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IMSA MI-4 Prob. Set #1 DUE: Friday, August 30 Fall 2013 General Directions for the Problem Sets: The purpose of these problem sets is threefold: a. To review, enhance and make connections with your past knowledge b. To work with current concepts being discussed in class in both familiar and new contexts. c. To preview ideas and techniques that will become important in the near future. In addition, some ideas will be introduced/explained in the problem sets. Usually the first time such an explanation is presented it will appear in a box. You should be sure to pay special attention to such boxed directions as you will be expected to be able to use that information from then on. Detailed - Correct - Neat & Legible Solutions are to be written on the answer sheets provided and turned in by the due date. You are permitted to obtain help from books, your teacher, other students, or the math department instructional aides in order to clarify anything that you don't understand, but the work must be your own. You are expected to solve problems marked with NC without your calculator. Be sure to review anything that you needed help with, in order to be sure that you can do it by yourself. You are ultimately held accountable for being able to perform any tasks related to the problems. The Problem Sets are to be completed along with your regular math class homework, which will be shorter and with a different emphasis than the Problem Sets. Budget your time to allow for you to get help when needed, before the due date. It does you no good to rush through these problems the night before they are due, because some of the concepts will be needed during the class lessons that meet before the due date. EACH Problem Set is due the following D-Day; early on C-Day. In addition to the written problem sets, you will also have problems on webwork (https://webwork.imsa.edu/webwork2) . Same rules apply for those problems as well. Instructions for webwork problems are provided for you (on moodle, student server or by your MI4 teacher). P.S. 1.1 IMSA MI-4 Prob. Set #1 DUE: Friday, August 30 Fall 2013 Note: NC designated the problem is to be done with no calculator or computer. NC NC (1) (2) A large wooden cube is formed by gluing together 512 small, congruent cubes and then it is painted red. After the paint is dry, the large cube is taken apart into the small cubes. How many of these cubes: (a) have 3 faces painted red? (b) have 2 faces painted red? (c) have 1 face painted red? (d) have no faces painted red? Let b 0 and let y log b (24) 2 log b (4) log b (54) . (a) NC Find b if y 4 . (b) Find y if b (3) For the unit circle at the right: 1 . 3 A C (a) Find the coordinates of point A. 1 (b) Find sin . 3 4 (c) Find sin . D (d) Find cos . B 3 (e) Find cos . 2 NC (4) Find values of a and b such that the sequence 960, 720, a, b is: (a) arithmetic (b) geometric (c) harmonic NC (5) Find the equation of a cubic polynomial with roots 2 / 3 and 1 4i containing the point ( 2,5) . NC (6) Let i 1 . Simplify the following, leaving your answer in the form a bi . (a) NC (7) (3i 1)3 (3i 1)3 (b) 3 5i (2 i ) 2 Find all solutions to the equation 3cot 2 2 x 1 0 . 3 P.S. 1.2 IMSA NC (8) DUE: Friday, August 30 Fall 2013 x 1 1 x 3x 2 2 (Be careful!) (b) log 5 ( x 2 20 x 200) 3 Let f (x) be a function whose set of zeroes is 4,0,1,5 . Find the set of zeroes of: (9) (a) NC Prob. Set #1 Solve each inequality: (a) NC MI-4 f(x+3) Let f ( x) (10) (b) f ( -2x ) (c) f ( |x| ) (d) f ( -x2 – 1 ) p ( x) be a rational function. q ( x) (a) The graph of f (x) has a hole at x = -2. Therefore there is a factor of in (b) The graph of f (x) has a bounce point at x = -3. Therefore there is a factor of . in . (c) The graph of f (x) has the line y x / 2 6 an asymptote. Therefore, the degree of p(x) is . NC (11) Identify each of the following problems as one that involves permutations, combinations, neither, or both. Then solve the problem. a. There are 14 girls on IMSA’s volleyball team. Only 7 of them can be on the court at one time. How many different teams can the coach put on the floor for the start of a game? b. How many different license plates consisting of 4 letters followed by 3 digits can be formed if the letters A and I are not used on the license plate? c. Suppose there are 19 students in your MI-4 section this semester. In how many different ways can four of them be chosen to present solutions to four different problems to the class? P.S. 1.3