PECT Study Guide

Pre-service Academic Performance Assessment (PAPA)
Sample Selected-Response Questions

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Module 1

Use the passage below to answer the four questions that follow.

1    The one-room school is on the verge of extinction. Over the last century, the number of such schools has dropped from 190,000 to less than 400. They are now found only in the most isolated places. Although these buildings will never be seen by most of the population, the students and communities they serve hold them in high regard. The next few years will be critical in determining whether we can preserve this connection to our past or let it become a fading memory of a more innocent time.

2    One-room schools typically serve rural communities isolated from more developed areas. Each school has one teacher and between 4 and 16 students in kindergarten through eighth grade. The grades taught vary each year, but the teachers' approach is fairly consistent. At any given time, a portion of their classes will be working independently or in small groups as they provide more focused instruction to other students. It is a learning environment in which older children help younger children and all do their part to carry out daily tasks. This collaborative atmosphere largely eliminates disciplinary problems and gives students the support needed to perform at a high level.

3    Ensuring the survival of one-room schools will not be easy. If these schools existed in highly populated areas, parents would go to great lengths to guarantee their children a spot. But few families are willing to move to the most sparsely populated areas of the country to take advantage of the schools' benefits. The best course of action may be for researchers to study these schools while they still have the chance. Information gathered on their operating style and the unique communities they provide might generate ideas that can be incorporated into other school environments. If the one-room school cannot survive as a physical entity, the least we can do is try to find ways to keep it alive in spirit.

Objective 0001
Determine the meanings of words and phrases used in a variety of texts.

1. Which of the following words is a synonym for collaborative as it is used in Paragraph 2?

  1. informal
  2. creative
  3. flexible
  4. cooperative
Answer and Rationale
Correct Response: D.
This question requires the candidate to recognize synonyms and antonyms for words and phrases. In Paragraph 2, the author describes how older students help younger students and how all students "do their part to carry out daily tasks" in one-room schools. Given this description of students working together and sharing responsibilities, an appropriate synonym for the word collaborative as used in Paragraph 2 is the word cooperative.
Objective 0002
Recognize purpose, main idea, and organization in a variety of texts.

2. Which of the following organizational approaches does the author use to develop ideas in the passage?

  1. decreasing importance
  2. problem and solution
  3. increasing complexity
  4. comparison and contrast
Answer and Rationale
Correct Response: B.
This question requires the candidate to recognize organizational structures. In Paragraph 1, the author presents the problem of decreasing numbers of one-room schools. A description of the positive attributes of one-room schools in Paragraph 2 supports the idea that the schools are worth preserving. In Paragraph 3, the author proposes a solution to the problem presented in Paragraph 1: "The best course of action may be for researchers to study these schools" for the purpose of generating ideas that can be used in other school environments, thus allowing the one-room school to remain "alive in spirit" if not as a physical building.
Objective 0003
Analyze and evaluate ideas and information presented in a variety of texts.

3. According to information presented in the passage, one major reason for the decline of one-room schools is:

  1. the schools' inability to recruit teachers.
  2. the organization of the schools.
  3. the teaching method used in the schools.
  4. the schools' location in isolated areas.
Answer and Rationale
Correct Response: D.
This question requires the candidate to analyze relationships between ideas (e.g., cause and effect, problem and solution, comparing and contrasting). In Paragraph 3, the author states that "parents would go to great lengths to guarantee their children a spot" in the schools if they were located in highly populated areas. According to the author, however, few families are willing to move to sparsely populated areas for the sole purpose of sending their children to a one-room school. Through these statements, the author establishes the cause-and-effect relationship between one-room schools' location in isolated areas and their decline.
Objective 0004
Make inferences from ideas and information presented in a variety of texts.

4. In the passage, the author expresses most clearly which of the following opinions of one-room schools?

  1. Their structures leave much to be desired.
  2. They are only effective with highly motivated students.
  3. There is much to be learned from them.
  4. They are most effective at teaching basic skills.
Answer and Rationale
Correct Response: C.
This question requires the candidate to identify the author's tone, opinion, or point of view. In Paragraph 3, the author proposes that researchers study one-room schools to gather information that could generate ideas for use in other school environments. This proposal suggests that the author believes researchers and educators have much to learn from one-room schools.

Module 2

Definitions and Formulas

Objective 0005
Understand numbers and the number system.

1. If , then which of the following integers could n equal?

  1. 17
  2. 64
  3. 75
  4. 81
Answer and Rationale
Correct Response: C.
This question requires the candidate to demonstrate knowledge of real numbers. It is given that . Squaring all of the values in the expression eliminates the square root, resulting in the expression 64 < n < 81. Therefore, n can represent values greater than 64 and less than 81. Of the integers given, only 75 falls within this range.
Objective 0006
Apply principles of algebra to expressions and equations.

2. The cost to heat a house will increase by 5% next year. If the current cost is x, which of the following expressions represents the cost to heat the house next year?

  1. (0.05)x
  2. (1.0 + 0.05)x
  4. x + 0.05
Answer and Rationale
Correct Response: B. This question requires the candidate to demonstrate knowledge of the concepts of variable and equality to generate an algebraic expression based on a verbal description. Since the current cost to heat a house is x and the increase is 5% = 0.05, the increase is represented by 0.05x. The total cost for next year must include the current cost plus the increase, thus x + 0.05x = (1.0 + 0.05)x.
Objective 0007
Apply principles of algebra to linear and nonlinear functions.

3. A child has $2.60 in dimes and nickels. The number of nickels is twice the number of dimes. If n is the number of nickels and d is the number of dimes, which of the following pairs of equations can be used to determine the number of nickels and dimes?

  1. 0.10d + 0.05n = 2.60
    n = 2d
  2. d + n = 2.60
    2n = d
  3. d + n = 2.60
    n = 2d
  4. 0.10d + 0.05n = 2.60
    2n = d
Answer and Rationale
Correct Response: A. This question requires the candidate to demonstrate knowledge of translating between different representations of linear functions. It is given that the number of nickels is twice the number of dimes, or n = 2d. Since the total value of the coins is $2.60, and the value of a dime is $0.10 and the value of a nickel is $0.05, then 0.10d + 0.05n = 2.60. Thus, the system of equations that describes the situation includes n = 2d and 0.10d + 0.05n = 2.60.
Objective 0008
Understand measurement concepts and geometry principles.

4. The speed of sound in air is approximately 1126 feet per second. Which of the following expressions gives the speed of sound in miles per hour?

Answer and Rationale
Correct Response: D.
This question requires the candidate to demonstrate knowledge of calculating measurements using dimensional analysis in a real-world situation. There are 5280 feet in one mile, 60 minutes in one hour, and 60 seconds in one minute. The conversion of 1126 feet per second to miles per hour is represented by:

.
Objective 0009
Demonstrate knowledge of data, statistics, and probability.

5. The Venn diagram below represents the inventory of cars available at a car dealership.

In the dealer's lot there are 50 cars. Twenty-five have a blue exterior, 15 have a tan interior, and 5 have a blue exterior with a tan interior. Based on this information, what is the probability that a randomly selected car on the lot will have a tan interior and an exterior that is not blue?

Answer and Rationale
Correct Response: B.
This question requires the candidate to calculate probabilities of events. In the Venn diagram, the non-overlapping part of the right circle indicates that there are 10 cars with a tan interior whose exterior is not blue. Since there are 50 cars in the dealer's lot (15 + 20 + 10 + 5), the probability of a randomly selected car having these same characteristics is given by .
Objective 0010
Understand problem solving, reasoning, and mathematical communication.

6. The effectiveness of computer passwords depends on the number and type of characters that can be used in creating them. Developing effective passwords is a direct application of which of the following mathematical concepts?

  1. factors and common multiples
  2. functions and abstract algebra
  3. permutations and combinations
  4. trigonometry and calculus
Answer and Rationale
Correct Response: C.
This question requires the candidate to identify connections between mathematical concepts and technology. The most secure passwords are long strings of randomly chosen characters that do not follow an easily recognizable order or pattern, such as letters in words. When the order of characters is not limited to words or other patterns, then the ordering can be guided by permutations and combinations of the characters. The number of permutations and combinations increases rapidly when the set of available characters (e.g., letters, numbers, symbols) and the length of the password are increased.

Module 3

Use the writing sample below to answer the two questions that follow.

1The pineapple, the pear, and the orange are all
straightforward fruits: they smell as good as they taste.
2Other fruits, however, are not so simple. 3__________
_____________________________________________
4While descriptions of the durian's sweet almond flavor are
brief and to the point, commentary on its aroma could fill
volumes. 5One writer has likened the smell to a cross between
rotten onions, turpentine, sweaty socks, and a pig pen, and
more foul comparisons are made by others. 6Grown
exclusively in Southeast Asia, the durian has an odor so
offensive that it is commonly banned from hotels, offices,
subways, shopping malls, and other public areas. 7People are
best advised to eat it in the privacy of their homes, holding
their noses and accepting the fruit's sulfurous bouquet as the
price for such a rare taste sensation.

Objective 0011
Understand effective writing.

1. Which of the following edited versions of Part 5 is most effective?

  1. One writer has used rotten onions, turpentine, sweaty socks, and a pig pen to describe the smell; more foul things can be used to describe it.
  2. The smell has been likened to a cross between rotten onions, turpentine, sweaty socks, and a pig pen by one writer, and others have made even more foul comparisons.
  3. One writer has likened the smell to a cross between rotten onions, turpentine, sweaty socks, and a pig pen; others have made even more foul comparisons.
  4. Likening the smell to crossing rotten onions, turpentine, sweaty socks, and a pig pen, one writer and others have made foul comparisons.
Answer and Rationale
Correct Response: C.
This question requires the candidate to revise text to create or improve the parallel structure of words, phrases, or ideas. The most effective edited version of Part 5 comprises two independent clauses joined by a semicolon: "One writer has likened the smell to a cross between rotten onions, turpentine, sweaty socks, and a pig pen; others have made even more foul comparisons." Using subject-verb order and the present perfect tense ("One writer has likened," "others have made") in both clauses creates parallel structure.
Objective 0012
Understand clear, concise, and coherent writing.

2. Which of the following sentences, if inserted as Part 3, would be the most effective topic sentence for the paragraph?

  1. People use the durian to sweeten a broad range of dishes.
  2. The durian might be the world's most confusing fruit.
  3. People have been eating the durian since prehistoric times.
  4. The durian can be eaten at various stages of ripeness.
Answer and Rationale
Correct Response: B.
This question requires the candidate to recognize a clear and concise topic sentence. The sentence "The durian might be the world's most confusing fruit" effectively introduces the general topic of the durian's claim to fame. The writer elaborates on this topic by describing the durian's "sweet almond flavor" and extremely offensive odor, two characteristics whose inherent contradiction makes the durian "the world's most confusing fruit."
Objective 0013
Understand grammatical writing.

3. Which of the following phrases would be most appropriate to use in the blank in the sentence below?

I am good at gymnastics, but __________.
  1. my sister is even better
  2. even better, is my sister
  3. my sister, even, is better
  4. better is my sister, even
Answer and Rationale
Correct Response: A.
This question requires the candidate to apply knowledge of the construction of simple, compound, and complex sentences. Using the phrase "my sister is even better" in the blank creates a compound sentence that comprises two main clauses ("I am good at gymnastics," "my sister is even better") joined by a comma and the coordinating conjunction but.
Objective 0014
Understand writing mechanics and the conventions of Standard American English.

4. Which of the following sentences contains an error in capitalization?

  1. His Father especially enjoyed the month of September.
  2. Our class president will attend the University of Pittsburgh.
  3. I sent my federal tax forms to the Internal Revenue Service.
  4. The artist Winslow Homer lived in Maine for many years.
Answer and Rationale
Correct Response: A.
This question requires the candidate to apply knowledge of the rules of capitalization and the standard use of capital letters. When the word father refers to a male parent, it should only be capitalized if it functions as a substitute for a proper name, as in the sentence "If you want Father to help, ask him politely." In the sentence "His Father especially enjoyed the month of September," "Father" is not used as a substitute for a proper name, so it should not be capitalized.