Test #3 is scheduled for Thursday, April 15, Day 26, and covers sections 7.1, 7.2, 7.5, 3.3, 3.4, 10.1-3 and earlier material. While the individual sections are not particularly difficult, this conglomeration of sections makes preparation for test #3 a formidable task. To this end, I have composed this preview. The problems here are only indicative of the sort of problems that will be on the test. I expect the test to have less than 12 problems, not all of which will be similar to these. Additional sources for test questions are homework (both in-class and regular), quizzes, and chapter examples. Your focus should be on how each problem is solved with the aim of understanding the underlying principles.

1. Use summation notation to express the sum, then calculate the value of this sum.
   4 + 12 + 36 + ... + 78,732.
   Solution
2. Find the n^th term of
   1. the geometric sequence, a₁ = 16, a₄ = 27/4, n = 5.
   2. the arithmetic sequence a₃ = 94, a₆ = 85.
   
   Solution
3. Write the first five terms of the geometric sequence. Determine the common ration and write the n^th term of the sequence as a function of n. a₁ = 12, a_k + 1 = (-3/2)a_k.
   Solution
4. Find the sums:

   .

   
   Solution
5. Write an expression for the most apparent n^th term of the sequence. (Assume n begins with 1.)
   1. 3, 7, 11, 15, 19, ...
   2. 5, 25, 125, 625, ...
   
   Solution
6. Find a polynomial to match the graph:
   
   Solution
7. Find a polynomial with integer coefficients that has the given zeros: 2, 2, 2, 4i, -4i.
   Solution
8. Given a = 4x³ - 9x + 8x² - 18, b = x + 2, find a/b.
   Solution
9. Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. f(x) = x⁴ + 4x² - 12.
   Solution
10. Find all solutions to the triangle given a = 12ft., b = 30ft., and A = 20^o.
    Solution
11. The course of a boat race starts at point A and proceeds 3.216 miles along S 52^o W to B, then to point C which is 5 miles due South of point A, and finally back to A. Approximate the total distance of the race course.
    
    Solution
12. Let z = (1 - 5i). Represent z graphically. Use DeMoivre's Theorem to find 2z⁸. Express the result in standard form.
    Solution, Top

by Jack Tompkins