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

Section II: Mathematics
Practice Test 1

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.   Which of the following numbers is the value of 342,499 rounded to the nearest thousand?

A.  342,000

B.  342,400

C.  342,500

D.  343,000

E.  343,400

2.   Which of the following is the largest in value?

A.  0.09

B.  

C.  

D.  0.084

E.  

3.   A Zumba fitness class has 48 students enrolled. One-third of the females are less than 6 feet tall, and three-fourths of the class are males. How many females are 6 feet tall or taller?

A.  4

B.  8

C.  12

D.  16

E.  36

4.   The La Jolla track team ran the following distances in April: miles, miles, 6 miles, and miles. What was the average distance the team ran in miles?

A.  

B.  5

C.  

D.  6

E.  22

5.   A square 4 inches on a side is cut up into smaller squares 1 inch on a side. What is the maximum number of squares that can be formed?

A.  4

B.  8

C.  16

D.  36

E.  64

Question 6 refers to the following table.

6.   Students at Oak Park High School recorded outdoor temperatures at 2:00 p.m. for five afternoons. What is the difference between the week’s highest and lowest temperatures?

A.  —34°

B.  —17°

C.  —7°

D.  17°

E.  34°

7.   A bowl contains 18 gumballs. If there are 8 red, 7 white, and 3 green gumballs in the bowl, what is the minimum number of gumballs one must pick from the bowl to be assured of picking one of each color?

A.  3

B.  6

C.  8

D.  9

E.  16

Question 8 refers to the following two graphs.

8.   What is the sum of the shaded areas of Figure R and the unshaded areas of Figure S above if each circle represents a circle divided into equal parts?

A.  

B.  

C.  

D.  

E.  

9.   Amir was given the expression 9x² + 3y — 5 to evaluate. Although he was given the values of —3 for x and —2 for y, he was unsure of his method for evaluating. If Amir evaluated the expression correctly, what value should he have?

A.  —92

B.  —65

C.  70

D.  80

E.  82

10.  An investor bought 200 shares of Stock A at a price of $16.50 per share and 500 shares of Stock B at a price of $19.50 per share. Later that month, the investor sold the 200 shares of Stock A and the 500 shares of Stock B, all at a price of $20 per share. The profit from Stock B represents what percent of the combined profits from the sales of Stock A and Stock B?

A.  21%

B.  25%

C.  26%

D.  28%

E.  36%

Question 11 refers to the following pictograph.

11.  Use the ruler above and math reasoning to solve this question. A tortoise travels inches every hour. At this pace, how long will it take the tortoise to move 26 inches?

A.  

B.  

C.  

D.  6 hours

E.  

12.  Gabrielle is making a salad from the following ingredients: three different varieties of lettuce, three different varieties of tomatoes, and four different varieties of beans. If Gabrielle wants to use only one type of lettuce, one type of tomato, and one type of bean, how many different combinations of salads can she possibly make?

A.  3

B.  6

C.  10

D.  15

E.  36

13.  A naval base in San Diego has a ship with 250 sailors on board. The ages of the sailors on board range from 20 to 35 years old, and 12% of this population is age 25 or younger. If the remaining population is evenly distributed, how many sailors on this ship are age 30 years old?

A.  22

B.  24

C.  25

D.  27

E.  30

14.  If 3 divided by a number y is 18, then what is the value of the number y plus 2?

A.  

B.  

C.  

D.  

E.  

15.  An art class has 30 students. Each student needs a piece of ribbon 2 feet, 6 inches in length. What is the total length of ribbon needed?

A.  75 feet

B.  78 feet

C.  78 feet, 6 inches

D.  240 feet

E.  780 feet, 6 inches

Question 16 refers to the following chart.

16.  The chart above shows the amount of automobile fuel sold in 1 hour at a local gas station. Regular unleaded gas sold for $3.50 per gallon, and diesel fuel sold for $3.45 per gallon. The total sales of all three grades of fuel is $1,612. If each gallon of premium unleaded gas sold for d dollars, what is the percent increase in the cost of gasoline if you decide to purchase premium unleaded instead of regular unleaded?

A.  5%

B.  6%

C.  7%

D.  10%

E.  21%

17.  A flat-screen television is marked down 20% to $320. Which of the following equations could be used to determine its original price, P?

A.  320 — 0.20 = P

B.  0.20P = $320

C.  P = $320 + 20

D.  0.80P + 0.20P = $320

E.  0.80P = $320

Question 18 refers to the following table.

Annual Teacher Salaries

18.  Hazel estimated the sum of these tiered salaries by first rounding each to the nearest thousand. Ivan estimated the sum of these salaries by first rounding each to the nearest ten. By how much do these estimates differ?

A.  $110

B.  $490

C.  $530

D.  $600

E.  $3,490

19.  Wei-Jen can run 8 miles in one day while training for a long distance race. This year, the average number of days Wei-Jen ran each month was 20 days. Which of the following questions can be answered on the basis of these facts?

A.  How many miles did Wei-Jen run in the first 2 weeks?

B.  What is the average number of miles Wei-Jen ran last year?

C.  How many miles can Wei-Jen run in 3 hours?

D.  What is the maximum number of miles Wei-Jen could have run this year?

E.  What is the minimum number of days Wei-Jen ran each month?

20.  What percent of 60 is 15?

A.  4%

B.  15%

C.  25%

D.  40%

E.  60%

21.  Travis rides the bus from home to work each day. If his bus stops four times every mile to pick up passengers, how many stops does it make in 8 miles?

A.  2

B.  4

C.  8

D.  16

E.  32

22.  Which of the following steps is the best method to convert the fraction into percent form?

A.  Divide a into b, move the decimal point two places to the left, and add a percent sign.

B.  Divide a into b, move the decimal point two places to the right, and add a percent sign.

C.  Multiply the fraction by 100%.

D.  Solve the proportion and add a percent sign to the value of x.

E.  Divide b into a, move the decimal point two places to the left, and add a percent sign.

23.  Ms. Acosta can grade three tests in 9 minutes. At this rate, how long will it take her to grade 30 tests?

A.  27 minutes

B.  54 minutes

C.  1 hour, 27 minutes

D.  1 hour, 30 minutes

E.  2 hours, 30 minutes

Question 24 refers to the following diagram.

24.  A tablecloth covers a square table, with each side measuring 40 inches. If the tablecloth is 6 inches wider than the table on each side, what is the perimeter of the tablecloth?

A.  104 inches

B.  160 inches

C.  184 inches

D.  200 inches

E.  208 inches

25.  A sixth-grade English teacher notices that one of her students, Julian, is struggling in English. The teacher reviews Julian’s English standardized test results to determine intervention and placement strategies.

26.  Which of the following is a true statement regarding Julian’s stanine test score?

A.  Julian answered 80% of the questions correctly.

B.  Julian’s raw score and percentile show that he scored above average.

C.  Julian achieved a score that is higher than 80% of other students who took the test.

D.  Julian’s performance was at the same level as other students who took the test.

E.  Julian answered 80% of the questions correctly.

27.  Ninety percent of 80% of 70% is approximately equal to which of the following?

A.  25%

B.  40%

C.  50%

D.  65%

E.  80%

28.  How many buses are needed to carry 98 children to the park if each bus holds 42 children?

A.  2

B.  2.14

C.  

D.  3

E.  

29.  If 5x is the average of two numbers and one of the numbers is 3, what is the other number?

A.  5x

B.  10x

C.  10x — 7

D.  10x — 3

E.  10x + 7

Question 29 refers to the following diagram.

29.  To illustrate how pyramids are constructed, sixth-grade students construct pyramids using sugar cubes. The teacher gives each student 55 sugar cubes. If there is only one sugar cube on top and each layer below the top forms a square with one additional cube per side, how many layers of sugar cubes will there be?

The illustration above shows the first three layers.

A.  4

B.  5

C.  6

D.  7

E.  8

30.  A school is going to build a new playground. State regulations require no more than 50% asphalt and no less than 20% grass for any school playground. If the school plans to build a playground of exactly 200 square feet, which of the following is acceptable?

A.  50 square feet grass, 110 square feet asphalt, and the rest sand

B.  30 square feet grass, 90 square feet asphalt, and the rest sand

C.  20 square feet grass, 95 square feet asphalt, and the rest sand

D.  50 square feet grass, 95 square feet asphalt, and the rest sand

E.  45 square feet grass, 115 square feet asphalt, and the rest sand

31.  If a store purchases several items for $1.80 per dozen and sells them at three for $0.85, what is the store’s profit on six dozen of these items?

A.  $4.20

B.  $5.70

C.  $9.60

D.  $10.60

E.  $20.40

32.  Adrian takes eight weekly tests in his history class and the scores range from a low of 72% to a high of 94%. Which of the following must be true regarding Adrian’s average for all eight tests?

A.  His average for all eight tests is 83%.

B.  His average for all eight tests is above 83%.

C.  His average for all eight tests is lower than 83%.

D.  His average for all eight tests is any score between 1% and 100%.

E.  His average for all eight tests is between 72% and 94%.

33.  Assume that inflation will increase the prices of everything at a rate of 5% a year over the next 10 years. In 3 years, what will be the price of headphones that now cost $100? Round your answer to the nearest hundredth.

A.  $105

B.  $115

C.  $115.52

D.  $115.76

E.  $150

34.  A container weighs 220 pounds. Which of the following is the best approximation of its weight in kilograms? (Note: 1 kilogram weighs approximately 2.2 pounds.)

A.  48.4

B.  100

C.  110

D.  220

E.  484

35.  In an election poll, 84 voters favored candidate x, 65 voters favored candidate y, and 11 voters were undecided. What fraction of those polled favored candidate x?

A.  

B.  

C.  

D.  

E.  

36.  The PTA is making school banners that measure square yards. PTA members purchased yards of purple fabric and yards of yellow fabric. What is the total amount of fabric purchased?

A.   yards

B.  yards

C.   yards

D.  yards

E.  yards

37.  Pedro is taking a math quiz. One of the problems on his quiz requires him to add the fractions , , and . Which of the following methods should Pedro use to answer this question most efficiently?

A.  Use a common denominator of 90.

B.  Use a common denominator of 15.

C.  Use a common denominator of 30.

D.  Use the “invert and multiply” technique.

E.  Multiply the denominators.

38.  What is the probability that Jayden can roll two dice that total 7?

A.  

B.  

C.  

D.  

E.  

Questions 39—40 refer to the following graph.

39.  According to the graph, which county had the most bear sightings before the conservation measures?

A.  1

B.  2

C.  3

D.  4

E.  5

40.  Which single piece of information is necessary to determine in which county the sightings increased by approximately 25%?

A.  Find the county that had 250 more sightings after the conservation measures.

B.  Find the county that had 25 more sightings after the conservation measures.

C.  Find the county in which the “B” bar is taller than the “A” bar.

D.  Find the county in which the number of sightings indicated by the “A” bar is 250 more than those indicated by the “B” bar.

E.  Find the county in which the number of sightings indicated by the “A” bar is more than those indicated by the “B” bar.

41.  How long will it take a school bus averaging 40 miles per hour to reach its destination 10 miles away?

A.  15 minutes

B.  20 minutes

C.  30 minutes

D.  1 hour

E.  4 hours

42.  A commission of $6.80 is paid to Sofia for each $50 of sales. How much did her sales total if her commissions equaled $156.40?

A.  $1,100

B.  $1,150

C.  $1,200

D.  $1,250

E.  $1,300

43.  There are 36 students in a geometry class. If of the students are boys and of the boys are under 6 feet tall, how many boys in the class are under 6 feet tall?

A.  6

B.  12

C.  18

D.  24

E.  27

44.  An astronaut weighing 207 pounds on Earth would weigh 182 pounds on Venus. The weight of the astronaut on Venus would be approximately what percent of his weight on Earth?

A.  50%

B.  60%

C.  70%

D.  80%

E.  90%

Question 45 refers to the following table.

45.  The table above shows the results of a student’s scores for 15 different chemistry quizzes. What was the student’s average (arithmetic mean) score for the quizzes?

A.  70

B.  

C.  

D.  

E.  80

46.  At Franklin High School, one out of four seniors takes physics. If there are 1,260 seniors, how many do not take physics?

A.  126

B.  315

C.  420

D.  630

E.  945

Question 47 refers to the following information.

Daniel’s four paychecks total $2,520, and the largest paycheck is $300 more than the average for the four paychecks and $600 more than the smallest paycheck.

47.  Which of the following cannot be determined from the preceding information?

A.  The average of the four paychecks

B.  The largest paycheck

C.  The smallest paycheck

D.  The sum of the largest and the smallest paychecks

E.  The sum of the two largest paychecks

48.  What number could be added to the following set of data so that the median and mode of the set are equal?

23, 14, 16, 19, 21

A.  14

B.  18

C.  19

D.  21

E.  24

Questions 49—50 refer to the following graph.

49.  Based on the seven days shown, approximately what percent of the days did the maximum temperature exceed the average temperature?

A.  3%

B.  4%

C.  43%

D.  57%

E.  93%

50.  Between which two dates shown did the greatest increase in maximum temperature occur?

A.  July 11—12

B.  July 12—13

C.  July 13—14

D.  July 14—15

E.  July 15—16

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