### Report a question

ACT Diagnostic Exam

Welcome to your first online diagnostic ACT exam. We will use this exam to identify your strengths and weaknesses, allowing us to match you with the perfect instructor. This instructor will leverage your strengths to address any areas in need of improvement. If you'd like to view any images more clearly during the exam, simply click on the picture to zoom in or out. We encourage you to time yourself accurately as if this was the real exam. If you encounter a question you don't know, **please refrain from guessing and leave it blank.** This will enable your instructor to focus on the specific concepts that require attention. Thank you for choosing College Bound Tutoring. We look forward to working with you and are always available to answer any questions you may have. Please don't hesitate to reach out to us.

**75 QUESTIONS 45 MINUTES**

In the five passages that follow, certain words and phrases are underlined and numbered. In the

right-hand column, you will find alternatives for the underlined part. In most cases, you are to

choose the one that best expresses the idea, makes the statement appropriate for standard written

English, or is worded most consistently with the style and tone of the passage as a whole. If you

think the original version is best, choose “NO CHANGE.” In some cases, you will find a

question about the underlined part. You are to choose the best answer to the question.

You will also find questions about a section of the passage, or about the passage as a whole.

These questions do not refer to an underlined portion of the passage, but rather are identified by a

number or numbers in a box.

For each question, choose the alternative you consider best and bubble in the corresponding

answer choice. Read each passage through once before you begin to answer the questions that

accompany it. For many of the questions, you must read several sentences beyond the question to

determine the answer. Be sure that you have read far enough ahead each time you choose an

alternative.

1 / 214

1

2 / 214

2

3 / 214

3

4 / 214

4

5 / 214

5

6 / 214

6

7 / 214

(7)Which choice most effectively combines the sentences at the underlined portion?

8 / 214

8

9 / 214

9

10 / 214

10

11 / 214

11

12 / 214

12

13 / 214

Which choice results in the most effective transition from the preceding paragraph to the information that follows?

14 / 214

14

15 / 214

Which choice best concludes the passage and recalls an example given early in the passage?

16 / 214

16

17 / 214

17

18 / 214

18

19 / 214

19

20 / 214

20

21 / 214

21

22 / 214

At this point, the writer is considering adding the following sentence.

Cheap, convenient food drew customers to these trucks.

Should the writer make this addition here?

23 / 214

23

24 / 214

24

25 / 214

Which choice most effectively sets up the information that follows?

26 / 214

26

27 / 214

27

28 / 214

28

29 / 214

29

30 / 214

The writer wants a conclusion that addresses the development of the food truck industry over time. Which choice best accomplishes this goal?

31 / 214

31

32 / 214

At this point, the author is considering adding the following sentence:

In the case of textiles, light from a camera’s flash causes harmful chemical reactions and deterioration when absorbed by the cloth’s fibers.

Should this sentence be inserted here?

33 / 214

33

34 / 214

34

35 / 214

35

36 / 214

36

37 / 214

37

38 / 214

38

39 / 214

The writer is considering deleting the underlined portion (ending the sentence with a period). Should the writer make this deletion?

40 / 214

40

41 / 214

To make this paragraph most logical, sentence 4 should be placed

42 / 214

42

43 / 214

43

44 / 214

44

45 / 214

45

46 / 214

The writer wants to give two examples that show the diversity in theories. Which of the following best achieves this goal?

47 / 214

47

48 / 214

48

49 / 214

49

50 / 214

Which choice most effectively combines the sentences at the underlined portion?

51 / 214

51

52 / 214

52

53 / 214

53

54 / 214

The writer is considering adding the following sentence.

In smaller settlements, the combination of more open space and fewer people could contribute to a continuation of usual burial practices, even in the event of an unrelenting pestilence.

Should the writer make this addition here?

55 / 214

Which choice most effectively maintains the contrast in the sentence and introduces the information that follows?

56 / 214

56

57 / 214

57

58 / 214

Given that all the choices are true, which most effectively introduces the information that follows in the paragraph?

59 / 214

59

60 / 214

60

61 / 214

61

62 / 214

62

63 / 214

63

64 / 214

Which choice most effectively combines the sentences at the underlined portion?

65 / 214

Which choice provides the best introduction to the paragraph?

66 / 214

66

67 / 214

67

68 / 214

68

69 / 214

69

70 / 214

69

71 / 214

70

72 / 214

At this point, the writer is considering adding the following sentence.

More primitive humans needed to process and react to negative stimuli much more quickly than positive stimuli.

Should the writer make this addition here?

73 / 214

72

74 / 214

73

75 / 214

74

76 / 214

Which choice most clearly ends the passage with a restatement of the writer’s primary claim?

#### 60 QUESTIONS

#### 60 MINUTES

** **

###### Solve each problem, choose the correct answer, and then bubble in the letter corresponding to that answer choice.

Do not linger over problems that take too much time. Solve as many as you can: then return to the others in the time you have left for this test.

###### You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.

**Note: **Unless otherwise stated, all of the following should be assumed.

- Illustrative figures are NOT necessarily drawn to scale.
- Geometric figures lie in a plane.
- The word
*line*indicates a straight line. - The word
*average*indicates arithmetic mean

77 / 214

A residential neighborhood is being built at a rate of 6 houses every 4 months. If the neighborhood continues to be built at this rate, how long will it take, in years, for the whole neighborhood to be completed if it contains 45 homes?

78 / 214

The yearly membership fee for an online retailer is $29. Jacob orders gift packages that cost $12.50 each. For one year, Jacob's membership and gift package costs were $116.50. How many gift packages did Jacob order that year?

79 / 214

A bike rental shop's rate is $24 a day. A customer wants to rent the bike for 4 days and made a down payment of $30. How much more money does the customer owe?

80 / 214

Out of the 50 classes offered at a summer math program, 25 of them are Algebra classes, 15 are geometry classes, and the remainder are calculus classes. If a class is randomly selected, what is the probability that it is a calculus class?

81 / 214

Let *b *represent the base of a triangle. If the height of a triangle is the same as the base, what is the area of the triangle?

82 / 214

83 / 214

The ratio of the lengths of the corresponding sides of two similar triangles is 1:3. If the area of the larger triangle is 36 square units, what is the area, in square units, of the smaller triangle?

84 / 214

In the xy-plane, the function of y= |x+5| intersects the line with equation y=3 at two points, R and S. What is the length of line RS?

85 / 214

If c and d are two distinct solutions to the equation $4x^2 - 64 = 0$, what is the value of c+d?

86 / 214

87 / 214

Dylan swam for 30 minutes and ran for 45 minutes. If swimming burns 460 calories per hour and running burns 640 per hour, how many calories did Dylan burn swimming and running?

88 / 214

89 / 214

Vikram is trimming a photo to fit into a frame. The original photo is 8 inches by 10 inches. If Vikram trimmed enough of the photo that it now has an area of 48 square inches, what are the possible dimensions for the trimmed photo?

90 / 214

Terrence is cutting large pieces of colored paper into smaller rectangles to make cards. If the colored paper is 16 inches by 23 inches, and he uses pieces that are 4 inches by 5 inches for cards, how many pieces of colored paper does he need to make 40 cards?

91 / 214

In preparation for returning to school Amina is buying school supplies. She plans to buy 5 notebooks, 2 containers of pencils, and a calculator. The notebooks cost $1.60 each, the containers of pencils cost $3.20 each, the calculator costs $89, and an 8% sales tax is applied to the total. How much will Amina pay for her school supplies?

92 / 214

In the coordinate plane shown, line k is perpendicular to line j. What is the value of a?

93 / 214

94 / 214

95 / 214

A dance instructor wants to determine how many students, s, she wants to enroll in her class. For each student who enrolls in her class, she will earn $12. She will spend $50 each week renting space to teach her class. If she wants to earn at least $400 per week, which of the following gives the possible values for s?

96 / 214

A ladder is propped against a wall, making an angle of 72*° *with the ground. If the ladder is 12 feet high, which of the following gives the distance in feet between the foot of the ladder and the wall?

97 / 214

98 / 214

99 / 214

If f(x)=3x-7, what is f(-4x+1) equal to?

100 / 214

Mr. Kress is creating a seating chart for five students to sit in a row. How many different seating arrangements are possible?

101 / 214

102 / 214

103 / 214

104 / 214

105 / 214

Arnold has taken 3 tests in Ms.K's math class so far this year. His current test average is 88%. What is the lowest grade he can get on his next test to have an overall test average of 90%?

106 / 214

107 / 214

If the mean and median of a set of three numbers, x,y,z are equal and x **≤** y **≤** z, which of the following must be true?

108 / 214

The equation $h=-4.9t^2 +9t$ expresses the approximate height, *h,* in meters, of a toy rocket *t* seconds after it is launched vertically upward from the ground with an initial velocity of 9 meters per second. Approximately how many seconds pass before the rocket hits the ground?

109 / 214

A triangle has side lengths of 14 inches and 8 inches. If the third side is an integer, what is the greatest possible length, in inches of the third side of the triangle?

110 / 214

111 / 214

112 / 214

2x-4y<8 y≥ -x+4 A system of inequalities is shown above. Which of the following ordered pairs could be a solution to this system of inequalities?

113 / 214

A local train and an express train travel in the same direction on parallel tracks. The local train departs at 8:00 AM, and the express train departs 4 hours later. They both arrive at the same destination at the 6:00PM. If the express train travels 20 miles per hour faster than the local train, how fast does the express train travel, in miles per hour?

114 / 214

115 / 214

If r is a rational number, which of the following could be an irrational number?

116 / 214

The product of two integers is between 230 and 247. Which of the following CANNOT be one of the integers?

117 / 214

118 / 214

119 / 214

In circuits, Ohm's Law states that V=IR, where V is the voltage, I is the current, and R is the resistance. According to Ohm's Law, if the voltage is quadrupled and the current is tripled, what value must be multiplied to the resistance?

120 / 214

In 1 hour, 16.4 liters of water drained from a tank. If the water continues to drain at this same rate, which of the following gives the expression for the number of milliliters of water that will drain from the tank in 2 minutes?

121 / 214

A group of 20 students visits a gelato shop. The shop has three flavors. The group gets 31 tastes altogether. If every student gets to taste at least one flavor, what is the greatest number of students who could have tasted all three flavors?

122 / 214

Let events *X,Y, and Z* be mutually exclusive events. If P(X)=0.2, P(Y)=0.5, and P(Z)=0.1, what is P(X or Y)?

123 / 214

124 / 214

125 / 214

126 / 214

What is the area, in square units, of the triangle formed by the x-axis, the y-axis and the equation 5x+3y=30

127 / 214

128 / 214

What is the value of the 100th term in the sequence shown: 7,13,19,25,...

129 / 214

I. The hole in the bottom was partly obstructed

II. Someone began pouring water into the container.

III. Someone began drinking from the container.

130 / 214

A neighborhood is choosing a 3 person committee to represent them. If there are 20 residents in then neighborhood, how many different committees can the neighborhood select?

131 / 214

132 / 214

Tashon has been on a hiking trip for three days. If his first day of hiking can be described by a vector (4,5), his second day of hiking by the vector (2,7), and his third day with the vector (5,3), which of the following vectors describes his trajectory from the beginning of his hiking trip to the end of the third day?

133 / 214

134 / 214

135 / 214

A meteorologist is comparing the rainfall in three areas. During a rainstorm, Region X received 40% less rain than Region Y, and Region Z received 10% more rain than Region Y. If Region X received 0.72 inches of rain during the rainstorm, how many inches of rain did Region Z receive?

#### 40 QUESTIONS

#### 35 MINUTES

** **

###### There are several passages in this test. Each passage is accompanied by several questions. After reading a passage, choose the best answer to each question and bubble in the corresponding answer choice. You may refer to the passages as often as necessary.

136 / 214

Which choice best describes what happens in the passage?

137 / 214

Which choice best describes the developmental pattern of the passage?

138 / 214

As it is used in line 13, the word "keen" can reasonably be said to mean all of the following EXCEPT:

139 / 214

In the passage, Morris views Catherine’s father as

140 / 214

In lines 37-38, the narrator uses which of the following literary devices to describe Catherine’s hesitation to argue with her father?

141 / 214

As used in line 52, “just” most nearly means

142 / 214

The passage indicates that Catherine intends to resolve her current predicament by

143 / 214

In the context of the passage, the primary function of lines 59-61 is to