**Mr. Hansen’s Scavenger Hunt
Questions**

March 13, 2000

(abbreviations may be viewed at www.modd.net/abbrevs.htm)

#### Form III (choose
any 2):

1. What is the formula for the surface area of a sphere?

2. What is Hero’s Formula for the area of a triangle in terms of the lengths
of the three sides?

3. What does equal? (Simplify your answer.)

**Form IV (choose any 2):**

4. The following is an erroneous proof that Circle the step in
which the error first appears, and write a concise explanation of why that step
does not follow from the one before it.

5. The following is an erroneous proof that –1 = 1. Circle the step in which
the error first appears, and write a concise explanation
of why that step does not follow from the one before it.

6. If *x* = –4.656, simplify the expression .

**Form V (do both, or substitute one of the Form IV problems for one of
these):**

7. What is the largest positive integer *n* for which there exists a general
formula for the roots of the polynomial equation *P*(*x*) = 0, where deg(*P*) = *n*?

8. In what year was the formula described in #7 first published?

#### Form VI (do both,
or substitute one of the Form IV or Form V problems for one of these):

9. For what values of *x*, if any, is the cube root of *x*^{3}
equal to the square root of *x*^{2}? State your answer as a
solution set.

10. Find the value of the following expression to the nearest power of ten
(show your work):