Name _________________________________ I.D. Number _______________________ Unit 6 Evaluation Evaluation 6 Precalculus: Analytic Geometry & Algebra (MTHH 043 059) This evaluation will cover the lessons in this unit. It is open book, meaning you can use your textbook, syllabus, and other course materials. You will need to understand, analyze, and apply the information you have learned in order to answer the questions correctly. To submit the evaluation by mail, follow the directions on your Enrollment Information Sheet. To take the evaluation online, access the online version of your course; use the navigation panel to access the prep page for this evaluation and follow the directions provided. You may use your calculator on this unit evaluation. Select the response that best completes the statement or answers the question. Use the following information to answer questions 1–8: Let z1  –3  4i, z2  2 – i, z3  –4i, z4  –24 10i _____ 1. z1  z2  a. b. c. d. _____ 2. z3 – z2  a. b. c. d. _____ 3. –1 + 5i –5 + 3i –1 + 3i –5 + 5i 2 – 5i –2 – 3i –2 – 5i 2 – 3i z4 · z2  a. b. c. d. Unit 6 Evaluation –58 – 4i –28 + 10i –38 + 44i –48 – 10i MTHH 043 _____ 4. z1  z2 a. –2 + 4i 2 4  i 5 5 2 11 c.   i 3 3 d. –2 + i b.  _____ 5.  z3  5  a. b. c. d. _____ 6. 1024 –1024i 1024i –1024 1  z3 1 i 4 b. 4i c. –4i 1 d.  i 4 a. _____ 7. z4  a. b. c. d. _____ 8. –24 – 10i 24 – 10i 24 + 10i –24 + 10i z1  a. b. c. d. Unit 6 Evaluation –1 1 –5 5 MTHH 043 _____ 9. Write the solution in the form a  bi . a. 7 i b. 7 i 7  c. 0  7i d. 0  7i _____ 10. Write the solution in the form a  bi . a. b. c. d.   4 3  9  6 + 6i –6 + 6i 6 – 6i –6 – 6i _____ 11. Find a polynomial function with real coefficients that has these numbers as roots: 4, 0, 3i. a. x 4 – 4x 3  9x 2 – 36x b. x3 – 4x 2 – 3x  1 2 c. x3 – 4x 2  3x – 12 d. x 4 – 4x 3 – 9x 2  36x _____ 12. Find the roots of this function: f  x   x2  2x  2 . a. 1  2 and  1  2 b. –1 + i and –1 – i c. 1  2i 2 and  1  2i 2 d. –1 + 2i and –1 – 2i _____ 13. Solve this function in factored form: f  x   x2  2x  2 . a. (x + 1 – i ) (x + 1 + i ) b.  x  1 i 2  x  1 i 2  c. (x – 1 + i ) (x – 1 – i ) d.  x  1 i 2  x  1 i 2  _____ 14. Find the roots of the function: g  x   x3  16x . a. b. c. d. Unit 6 Evaluation 0, 4i, –4i 0, –4, –4i 0, 4, 4i 0, 4, –4 MTHH 043 _____ 15. Solve this function in factored form: g  x   x3  16x . a. b. c. d. x ( x + 4) (x – 4) x (x + 4i ) (x – 4i) x (x + 4) (x + 4i) x (x – 4) (x – 4i) _____ 16. Find the first term of this sequence: an  1 3n . 1 3 b. 1 1 c. 9 d. –3 a. _____ 17. Find the first five terms of this sequence: an  1 3n . 1 , 3 1 b. , 3 1 1 1 1 , , , 9 27 81 243 1 1 1 1 , , , 6 9 12 15 1 1 1 1 c. 1, , , , 3 6 9 12 1 1 1 1 d. 1, , , , 3 9 27 81 a. _____ 18. Find the first term of this sequence: an  5  n2 . a. b. c. d. 5 4 3 1 _____ 19. Find the first five terms of this sequence: an  5  n2 . a. b. c. d. Unit 6 Evaluation 5, 4, 1, –4, –11 4, 1, –4, –11, –20 3, –1, –3, –5, –7 5, 3, –1, –3, –5 MTHH 043  2n  1   n  _____ 20. Find the first term of this sequence:  a. b. c. d. . 0 1 –1 2  2n  1 .  n  _____ 21. Find the first five terms of this sequence:  a. 0, 1, 2, 3, 4 5 8 11 14 , , , 2 3 4 5 3 5 7 c. 1, 1, , , 2 3 4 3 5 7 9 d. 1, , , , 2 3 4 5 b. 2, _____ 22. Find the third term of this sequence: a1  12, an1  a. b. c. d. an . n 1 4 6 2 1 _____ 23. Find the first five terms of this sequence: a1  12, an1  an . n 1 1 2 1 1 b. 12, 4, 1, , 5 30 1 1 c. 12, 6, 2, , 2 10 12 d. 12, 6, 4, 3, 5 a. 12, 12, 6, 2, 6 _____ 24. Find the numerical value of the finite sum: 5. k 1 a. b. c. d. Unit 6 Evaluation 75 25 30 105 MTHH 043 4 _____ 25. Find the numerical value of the finite sum:  k  1 k . k 1 a. b. c. d. 1114 75 700 90 _____ 26. Find the common difference of the arithmetic sequence: 6, 2, – 2, – 6, – 10, . . . a. b. c. d. –4 –3 3 4 _____ 27. Find a formula for the nth term of the arithmetic sequence: 6, 2, – 2, – 6, – 10, . . . a. b. c. d. 6 – 4n 6 – 2n 10 – 2n 10 – 4n _____ 28. Find the common ratio of the geometric sequence: 1 1 , , 2, 12, 72, . . . 18 3 1 6 2 b. 3 c. 6 3 d. 2 a. _____ 29. Find a formula for the nth term of the geometric sequence: a. 1 1 , , 2, 12, 72, . . . 18 3 1 n1 6 18 n 1 3 b. 27  2  1 1  c. 2 3n1 n 1 2 d. 12  3  Unit 6 Evaluation MTHH 043 _____ 30. Find the 4th term of the arithmetic sequence with a1  –6 and d  2 . a. –48 b.  3 2 c. 0 d. –12 _____ 31. Find a formula for the nth term of the arithmetic sequence with a1  –6 and d  2 . a. 2n – 8 b. – 2n – 4 c. – 6n d.  6 n _____ 32. For the geometric sequence with a1  5 and a5  405 , find the common ratio. 1 9 1 b. 3 c. 9 d. 3 a. _____ 33. For the geometric sequence with a1  5 and a5  405 , find the 5th partial sum. a. b. c. d. 605 455 1670 450 n _____ 34. 7 lim   . The limit x   8  a. b. c. d. _____ 35. = 0. does not exist. = 1. = 8. 3n  2 . The limit x n lim a. b. c. d. Unit 6 Evaluation = 0. does not exist. = 3. = 2. MTHH 043 _____ 36. lim 2n . The limit x  a. b. c. d. _____ 37. = 1. = – 1. does not exist. = 0. lim 2n2 x  n2 2 . The limit a. = 2. b. does not exist. c.   1 . 2 d. = 0. _____ 38. Find the sum of the geometric series: 5  5 5 5    ... . 3 9 27 15 2 b. –15 a. c. does not exist d. 10 3  k 1  1 _____ 39. Find the sum of the geometric series:  3   k 1  4  . 9 4 b. –12 a. c. does not exist d. 4 _____ 40. Evaluate the expression: 5! . a. b. c. d. Unit 6 Evaluation 120 720 24 15 MTHH 043 _____ 41. Evaluate the expression: a. b. c. d. 13 ! . 9! 1.4 24 17,160 46 8 _____ 42. Evaluate the expression:   . 3 a. b. c. d. 2.6 56 6720 336 _____ 43. Evaluate: C (12, 10) . a. b. c. d. 66 132 1.2 264 _____ 44. Use the Binomial Theorem to find the fifth term: (x 2  2)12 . a. 3960x8 b. 7920x16 c. 6930x14 d. 4950x10 _____ 45. Use the Binomial Theorem to find the term containing x 42 : (x3 – 3)16 . 42 a. 2160x b. 1620x 42 c. 1080x42 d. 540x 42 _____ 46. Ten persons compete in a race. In how many ways can the 1st, 2nd, and 3rd place awards be distributed, if only one person receives each award? What is the formula? a. b. c. d. Unit 6 Evaluation C (10, 3) P (10, 3) P (3, 10) C (3, 10) MTHH 043 _____ 47. Ten persons compete in a race. In how many ways can the 1st, 2nd, and 3rd place awards be distributed, if only one person receives each award? What is the answer? a. b. c. d. 2880 120 360 720 _____ 48. If 3 identical prizes are available for a contest with 50 entrants, in how many ways can the prizes be distributed? What is the formula? a. b. c. d. C (50, 3) C (3, 50) P (3, 50) P (50, 3) _____ 49. If 3 identical prizes are available for a contest with 50 entrants, in how many ways can the prizes be distributed? What is the answer? a. b. c. d. 3260 117,600 9800 19,600 6 _____ 50. Find the sum: 5. k 1 a. b. c. d. 5 + 10 + 15 + 20 + 25 + 30 5+5+5+5+5+5 5+5+5+5+5 5 + 10 + 15 + 20 + 25 Carefully check your answers on this evaluation and make any corrections you feel are necessary. When you are satisfied that you have answered the questions to the best of your ability, transfer your answers to an answer sheet. Please refer to the information sheet that came with your course materials. Unit 6 Evaluation MTHH 043
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