Exercises 5.12 Matching Exercises

Matching exercises come in two varieties. Their differences are most noticeable in interactive versions.

Cardsort: A <cardsort> asks users to match items in a 1-1 or many-1 fashion. The interactive version of these involves dragging “card”s from the left column (the <premise>s) into containers on the right (the <response>s).
Matching: A <matching> interactive asks users to form connections between the <premise>s in the left column and the <response>s on the right. This format supports many-many matches.

1. Cardsort Problem, Dates.

Match each event in United States history with the year it happened.

Review Encyclopedia Brittania, 25 Decade-Defining Events in U.S. Historyurl.

Monroe Doctrine
1823
Haymarket Riot
1886
Louisiana Purchase
1803
Battle of Gettysburg
1863

2. Cardsort Problem, Derivatives.

Match each function with its derivative.

Did you compute the derivative of each function in the premises (left column)?

\(x^3-6x^2+5\)
\(3x^2-12x\)
\(x^{-3}\)
\(-3x^{-4}\)
\((x+1)^2\)
\(2x+2\)

3. Cardsort Problem, Linear Algebra.

Match each subspace with a basis for that subspace. (You may assume that each set is really a basis for at least one of the subspaces.)

Each putative basis is a subset of exactly one of the three subspaces. So for each subspace, two of the three sets can be ruled out by simply testing that the vectors of the basis are members of the subspace, via the membership criteria.

\(\left\{\langle x,y,z\rangle\mid - y + z = 0\right\}\)
\(\left\{\langle -4, 3, 3\rangle, \langle 3, -2, -2 \rangle\right\}\)
\(\left\{\langle x,y,z\rangle\mid -3x - 5y + z = 0\right\}\)
\(\left\{\langle -4, 3, 3\rangle, \langle 5, -4, -5 \rangle\right\}\)
\(\left\{\langle x,y,z\rangle\mid -2x - 5y + 2z = 0\right\}\)
\(\left\{\langle 3, -2, -2 \rangle, \langle 5, -4, -5 \rangle\right\}\)

Hint.

For openers, a basis for a subspace must be a subset of the subspace.

4. Cardsort Problem, Function Types.

Sort the following functions into their correct categories.

Review Active Prelude to Calculus url.

\(y=5x+3\)
\(\pi x - 6y = \sqrt{2}\)
\(y=\frac{-1}{2}x+e\)
Linear
Quadratic
\(y=x^3-x\)
\(y=2^x\)
Exponential
\(y=x^3\)
\(y=\sqrt{x}\)
Power

5. Matching Problem, Playing Cards.

6. Matching Problem, Popular Music History.

7. Cardsort Problem, Basic Arithmetic.

This is a simple exercise to test some grading behavior.

2 + 3
4 + 1
5
\(12 + 2\)
14

8. Cardsort Problem, Graphs of Functions.

Each figure below shows the graph of a single function. Match each graph with the type of function it pictures.

a smooth curve that rises, falls, and rises again, crossing the horizontal axis three times — Figure 5.12.1. Graph One

a wave oscillating steadily between one high value and one low value, three full times across the view — Figure 5.12.2. Graph Two

three branches split by two dashed vertical lines; the central branch rises to a single peak between them — Figure 5.12.3. Graph Three

A polynomial is defined everywhere, with no breaks and no repetition. A trigonometric function repeats itself at regular intervals. A rational function may have vertical asymptotes where its denominator vanishes—and while the central branch of Figure 5.12.3 may resemble a downward-opening parabola, a parabola has no asymptotes.

Graph Two
Trigonometric Function
Graph One
Polynomial Function
Graph Three
Rational Function

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