# Assessment Items-129 Fall08

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Here are a few proposed items for our common assessment questions.

• A limit of a difference quotient problem: ${\displaystyle \lim _{h\rightarrow 0}{\frac {((3+h)^{2}-9)}{h}}}$
• Expand out power and cancel the 9's --2
• Factor out h and cancel (properly) --2
• find final limt --1

SR 17S/9US DK 19S/3US

• A chain-rule problem: Find the derivative of ${\displaystyle {\sqrt {1+x^{2}}}}$ and show all your work.
• Write sqrt as 1/2 power and Differentiate 1/2 power correctly --2
• Multiply by derivative of ${\displaystyle x^{2}}$ --3

SR 25S/1US DK 17S/5US

• A max-min problem: A cylindrical can is made from aluminum of a uniform thickness. If the volume of the can 40 cubic inches, find the dimensions of the can that uses the least amount of aluminum.
• Find volume formula -1
• Use SA to reduce to a one-variable problem -2
• Find minimum value -2
• Justify that it really is a minimum at this point. -1

SR 9S/17US DK 6S/16US

• A u-substitution problem: Find the integral ${\displaystyle \int _{0}^{1}\sin(2\pi s)ds}$
• Identify substitution as ${\displaystyle u=2\pi x}$ -1
• Correctly substitute and integrate --2
• Handle limits (or back-substitution) correctly. --2

SR 15S/11US DK 15S/7US

• An applied integral problem: If ${\displaystyle v(t)=t^{2}-8t+15}$ find a formula for displacement s(t), and the total distance traveled,d(t), ${\displaystyle 0\leq t\leq 10.}$
• Find displacement -2
• Realize that displacement is given by absolute value. -1
• Integrate the absolute value correctly. --2

SR 16S/10US DK 10S/12US

Conclusion: In both sections students learned to do the basic computations. Obviously, the students struggled with applying what they had learned. This is not surprising. If this were calculus 2 I might be more concerned, but my goal in this class is to try to get as many students as possible to be able to perform basic algebraic manipulation, understand the basics of calculus and get in the habit of studying and doing homework. In later classes I would hope to get the students to realize the importance of applying their knowledge and understanding concepts.