Algebra pretest for Calculus I

Answer the following questions and show your work. Allow 15 minutes for this pretest. A calculator should not be used in answering these questions.

If you are not able to answer 8 of these questions correctly, you may have difficulty with Calculus I.

1. Write as a single fraction

\frac{1}{x + 1} − \frac{1}{x − 1}.

2. If the two shorter sides of a right triangle are of length 1 and 2, what is the length of the hypotenuse?

3. Simplify by cancelling common factors.

\frac{cos x sin x + sin^{2} x}{sin^{2} x}.

4. Factor the numerator and denominator and cancel common factors.

\frac{x^{2} − 2x + 1}{x^{2} − x}.

5. Find the solution(s) of

x^{2} − x = 12.

Give exact answer(s).

6. Find the solution(s) of

x^{2} + x + 1 = 0.

Give exact answer(s).

7. Solve

\frac{1}{2}(x + 2) + \frac{1}{3}(x + 6) = 2.

8. Find the equation of the line that passes through (x, y) = (2, 4) and (x, y) = (−1, 9). Simplify to put the equation in the form y = mx + b.

9. If Lola runs 4 miles per hour for 20 minutes, how far will she run?

10. Write in the form x^{a}y^{b}.

xy^{2}(x^{2}y)^{2}