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Integrating WeBWorK into Textbooks: Sample Exercises

Robert Beezer, Alex Jordan

Section 7 Multiple Choice

While free-response questions are generally preferred, sometimes the nature of a question lends itself to multiple choice.
Note also that the solution to this problem uses an external link.
The number \(\sqrt{2}\) [1] rational, and it [2] algebraic.
[1]
[2]
Answer 1.
\(\text{is not}\)
Answer 2.
\(\text{is}\)
Solution.
If \(\sqrt{2}\) were rational, then \(\sqrt{2}=\frac{p}{q}\text{,}\) with \(p\) and \(q\) coprime. But then \(2q^2=p^2\text{.}\) By the Fundamental Theorem of Arithmetic 1 , the power of \(2\) dividing the left side is odd, while the power of \(2\) dividing the right side is even. This is a contradiction, so \(\sqrt{2}\) is not rational.
Since \(\sqrt{2}\) is a root of \(x^2-2\text{,}\) it is algebraic.
This exercise has a multiple choice following a paragraph, not part of one.
Salem is the capital of which US state?
  • Cornwall
  • Massachusetts
  • Oregon
Answer.
\(\text{Oregon}\)
This exercise has multiple choice in multiple tasks.

(a)

The capital of [1] is Paris.
[1]
Answer.
\(\text{France}\)

(b)

The capital of Georgia is not [2].
[2]
Answer.
\(\text{Savannah}\)
This exercise has multiple choice in multiple tasks and there is nesting.

(a)

An introduction to the first task.
(i)
Red and [1] make purple.
[1]
Answer.
\(\text{blue}\)
(ii)
In baseball, what is it called when the batter hits the ball and the ball lands in the stadium behind the batter?
  • foul
  • homerun
  • strike
Answer.
\(\text{foul}\)

(b)

An anagram for “PreTeXt” is [3].
[3]
Answer.
\(\text{pet T Rex}\)

(c)

An introduction to the third task.
(i)
What is a four-sided shape called?
  • triangle
  • quadrilateral
  • pentagon
Answer.
\(\text{quadrilateral}\)
(ii)
An introduction to the second subtask of the third task.
(A)
All three “c”s in “Pacific Ocean” are prounounced differently.
  • True
  • False
Answer.
\(\text{True}\)
(B)
The Maldives are in the [6] ocean.
[6]
Answer.
\(\text{Indian}\)
Which of the following suggest that differentiation and integration are inverse processes?
  • The Quadratic Formula
  • The Fundamental Theorem of Calculus
  • The Fundamental Theorem of Arithmetic
  • None of these
Answer.
\(\text{The Fundamental ... of Calculus}\)
Solution.
The correct answer is The Fundamental ... of Calculus.
en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Canonical_representation_of_a_positive_integer
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