Pretest for Calculus II

Answer the following ten elementary questions from Calculus I and algebra. Write your answer on a separate sheet of paper and show your work. You should not use a calculator to answer these questions. Allow 15 minutes for this pretest.

If you are not able to answer 8 of these questions correctly, you may have difficulty with Calculus II. Doing well on this quiz does not guarantee success in Calculus II.

1. Write as a single fraction and simplify.

\frac{x}{x − 2} + \frac{x}{x + 2}.

2. Solve for x. Give exact answers.

x^{2} + x − 3 = 0.

3. Determine if the following limit exists and if the limit exists, compute its value.

lim_{h→1} \frac{h − 1}{h^{2} − 1}.

4. Find the derivative, f′(x) if

f(x) = (2x + 1)^{5}.

5. Find the derivative f′(x) if

f(x) = cos(x^{2} + 1).

6. Find the derivative f′(x) if

f(x) = \frac{x + 1}{x − 1}.

Simplify your answer.

7. Evaluate the integral

∫_{0}^{1} x^{1/3} dx.

8. Evaluate the integral

∫_{0}^{π/2} cos(2x) dx.

9. Sketch the graph of f(t) = |t − 1| and use your graph to evaluate the integral

∫_{0}^{1} |t − 1| dt.

10. Suppose that we have 150 feet of fence which we use to make a rectangular pen. If we let x be one side of the pen, write a function A(x) which gives the area of the pen as a function of x.