# Integrating WeBWorK into Textbooks: Sample Exercises

## Section1.6Multiple Choice

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

### Checkpoint1.6.1.Drop-down/Popup.

Note also that the solution to this problem uses an external link.
The number $$\sqrt{2}$$
• is
• is not
rational.
$$\text{is not}$$
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 , 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.

### Checkpoint1.6.2.Choose one.

Which of the following suggest that differentiation and integration are inverse processes?
• The Fundamental Theorem of Calculus
• The Fundamental Theorem of Arithmetic
• None of these
$$\text{The Fundamental ... of Calculus}$$
Solution.
The correct answer is The Fundamental ... of Calculus.

### Checkpoint1.6.3.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
$$\text{Choice 2, Choice 4, Choice 5}$$
Solution.
The correct answer is Choice 2, Choice 4, Choice 5.

### Checkpoint1.6.4.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
$$\text{B, C, D}$$
Solution.
The correct answer is B, C, D.

### Checkpoint1.6.5.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.
$$\displaystyle e^{x^2} e^{1/x}$$
$$\displaystyle e^{x^2} + e^{1/x}$$
$$\displaystyle \dfrac{ e^{x^2} }{ e^x }$$
$$\displaystyle e^{ (x^3+1) / x}$$
$$\displaystyle e^{x^2} e^{x^{-1}}$$
None of the above
$$\text{TACO, SUSHI, PIZZA}$$