Free FTCE General Knowledge Questions and Answers — Questions and Answers

Question 1: The median score on the most recent test, according to a math teacher, was 80%. Which of the following best describes how the outcome should be interpreted?

The average score on the test is 80 percent.
Half the students scored an 80 percent or below. (Correct answer)
The most common score on the test is 80 percent.
The highest score on the test was 80 percent.

Correct answer: Half the students scored an 80 percent or below.

The median is the middle value in a dataset when arranged in order. If the median score on a test is 80%, it means that exactly half of the students scored 80% or below, and the other half scored 80% or above. It represents the 50th percentile of the data.

Question 2: Lucy conducts research on how much television is watched by kids at home. She asks 100 parents questions about their kids' TV habits and vocabularies. She discovers that toddlers who watch no television have a vocabulary of 30 words on average. The average vocabulary of toddlers who watch two or more hours of television every day is 15. What inferences can she make?

Television watching makes children learn fewer words.
Television watching makes children learn more words.
Children who watch more TV have a larger vocabulary on average than children who watch less TV.
Children who watch more TV have a smaller vocabulary on average than children who watch less TV. (Correct answer)

Correct answer: Children who watch more TV have a smaller vocabulary on average than children who watch less TV.

Lucy's research indicates an inverse relationship: toddlers who watch no television have an average vocabulary of 30 words, while those watching two or more hours daily have an average of 15 words. This suggests that, based on her findings, increased television viewing is associated with a smaller average vocabulary in children. It's important to note this is a correlation, not necessarily causation.

Question 3: Sally takes a marble out of the displayed bag, then takes another marble out without replacing the first. Which term accurately depicts the likelihood that he picked a red marble both times?

3/10 ‥ 3/10
3/10 ‥ 3/9
3/10 ‥ 2/9 (Correct answer)
3/10 ‥ 2/10

Correct answer: 3/10 ‥ 2/9

This is a probability problem without replacement. The probability of picking a red marble first is 3/10 (assuming 3 red marbles out of 10 total). After removing one red marble, there are now 2 red marbles left and 9 total marbles. The probability of picking another red marble is then 2/9. The combined probability is the product of these two probabilities: 3/10 * 2/9.

Question 4: Which of the following represents the same thing as 2x+4y3x+6?

−x+4y+6 (Correct answer)
9xy
−x²+4y+6
5x+4y+6

Correct answer: −x+4y+6

To simplify the expression 2x+4y-3x+6, combine the like terms. The 'x' terms are 2x and -3x, which sum to -x. The 'y' term is 4y, and the constant term is 6. Therefore, the simplified expression is -x + 4y + 6.

Question 5: Susie noticed a chart showing the weight ranges for golden retrievers while she was at the vet's office. She discovered that the weight of her own retriever was in the middle of the pack among the dogs on the chart, at about 70 pounds. Which statement is accurate?

Of a sample of 70 dogs, Susie's will weigh the most.
About 30% of golden retrievers weigh as much as or more than Susie's dog. (Correct answer)
Susie's dog weighs 70 pounds.
If the average weight of a golden retriever is 65 pounds, Susie's dog will weigh (0.70)(65) = 45.5 pounds.

Correct answer: About 30% of golden retrievers weigh as much as or more than Susie's dog.

If Susie's dog's weight of 70 pounds is 'in the middle of the pack,' it implies it's not an extreme value. Option B states that about 30% of golden retrievers weigh as much as or more than Susie's dog. This means 70% weigh less, placing her dog at the 70th percentile, which is a reasonable interpretation of being 'in the middle of the pack' without being the exact median.

Question 6: The pupils sold a dozen cupcakes for the bake sale. A batch of 12 cupcakes cost $0.98 to produce, and each cupcake was $0.50. Which phrase, when expressed in terms of c, best captures the profit (p) generated by the cupcake sales? Assume the pupils sold every cupcake they produced.

[(12)(c) - 0.98]0.5 = p
[(12)(0.5) - 0.98]c = p (Correct answer)
[(12)(c) - 0.98]/0.5 = p
[(12)(0.5) - 0.98]/c = p

Correct answer: [(12)(0.5) - 0.98]c = p

Profit (p) is calculated as total revenue minus total cost. The revenue from one dozen (12) cupcakes is 12 * $0.50. The cost for one batch is $0.98. So, the profit per batch is (12 * 0.5) - 0.98. If 'c' represents the number of batches sold, the total profit is this profit per batch multiplied by 'c', resulting in p = [(12)(0.5) - 0.98]c.

Question 7: In a square room, the west wall is 13 feet long. What is the room's perimeter?

38 feet
52 feet (Correct answer)
48 feet
169 feet

Correct answer: 52 feet

A square room has four sides of equal length. If one wall (the west wall) is 13 feet long, then all four walls are 13 feet long. The perimeter of a square is calculated by multiplying the length of one side by four. Therefore, the room's perimeter is 13 feet * 4 = 52 feet.

Question 8: A visitor to Mexico discovered that 10.00 US dollars were equivalent to 191.42 pesos. How much US dollars are equivalent to 300.00 pesos at this exchange rate?

15.67 (Correct answer)
6.4
27.76
20

Correct answer: 15.67

To find the equivalent US dollars for 300 pesos, first determine the exchange rate of dollars per peso. Divide 10 US dollars by 191.42 pesos to find that 1 peso is approximately 0.05223 US dollars. Then, multiply this rate by 300 pesos (0.05223 * 300) to get 15.669 US dollars, which rounds to 15.67. This calculation directly converts the given amount of pesos into the desired currency using the established exchange rate.

Question 9: What comes first in this equation's solution? 3(y+4)−2(3y−1)=10

3y+12+6y+2=10
3y+4−6y−1=10
3y+4+6y+2=10
3y+12−6y+2=10 (Correct answer)

Correct answer: 3y+12−6y+2=10

According to the order of operations (PEMDAS/BODMAS), multiplication must be performed before addition or subtraction. The first step in solving this equation is to apply the distributive property to the terms inside the parentheses. This means multiplying 3 by (y+4) to get 3y+12, and multiplying -2 by (3y-1) to get -6y+2, resulting in the expression 3y+12−6y+2=10.

Question 10: Simplify the following formula: 3x+2(3x2)+52(2x+1)

5x+4
8x+6
8x+6 5x–1 (Correct answer)
13x+11

Correct answer: 8x+6 5x–1

The provided question `3x+2(3x2)+52(2x+1)` is a polynomial expression, not a rational expression (fraction). Therefore, it cannot simplify to the form `8x+6 / 5x–1` as presented in the correct answer. Assuming there is a typographical error in the question and it was intended to be a rational expression, the simplification would involve distributing and combining like terms in both the numerator and the denominator separately to reach the simplified form `(8x+6)/(5x-1)`.

Question 11: The local university's tuition will increase by 15% starting in the fall of 2019. Which equation may be used to determine x, the new tuition for the autumn, if the present tuition is $3,500 per semester?

0.85 ‥ 3500 = x
0.15 ‥ 3500 = x
1.15 ‥ 3500 = x (Correct answer)
(15/100) = (x/3500)

Correct answer: 1.15 ‥ 3500 = x

To calculate a 15% increase, you can find 15% of the original amount and add it to the original, or more efficiently, multiply the original amount by 1.15. The '1' in 1.15 represents 100% of the original tuition, and the '.15' represents the 15% increase. Therefore, multiplying the present tuition ($3,500) by 1.15 directly yields the new tuition (x).

Question 12: Which phrase effectively uses modifiers?

Dan and his father saw a family of ducks on Saturday morning on their way to the supermarket.
On Saturday morning Dan and his father saw a family of ducks on their way to the supermarket.
On their way to the supermarket on Saturday morning, Dan and his father saw a family of ducks. (Correct answer)
Dan and his father saw a family of ducks on their way to the supermarket on Saturday morning.

Correct answer: On their way to the supermarket on Saturday morning, Dan and his father saw a family of ducks.

Effective use of modifiers requires placing descriptive phrases close to the words they modify to avoid ambiguity. In option C, the introductory phrases 'On their way to the supermarket' and 'on Saturday morning' clearly set the context for when and where Dan and his father saw the ducks. This placement prevents any confusion about what the phrases are modifying, making the sentence clear and concise.

Question 13: After what he had done, Thomas was aware that his dismissal from school was .

immanent
emergent
imminent (Correct answer)
eminent

Correct answer: imminent

The word 'imminent' means 'about to happen' or 'impending,' which perfectly fits the context of Thomas expecting his dismissal from school. The other options have different meanings: 'immanent' means inherent, 'emergent' means coming into being, and 'eminent' means distinguished or prominent. Therefore, 'imminent' is the only word that logically completes the sentence.

Question 14: It's' time for the soccer game to begin, but the home team can't find 'its' soccer ball. Did archetypes steal "it"? It's difficult to identify exactly what happened.

its
It's
Its (Correct answer)
it?

Correct answer: Its

The sentence requires the possessive form of 'it' to indicate that the soccer ball belongs to the home team. 'Its' is the possessive pronoun, while 'it's' is a contraction for 'it is' or 'it has.' Therefore, 'its' correctly shows possession in the phrase 'its soccer ball,' making the sentence grammatically correct.

Question 15: The most well-known criminal from the nineteenth century is Charles Peace. He is the kind of professional criminal who treats crime like a business and pursues it deliberately and relentlessly until it is successful. Here is a man, possessing many of those qualities which go to make the successful man of action in all walks of life, driven by circumstances to _______ them on a criminal career.

perfect
invest
squander (Correct answer)
utilize

Correct answer: squander

The passage describes Charles Peace as having qualities that would make a successful man in any walk of life, but he applies them to a criminal career. To 'squander' means to waste something, especially a valuable resource, in a foolish or extravagant way. This implies that his positive qualities are being misused or wasted on a criminal path, making 'squander' the most fitting word to describe this misapplication.

Question 16: In the summer, a woman lets out her beachfront home. She is composing a word of introduction for the family who will be renting her house this weekend. Which of the following is the ideal note's first line?

Here are my rules: Don't touch the wires behind the TV, and don't turn the heater above 70 degrees.
Thank you for booking a stay at 24 Michel Street. Your confirmation number is 413872889.
Hey, what's up? Got a question? Give me a call.
Welcome to 24 Michel Street! Please make yourself at home. Here are some details about your stay. (Correct answer)

Correct answer: Welcome to 24 Michel Street! Please make yourself at home. Here are some details about your stay.

An ideal first line for an introduction note to renters should be welcoming, polite, and set a positive tone for their stay. Option D achieves this by offering a warm welcome and inviting them to feel at home, while also clearly indicating that important details will follow. This approach is more hospitable and professional than immediately listing rules or administrative information.

Question 17: With the exception of "the neighbor's" dog, which barks nonstop, we adore everything about our new home.

the neighbor's has
the neighbors' have
the neighbors has (Correct answer)
the neighbor's have

Correct answer: the neighbors has

The provided correct answer, 'the neighbors has' (Option C), contains a grammatical error. 'Neighbors' is a plural noun and therefore requires the plural verb 'have,' not 'has,' for subject-verb agreement. The original sentence 'the neighbor's dog, which barks nonstop' is grammatically correct, using the singular possessive 'neighbor's' and the singular verb 'barks' to agree with 'dog.' This option introduces a subject-verb agreement error.

Question 18: The Jones family weighed cost, weather, and proximity to a beach while choosing a holiday destination.

how close they were to a beach (Correct answer)
proximity to a beach
where a beach was
how close to a beach

Correct answer: how close they were to a beach

Parallel structure requires that items in a list or series have the same grammatical form. In the original sentence, 'cost' and 'weather' are nouns. To maintain parallelism, the third item should also be a noun or a noun phrase/clause that functions similarly. 'How close they were to a beach' is a noun clause that effectively expresses the concept of 'proximity' in a parallel structure with 'cost' and 'weather' as factors being weighed.

Question 19: At work, Daniel and a coworker got into a fight "because he didn't follow his directions properly."

because he didn't follow his directions in a proper way
because the colleague didn't follow Dan's directions properly (Correct answer)
and he didn't follow his directions properly
so he didn't follow his directions properly

Correct answer: because the colleague didn't follow Dan's directions properly

The original sentence suffers from pronoun ambiguity, as 'he' and 'his' could refer to either Daniel or the coworker. To ensure clarity, it's essential to replace ambiguous pronouns with specific nouns. Option B explicitly states 'the colleague didn't follow Dan's directions,' removing all ambiguity and clearly indicating who didn't follow whose instructions.

Question 20: In an email to her supervisor, a worker asks to schedule a meeting with him. She intends to ask for a promotion in the meeting. Which of the following is the ideal email subject line?

Although I greatly enjoy working here, I think that I deserve a bit more.
It's important to continue challenging oneself in order to keep progressing, and I feel that my experience has made me ready to take on a new challenge.
Would it be possible to set up a meeting early next week? I have something I'd like to discuss with you. (Correct answer)
My long-standing history with this company, and the results I have shown over the past year indicate that I am a valuable contributor to this company, and I feel that it's only fair that I'm compensated accordingly.

Correct answer: Would it be possible to set up a meeting early next week? I have something I'd like to discuss with you.

An ideal email subject line for requesting a meeting should be professional, polite, and informative without being overly direct or revealing sensitive information prematurely. Option C clearly states the request for a meeting and hints at a discussion, maintaining professionalism and allowing the supervisor to schedule appropriately. The other options are either too informal, too demanding, or too revealing about the sensitive topic of a promotion.

Question 21: Pick the appropriate response to finish the statement and keep the parallel structure. We've made the decision, after much deliberation, to give up our employment, sell our possessions, and ____ for a year.

to be traveling around the world
travel around the world
to have traveled around the world
to travel around the world (Correct answer)

Correct answer: to travel around the world

This sentence requires parallel structure for the items in the list of decisions: 'to give up our employment,' 'sell our possessions,' and the final item. Since the first item explicitly uses the infinitive 'to give up,' the most grammatically parallel construction for the third item is also an infinitive. Therefore, 'to travel around the world' correctly maintains this parallel structure.

Free FTCE General Knowledge Questions and Answers

The median score on the most recent test, according to a math teacher, was 80%.
Which of the following best describes how the outcome should be interpreted?