Assessing the Mathematics Major with a Bottom-Up Approach

Sarah V. Cook
Washburn University

Appendix A

Calculus I pre-test and corresponding Calculus I post-test questions

(1) Find the equation of the line through the point  and having slope .

POST:  Find an equation of the line tangent to  at .

(2) Solve the inequality: .

POST:  Give the intervals of increasing and decreasing for the function

.    

(3) Solve the equation .

POST:  Find the absolute extrema of  on the interval .

(4) Rationalize the denominator.

POST:  Find the limit, if it exists. 

(5) Simplify the expression.

POST:  Find the limit, if it exists.

(6) Simplify the expression.

POST:  Find the indicated antiderivative.

(7) Solve the equation for all x in .         

POST:  Find the critical numbers of the function  on the interval . 

(8)  A 16-foot ladder is leaning against a house as shown.  If the top of the ladder is 4 feet off of the ground, how far is the base of the ladder from the house?

POST:  A 16-foot ladder is leaning against a house as shown.  The ladder begins to slide in such a way that the top of the ladder moves directly downward at 3 feet per second.  When the top of the ladder is 4 feet off of the ground, how fast is the base of the ladder moving?

Calculus II pre-test and corresponding questions on Calculus I and/or Calculus II post-test

(1) Differentiate.

            POST Calc I: Find  if .

            POST Calc II: Given the parametric curve,  find at the point where .

(2) Find  if .

            POST Calc I: same

            POST Calc II: none

(3) Evaluate the definite integral.

            POST Calc I: same

            POST Calc II: none

(4) Find the critical numbers of .

            POST Calc I: Find the critical numbers of the function  on the interval . 

            POST Calc II: Set up the definite integral to find the total area enclosed by the limacon .

(5) Find the intersection points of the graphs  and .

            POST Calc I: none

            POST Calc II: Consider the region in the first quadrant bounded by  and . 
            Sketch the region then set up (but do not evaluate) the definite integral required to compute the area of the region.

(6) Find the indicated antiderivative.   

            POST Calc I: same

            POST Calc II: none

(7) Evaluate the integral.

            POST Calc I: same

            POST Calc II: Evaluate the integral.

(8)  A 16-foot ladder is leaning against a house as shown.  The ladder begins to slide in such a way that the top of the ladder moves directly downward at 3 feet per second.  When the top of the ladder is 4 feet off of the ground, how fast is the base of the ladder moving?

            POST Calc I:  same

            POST Calc II: none

Calculus III pre-test and corresponding questions on Calculus II and/or Calculus III post-test

(1)  Integrate.

            POST Calc II: Integrate.

            POST Calc III: If  and , find .

(2) Integrate.

* Will be included in the Calc I post-test and/or Calc II pre-test.

(3) Integrate.

             POST Calc II: Integrate.

            POST Calc III:  none

 (4) SET UP, but do not evaluate, the integration that will give the area of the region bounded by the graphs of  and .

            POST Calc II:  same

            POST Calc III: Let R be the region between the curves  and .  Set up, but do not evaluate,
            the iterated integral to find the surface area of the surface  over R.

(5) Find the indicated limit, if it exists.

            POST Calc II: Find the limit, if it exists.

            POST Calc III: none

(6) Find an equation of the plane that contains the point  and has normal vector .

            POST Calc II: Find the equation of the line passing through the points  and . 
            Write both the vector representation and symmetric equations.

            POST Calc III: Find the tangent plane to the surface given by  at the point .

 (7) Sketch the curve represented by the parametric equations, including the orientation. 

            POST Calc II: Sketch the cycloid  and set up but
            do not evaluate the integral for the arc length of on arch on the curve.

POST Calc III:  none