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Quiz Session - Attempts With Random Questions

FTCE Exam Questions

Page 1 of 31

1.

Solve for y:

3x + y = 50
x = 4

  • 38

  • 28

  • 47

  • 12

Correct answer: 38

Plug in the variables:

3x + y = 50

3(4) + y = 50

Simplify and rearrange for y:

y = 50 - 3(4)

y = 50 - 12

Solve:

y = 38

2.

Read the passage, then answer the question that follows. 

This passage would most likely appear in:

  • A magazine article

  • An editorial

  • A doctoral thesis

  • A technology journal

Correct answer: A magazine article

The information is not too complex; therefore, a doctoral thesis and a technology journal should be eliminated. Very little opinion is stated, if any, so eliminate an editorial. 

Since the information is described as recent, it would most likely appear in a magazine article.

3.

In the diagram, two congruent circles share one point, and each circle shares three points with the rectangle. The radius of each circle is 4 cm. What is the area of the shaded region, rounded to the nearest hundredth?

  • 27.52 cm²

  • 100.48 cm²

  • 128.00 cm²

  • 54.98 cm²

  • 50.25 cm²

Correct answer: 27.52 cm²

1. Find the area of the rectangle.

Area = l × w

A = (4 × 4)(2 × 4) = 16 × 8 = 128 cm² 

2. Find the area of one circle.

A = πr²  

A = π(4²) = 16π

3. Multiply the area of the circle by 2.

16π × 2 = 32π

4. Simplify.

32π = 32(3.14) = 100.48 cm² 

5. Subtract the area of the circles from the area of the rectangle.

128 - 100.48 = 27.52 cm² 

4.

To improve reading fluency, a middle school ELA teacher should ensure that independent reading assignments are:

  • At each student's individual reading level

  • Below a student's reading level, so that the student develops confidence in reading

  • Above a student's reading level, so the student develops strategies for dealing with complex texts

  • At a reading level that reflects the class average, so that all students are reading consistently challenging texts

Correct answer: At each student's individual reading level

Research shows that, when students are practicing fluency, they should read at their individual independent reading level. Rereading familiar texts at the individual reading level can further improve fluency.

5.

Find the area of the shaded region.

  • 54 cm2

  • 72 cm2

  • 18 cm2

  • 60 cm2

  • 90 cm2

Correct answer: 54 cm2

1. Find the area of the triangle.

Area = (1/2)(base)(height)

A = (1/2)(12)(12)

A = (1/2)(144) = 72 cm2

2. Find the area of the parallelogram.

Area = (base)(height)

A = (6)(3) = 18 cm2

3. Subtract the area of the parallelogram from the area of the triangle.

72 - 18 = 54 cm2

6.

Read the passage, then answer the question that follows. 

Which of the following statements would the author most likely support?

  • Bicycle riding is a mode of transportation that should be considered

  • Riding bicycles is only for young adults who enjoy exercise

  • Only people in large cities can ride bicycles

  • Companies should not promote the use of bicycles as their employees’ mode of transportation

Correct answer: Bicycle riding is a mode of transportation that should be considered

In the passage, the author describes the benefits of using a bicycle as a mode of transportation.

7.

Read the passage, then answer the question that follows. 

An appropriate title for this passage is:

  • Transportation: Think About Bicycles

  • How to Save Money

  • How to Get to Work Fast

  • Stop Paying for Parking

Correct answer: Transportation: Think About Bicycles

This answer choice provides a title that relates to the general theme of the passage, whereas the other answer choices are too specific to individual points made in the passage.

8.

When placed into the blank space in the number sequence, which of the following numbers creates a list of numbers ordered from greatest to least?

-1/7, _____, -1/3

  • -1/5

  • -1/2

  • 0

  • -1/8

  • None of these

Correct answer: -1/5

The number placed in the blank space must be less than -1/7 but greater than -1/3. Remember to take into account that negative numbers are the opposite of positive numbers in that the lower the number in the denominator, the greater the fraction.

  • -1/2 is less than -1/3, so it is incorrect
  • 0 is greater than both -1/7 and -1/3, so it is incorrect
  • -1/8 is greater than both -1/7 and -1/3, so it is incorrect
  • -1/5 is less than -1/7, but greater than -1/3, so it is the correct answer

9.

Solve for n:

2ⁿ = 8

  • 3

  • 2

  • 4

  • 6

Correct answer: 3

Solve by multiplying 2 times itself until reaching 8.

n then becomes 3:

  • 2 x 2 x 2 = 8
  • 2³ = 8
  • x = 3

10.

Read the sentence, then determine which of the answer choices is an error in diction, usage, idiom, or grammar.

After she had drove the car that her father had found for her, she asked him to buy it for her.

  • had drove

  • had found

  • her

  • No error

Correct answer: had drove

This sentence contains a verb error. The verb “had” calls for the past participle form of the verb “drive,” which is “driven.”

All of the other answer choices are acceptable in standard written English. The answer choice “had found” is the past perfect form of the verb to indicate action completed in the past before the action of the verb in the main clause. The answer choice “her” is the object of the preposition “for.”

11.

Which of the following is a factor of 18a2b3c4?

  • 6ab2c3

  • 12abc

  • 2ab4c2

  • 36ab4c3

  • 18ab4c5

Correct answer: 6ab2c3

1. Write out the factorization of 18a2b3c4.

18: 1 ∙ 2 ∙ 3 ∙ 3 ∙ a ∙ a ∙ b ∙ b ∙ b ∙ c ∙ c ∙ c ∙ c

2. Choose which number can be factored out of 18.

6 (2 ∙ 3) can be factored out of 18.

3. Choose the variables that can be factored out.

a: a can be factored out

b: b ∙ b can be factored out

c: c ∙ c ∙ c can be factored out

4. Combine all the terms.

6ab2c3

  • 12abc is incorrect because 12 is not a factor of 18.
  • 2ab4c2 is incorrect because b4 is greater than b3
  • 36ab4c3 is incorrect because 36 is a multiple of 18, not a factor
  • 18ab4c5 is incorrect because b4 is greater than b3and c5 is greater than c4

12.

What should be done to the expression to change it to scientific notation?

3617.09 × 10-9

  • Move the decimal three places to the left and make the exponent three higher

  • Move the decimal three places to the left and make the exponent three lower

  • Move the decimal two places to the left and make the exponent four higher

  • Move the decimal two places to the left and make the exponent four lower

  • Move the decimal two places to the right and make the exponent two higher

Correct answer: Move the decimal three places to the left and make the exponent three higher

In order to write a number in scientific notation, move the decimal until the number is between 1 and 10. In this case, the decimal would be moved three places to the left, which would be added to the exponent.

3617.09 × 10-9 = 3.61709 × 10-9+3 = 3.61709 × 10-6 

13.

View the supporting details to answer the following question.

Assume that there are 50 people in Mrs. Smith's class. How many people prefer drama, foreign, or science fiction films?

  • 15

  • 22

  • 30

  • 27

Correct answer: 15

1. Determine the percentages of the people represented in drama, foreign, and science fiction categories.

Drama = 14%

Foreign = 8%

Science fiction = 8%

2. Determine the numbers of students based on the percentages.

14% = 0.14 

0.14 × 50 = 7

8% = 0.08

0.08 × 50 = 4

3. Add the total numbers together.

Drama = 7

Foreign = 4

Science fiction = 4

7 + 4 + 4 = 15

14.

Suppose Sam worked for 37 hours this week. Sam makes $12/hour, but 10% of his total pay is subtracted for employment insurance. What is the final amount Sam gets to take home?

  • $399.60

  • $444.00

  • $44.40

  • $400.00

Correct answer: $399.60

Sam earned a total of $12 × 37 hours, or $444.

10% of $444 is $44.40

$444 - $44.40 is $399.60. 

Therefore, Sam takes home $399.60.

15.

Choose the sentence option that demonstrates proper verb usage.

  • Ten hours is a long workday.

  • Ten hours have a long workday.

  • Ten hours are a long workday.

  • Ten hours have been a long workday.

Correct answer: Ten hours is a long workday.

The sentence that contains appropriate verb usage is: Ten hours is a long workday. 

Sentences that contain nouns expressing time, distance, weight, and measurement are singular when they refer to a unit. The verb “is” is singular, while the verbs “have,” “are,” and “have been” are all plural.

16.

In accordance with The Race to the Top for Student Success Act, passed in 2011, what must be the single greatest component of any teacher evaluation system?

  • Student performance

  • Classroom observations conducted by building administrators

  • Review of teachers' instructional plans

  • Summative assessments administered to all teachers

Correct answer: Student performance

According to The Race to the Top for Student Success Act, teacher appraisal systems must use student performance as the single greatest component of teachers' evaluations.

17.

Read the passage, then answer the question that follows.

Where would this student look to learn more about that word?

  • In the glossary

  • In the index

  • In the table of contents

  • In the preface

Correct answer: In the glossary

The glossary is where definitions are listed. This student would use the glossary to learn the definition of the word in question.

18.

Which of the following activities will most effectively promote critical thinking skills for elementary school students?

  • In math, developing a rule that describes a pattern observed in a series of problems

  • In science, making a list of key words from a reading assignment

  • In social studies, making a timeline of events during the civil war

  • In English, defining unfamiliar words in a reading assignment using context clues

Correct answer: In math, developing a rule that describes a pattern observed in a series of problems

Developing a rule to describe a pattern requires synthesis, a higher order thinking skill that calls on a student's ability to apply prior learning to a new problem and combine skills to create a new understanding.

19.

Evaluate the following expression for a = 7, b = 4, and c = -1.

5a + 9b - 2c

  • 73

  • 52

  • 69

  • 16

  • 61

Correct answer: 73

1. Replace each variable with its value.

5a + 9b - 2c = 

5(7) + 9(4) - 2(-1)

2. Simplify.

5(7) + 9(4) - 2(-1) = 

35 + 36 + 2 = 73

20.

Arrange in the correct ascending order:

5/8, 0.25, 87.5%

  • 0.25, 5/8, 87.5%

  • 87.5%, 0.25, 5/8

  • 0.25, 87.5%, 5/8

  • 87.5%, 5/8, 0.25

Correct answer: 0.25, 5/8, 87.5%

Let's convert all the values to decimals to determine which is the largest:

  • 5/8 = 0.625
  • 0.25 = 0.25
  • 87.5% = 0.875

In ascending order, the values would be:

0.25, 5/8, 87.5%

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