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Integrating WeBWorK into Textbooks: Sample Exercises

Robert Beezer, Alex Jordan

Section 1.6 Multiple Choice

While free-response questions are generally preferred, sometimes the nature of a question lends itself to multiple choice.

Checkpoint 1.6.1. Drop-down/Popup.

Note also that the solution to this problem uses an external link.
The number \(\sqrt{2}\)
  • ?
  • is
  • is not
rational.
Answer.
\(\text{is not}\)
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 
en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic#Canonical_representation_of_a_positive_integer
, 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.

Checkpoint 1.6.2. Choose one.

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.

Checkpoint 1.6.3. Choose a Subset of Options.

Select all expressions that are equivalent to \(e^{x^2 + 1/x}\text{.}\) There may be more than one correct answer.
  • \(\displaystyle e^{x^2} + e^{1/x}\)
  • \(\displaystyle e^{ (x^3+1) / x}\)
  • \(\displaystyle \dfrac{ e^{x^2} }{ e^x }\)
  • \(\displaystyle e^{x^2} e^{1/x}\)
  • \(\displaystyle e^{x^2} e^{x^{-1}}\)
  • None of the above
Answer.
\(\text{Choice 2, Choice 4, Choice 5}\)
Solution.
The correct answer is Choice 2, Choice 4, Choice 5.

Checkpoint 1.6.4. Choose a Subset of Options with Automated Labeling.

Select all expressions that are equivalent to \(e^{x^2 + 1/x}\text{.}\) There may be more than one correct answer.
  1. \(\displaystyle e^{x^2} + e^{1/x}\)
  2. \(\displaystyle e^{x^2} e^{x^{-1}}\)
  3. \(\displaystyle e^{x^2} e^{1/x}\)
  4. \(\displaystyle e^{ (x^3+1) / x}\)
  5. \(\displaystyle \dfrac{ e^{x^2} }{ e^x }\)
  6. None of the above
Answer.
\(\text{B, C, D}\)
Solution.
The correct answer is B, C, D.

Checkpoint 1.6.5. Choose a Subset of Options with Explicit Labeling.

Select all expressions that are equivalent to \(e^{x^2 + 1/x}\text{.}\) There may be more than one correct answer.
TACO
\(\displaystyle e^{x^2} e^{1/x}\)
BURRITO
\(\displaystyle e^{x^2} + e^{1/x}\)
BURGER
\(\displaystyle \dfrac{ e^{x^2} }{ e^x }\)
SUSHI
\(\displaystyle e^{ (x^3+1) / x}\)
PIZZA
\(\displaystyle e^{x^2} e^{x^{-1}}\)
HUNGRY
None of the above
Answer.
\(\text{TACO, SUSHI, PIZZA}\)
Solution.
The correct answer is TACO, SUSHI, PIZZA.
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