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PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

Thomas W. Judson, Isaac Newton (Editor)

Section 3.15 Exercises that are Timed

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This is a section that merely explains and holds an <exercises> division, which will be at the level of a <subsection>. There is a @time-limit attribute on <exercises>, set to the value 10, which implies (a) the collection of (two) exercises is a “timed exam” when hosted on Runestone, and (b) a student will have 10 minutes to complete the collection.
Showing results, showing feedback, displaying a timer, and allowing pausing are all enabled by default. To disable any of these features, set the corresponding attributes on the <exercises> division, @results, @feedback, @timer, @pause, to the value no. As a test, we have turned off pausing. Don't panic!
Of course, if you are not viewing this while online and hosted on a Runestone server, then these exercises will not look any different than in other places.
(Since this is an unstructured division, the number of the <exercises> is not displayed when born. It does have a number, which is the same as the enclosing <section>. To wit: Section 3.15 versus Exercises 3.15.)

Exercises Timed Exercises

    You have 10 minutes to do these exercises when hosted online on a Runestone server.

    1. True/False.

      Every vector space has finite dimension.

    • True.

    • The vector space of all polynomials with finite degree has a basis, \(B = \{1,x,x^2,x^3,\dots\}\text{,}\) which is infinte.

    • False.

    • The vector space of all polynomials with finite degree has a basis, \(B = \{1,x,x^2,x^3,\dots\}\text{,}\) which is infinte.
    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 \(n\text{?}\)

    2. Multiple-Choice, Not Randomized, One Answer.

      What color is a stop sign?
    • Green
    • Green means “go!”.
    • Red
    • Red is universally used for prohibited activities or serious warnings.
    • White
    • White might be hard to see.
    Hint 1.
    What did you see last time you went driving?
    Hint 2.
    Maybe go out for a drive?
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