Multiple-Choice Questions and Set Builder Notation

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Questions and Answers

Which of the following is a true statement about the stem of a multiple-choice question?

It should not include the phrase 'according to the text' or similar language. (correct)
It should be phrased in a way that is clear and concise, even if it is tricky.
It should only include essential information, avoiding irrelevant details. (correct)
It should not be worded negatively unless it is crucial for the learning objectives. (correct)

What is the primary purpose of distractors in a multiple-choice question?

To confuse the student and make the question more challenging.
To ensure that the correct answer is clearly the best option.
To represent common misconceptions students might have about the topic. (correct)
To provide more options for the student to choose from, making the question more comprehensive.

Which of these is NOT a characteristic of effective multiple-choice question options?

Distractors should be designed to trick the student into selecting the wrong answer. (correct)
Options should be clearly and concisely stated, preventing ambiguity.
Options should be mutually exclusive to prevent overlap in meaning.
All options should be plausible, avoiding irrelevant information.

Which of these is a recommended practice for constructing multiple-choice question options?

Avoid using phrases that directly reference the original text, as they should not be necessary for answering the question. (C) Signup and view all the answers

How do appropriate distractors help improve the effectiveness of a multiple-choice question?

They reflect common misconceptions about the topic, allowing the question to identify students' areas of misunderstanding. (D) Signup and view all the answers

Which set builder notation represents the set of all even numbers?

{x: x is a multiple of 2} (A), {x: x is an integer, x is divisible by 2} (D) Signup and view all the answers

Which of the following set builder notations represents the set of all prime numbers between 1 and 20?

{x: x is a prime number, 1 < x < 20} (A), {x: x is a prime number and 1 < x < 20} (D) Signup and view all the answers

Which set builder notation represents the set of positive integers?

{x: x is an integer, x > 0} (A), {x: x is a positive integer} (D) Signup and view all the answers

Which set builder notation represents the set of all multiples of 5 less than 100?

{x: x is an integer, and x is a multiple of 5, x < 100} (A), {x: x is a multiple of 5, and x is less than 100} (B), {x: x is divisible by 5, x < 100} (D) Signup and view all the answers

Which set builder notation represents the set of all integers greater than 5?

{x: x is an integer, x > 5} (A) Signup and view all the answers

What is the complement of the set B = {4, 8, 12, 16} if the universal set is U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}?

{2, 6, 10, 14, 18, 20} (D) Signup and view all the answers

Which of the following sets is a subset of the set {x | x is a factor of 12}?

{1, 2, 3, 4, 6} (A), {2, 4, 6, 12} (C) Signup and view all the answers

What is the set P = {x | 2(x-1) ≤ 8} represented in set notation?

{x | x ≤ 5} (C) Signup and view all the answers

Which of the following statements is FALSE about the sets P = {..., -2, -1, 0, 1, 2, 3, 4, 5} and Q = {-8, -7, -6, -5,...}?

P is a subset of Q (B) Signup and view all the answers

Given that A = {1, 3, 5} and B = {2, 4, 5} are subsets of the universal set U = {1, 2, 3, 4, 5}, what is the complement of A, denoted as A'?

{2, 4, 5} (A) Signup and view all the answers

In the context of Problem 1, how would the relationship between the sets 'university graduates' and 'wise people' be represented in a Venn diagram?

Two separate circles, with no overlap. ('University Graduates') would be entirely contained within ('Wise People'). (D) Signup and view all the answers

In Problem 2, which Venn diagram would represent the relationship between final year students, SRC students, and good students?

Three overlapping circles, with the center section where all three sets intersect. ('Final Year Students') would be entirely contained within ('SRC Students'), and ('SRC Students') would be entirely contained within ('Good Students'). (C) Signup and view all the answers

In the context of Problem 3, which of the following statements would be TRUE if it were to be added? (Select all that apply)

No one who likes coca-cola is not studious. (A), Some students are both studious and not my friend. (C), There are people who are not studious, and they do not like coca-cola. (D) Signup and view all the answers

Which of the following sets is not a valid subset based on the statements provided in Problems 1 - 4?

The set of 'good students' contains the set of 'final year students'. (B) Signup and view all the answers

Which of the following would NOT necessarily be true if a student was BOTH a sprinter and a hurdler?

The student is counted twice in the total count of athletes. (A) Signup and view all the answers

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