construction workers build a house containing 16 rooms. The house has four floors, and the workers take exactly 4 months (without stopping) to build the house. Based on this information, which of the following must be true?

A. They build four rooms each month.

B. Each floor has four rooms.

C. No floor has fewer than three rooms.

D. They build an average of one floor per month.

E. The house averages three rooms per floor.

48. Max is installing new hardwood floors in the family room. If the total floor area is 420 square feet and he has completed 45% of it, how many square feet has he covered?

A. 19 square feet

B. 27 square feet

C. 153 square feet

D. 189 square feet

E. 231 square feet

49. Deena spent $200 for earrings and a necklace. If the necklace cost $20 more than the earrings, how much did she pay for the necklace?

A. $70

B. $80

C. $90

D. $100

E. $110

Question 50 refers to the following information.

Bob is taller than Sam. Sam is shorter than Ed. Ed is taller than Cecil but shorter than Amir. Ricardo is taller than Amir but shorter than Bob.

50. From the information given, who is the tallest?

A. Bob

B. Amir

C. Ricardo

D. Cecil

E. Ed

IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS SECTION ONLY. DO NOT WORK ON ANY OTHER SECTION IN THE TEST.