<solutions divisional="hint answer solution">
<title>Hints and Answers to Selected Exercises</title>
</solutions>
Appendix D Hints and Answers to Selected Exercises
View Source for solutions
II Algebra (and Runestone)
3 Runestone Testing
3.8 True/False Exercises
3.8.1. True/False.
Hint.
View Source for hint
<hint>
<p>
<m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws"/>. [Cross-reference is just a demo,
content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
</p>
</hint>
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 1.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
3.9 Multiple Choice Exercises
3.9.1. Multiple-Choice, Not Randomized, One Answer.
3.9.3. Multiple-Choice, Not Randomized, Multiple Answers.
3.9.4. Multiple-Choice, Randomized, One Answer.
3.9.5. Multiple-Choice, Randomized, One Answer but with Checkboxes.
3.9.6. Multiple-Choice, Randomized, Multiple Answers.
3.9.7. Mathematical Multiple-Choice, Not Randomized, Multiple Answers.
Hint.
View Source for hint
<hint>
<p>
You can take a derivative on any one of the choices to see if it is correct or not,
rather than using techniques of integration to find
<em>a single</em> correct answer.
</p>
</hint>
You can take a derivative on any one of the choices to see if it is correct or not, rather than using techniques of integration to find a single correct answer.
3.9.8. Multiple-Choice, Not Randomized, One Answer.
3.10 Parsons Exercises
3.10.1. Parsons Problem, Mathematical Proof.
3.10.6. Parsons Problem, Mathematical Proof, Numbered Blocks.
3.12 Matching Exercises
3.12.3. Cardsort Problem, Linear Algebra.
3.13 Clickable Area Exercises
3.13.3. Clickable Areas, Text in a Table.
3.18 Fill-In Exercises
3.18.6. Fill-In, New Markup Strings.
3.18.10. Fill-In, Dynamic Math with Simple Numerical Answer.
3.18.11. Fill-In, Dynamic Math with Formulas as Answers.
3.18.12. Fill-In, Dynamic Math with Interdependent Formula Checking.
3.19 Hodgepodge
3.19.2. With Tasks in an Exercises Division.
3.19.2.a True/False.
Hint.
View Source for hint
<hint>
<p>
<m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws"/>. [Cross-reference is just a demo,
content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
</p>
</hint>
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 1.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
3.20 Exercises that are Timed
Timed Exercises
3.20.1. True/False.
Hint.
View Source for hint
<hint>
<p>
<m>P_n</m>, the vector space of polynomials with degree at most <m>n</m>,
has dimension <m>n+1</m> by <xref ref="theorem-exponent-laws"/>. [Cross-reference is just a demo,
content is not relevant.] What happens if we relax the defintion and remove the parameter <m>n</m>?
</p>
</hint>
\(P_n\text{,}\) the vector space of polynomials with degree at most \(n\text{,}\) has dimension \(n+1\) by Theorem 1.2.16. [Cross-reference is just a demo, content is not relevant.] What happens if we relax the defintion and remove the parameter \(n\text{?}\)
