Exercises 3.9 Multiple Choice Exercises
When this
<exercises> division is hosted on Runestone Academy, it will be enabled for group work. See group selection and submission features are at the end of the division. See Worksheet 3.26 for more detail. (2024-07-24: experimental.)
2. Multiple-Choice, Math in Feedback.
- \(6\)
- Have you accounted for the \(2\) and \(5\) that are in the original binomial?
- \(60\)
- What should the exponents on \(2\) and \(5\) be when you expand \((2x+5xy^2)^4\text{?}\)
- \(100\)
- Have you included something of the form \(\binom{n}{k}\) in your computations?
- \(600\)
- Correct! Using the binomial theorem, we get a term containing the monomial \(x^4y^4\) by taking two of the first term, and two of the second term in the expansion of \((2x+5xy^2)^4\text{,}\) and so this term is equal to\begin{equation*} \binom{4}{2} (2x)^2 (5xy^2)^2 = 6 \cdot 2^2 5^2 x^4 y^4 = 600 x^4 y^4\text{.} \end{equation*}
3. Multiple-Choice, Not Randomized, Multiple Answers.
4. Multiple-Choice, Randomized, One Answer.
5. Multiple-Choice, Randomized, Multiple Answers.
Which colors might be found in a rainbow? (Note that the radio buttons now allow multiple buttons to be selected.) [Static versions retain the order as authored.]
- Red
- Red is a definitely one of the colors.
- Yellow
- Yes, yellow is correct.
- Black
- Remember the acronym…ROY G BIV. “B” stands for blue.
- Green
- Yes, green is one of the colors.
6. Mathematical Multiple-Choice, Not Randomized, Multiple Answers.
Which of the following is an antiderivative of \(2\sin(x)\cos(x)\text{?}\)
- \(\sin^2(x)+832\)
- Remember that when we write \(+C\) on an antiderivative that this is the way we communicate that there are many possible derivatives, but they all “differ by a constant”.
- \(\sin^2(x)\)
- The derivative given in the statement of the problem looks exactly like an application of the chain rule to \(\sin^2(x)\text{.}\)
- \(-\cos^2(x)\)
- Take a derivative on \(-\cos^2(x)\) to see that this answer is correct. Extra credit: does this answer “differ by a constant” when subtracted from either of the other two correct answers?
- \(-2\cos(x)\sin(x)\)
- The antiderivative of a product is not the product of the antiderivatives. Use the product rule to take a derivative and see that this answer is not correct.
7. Multiple-Choice, Not Randomized, One Answer.
What color is a stop sign?
Note: we are experimenting with choices in columns (2025-05-17). Three columns here.
- Green
- Green means “go!”.
- Red
- Red is universally used for prohibited activities or serious warnings.
- White
- White might be hard to see.
- Purple
- Hmmmmmmm.
- Pink
- I have never seen a pink road sign!
