Course Name: Precalculus: Analytic Geometry and Algebra Student: Aguistin Spaan Course ID: MTHH043059 ID: G87557040 Submittal: 59 Progress Test 3 Progress Test 3 (Evaluation 59) covers the course materials that were assigned in Units 5 and 6. Although the progress test is similar in style to the unit evaluations, the progress test is a closed-book, proctored test. You may not have access to notes or any of the course materials while you are taking the test. You may use your graphing calculator on this test. ____ 1. Given: logb2 = .4, logb3 = .5, logb5 = .6. Use properties of logarithms to find the following value: logb0.4 = a. b. c. d. ____ 2. ____ 3. .6 –.04 –.84 –0.2 Solve for x: log8(x2 – 8) = 0 a. ±2 b. c. 3 2 d. ±3 Let z1 = 2 + 3i and z2 = 1 – i. Find a. b. – 2 – 3i c. d. 2 – 3i – 2 + 3i a. b. c. =1 does not exist. d. =0 . ____ 4. ____ 5. Use this system to find the value of the y: a. b. c. d. 4 3 –3 –4 . ____ 6. Which shows the graphs of the equations: ? a. b. c. d. ____ 7. Use a geometric series to find the rational number represented by the decimal a. b. c. d. ____ 8. .01 .1 48 .48 Write 2 loga6 + loga3 as a single logarithm. a. b. c. d. .r= ____ 9. Solve for x: a. b. c. d. 1 –1 ____ 10. Use the Binomial Theorem to find the fourth term of the expression (x3 – 4)6. ____ 11. a. 240x12 b. –240x12 c. –1280x9 d. 1280x9 Let z1 = 3 – 4i and z2 = −1 – i. Find . a. b. c. d. ____ 12. a. b. c. d. does not exist. =1 =0 ____ 13. Given: logb2 = .4, logb3 = .5, logb5 = .6. Use properties of logarithms to find the following value: logb75 = a. b. c. d. .86 1.7 .41 .6 ____ 14. Find the solution set of this equation: a. b. c. d. ____ 15. 1 2 3 2, 1 Solve the system: . What is one solution? a. b. c. d. ____ 16. Find the value of r for this series: a. b. c. 3 d. ____ 17. Use the Binomial Theorem to expand the expression (3x + 2)4 . a. 81x4 + 216x3 + 144x2 + 72x + 16 b. 81x4 + 108x3 + 144x2 + 96x + 16 c. 81x4 + 108x3 + 216x2 + 72x + 16 d. 81x4 + 216x3 + 216x2 + 96x + 16 ____ 18. Evaluate the given expression: a. b. c. d. 3024 90 1512 72 ____ 19. Use this system to find the value of the determinant: a. b. c. d. . −18 18 6 −6 ____ 20. Evaluate the determinant a. b. c. d. . 0 36 138 −36 ____ 21. If 3 books are chosen from a list of 10, how many ways can a student choose a book if the books are all different? a. b. c. d. ____ 22. What are the roots of f(x) = x4 – 81? a. b. c. d. 3, 3i 3i, −3i 3, −3, 3i, −3i −3, 3 ____ 23. The perimeter of a triangle is 26 inches. If the longest side is twice as long as the shortest side, and the third side is 2 inches longer than the shortest side. Which algebraic equation would best represent the side lengths of the triangle? a. b. c. d. x + 2y + z + 2 = 26 x + x + 2 + 2x = 26 x + 2y + 2z = 26 x + 2x + 3x = 26 ____ 24. Use the elimination method to find the solution for y: a. b. c. d. 0 1 2 3 ____ 25. Use a geometric series to find the rational number represented by the decimal . What does the rational number equal? a. b. c. d. ____ 26. Use the Binomial Theorem to find the coefficient of the fourth term: (x3 – 4)6. a. b. c. d. ____ 27. C (6, 4) C (5, 4) C (6, 3) C (5, 3) Solve this system: a. b. c. d. . What is one solution? (4, 0) (4, 2) (4, 4) (4, 16 ____ 28. Find the value of log2 . a. b. c. d. –2 2 ____ 29. The sum of three numbers is 35. The second number is twice the first, and the third number is twice the second. If the three numbers are x, y, and z in that order, then two equations can be written as a. b. c. d. x = 2y and z = 2x. y = 2x and z = 2y. x = 2y and z = 4x. y = 2x and z = 2x. ____ 30. Write f(x) = x3 + 25x in factored form. f(x) = a. b. c. d. x (x + 5) (x – 5) x (x + 5i) (x – 5i) (x + 25) (x + i) (x – i) (x + 25i) (x + 1) (x – 1) ____ 31. Given g(x) = (2)2x + 1; find g(−1). a. b. c. 2 1 d. ____ 32. Solve this system by using a matrix. a. b. c. d. x= −1, y = 1 x = 1, y = −1 x = −1, y = 0 x = 0, y = −1 ____ 33. Let z1 = −1 – 3i and z2 = 4 + 5i. Find z1 + z2. a. b. c. d. −2 + 2i 3 – 8i −3 + 8i 3 + 2i ____ 34. Find the first 5 terms of this sequence: a. b. c. d. . 0, 2, 4, 8, 16 2, 4, 6, 8, 10 2, 2, 2, 2, 2 2, 4, 8, 16, 32 ____ 35. Use the elimination method to find the solution for z: a. b. c. d. −1 no solution infinite solutions 0 ____ 36. Find the sum of this series: a. b. c. d. ____ 37. Find a polynomial function with real coefficients that has 1 and 4i as it roots. a. b. c. d. ____ 38. x³ – x² – 16x + 16 x³ – x² + 16x – 16 x³ – x² – 16x – 16 x³ + x² + 16x + 16 Use this system to find the value of the x: a. b. c. d. . –3 –4 3 4 ____ 39. The perimeter of a triangle is 26 inches. If the longest side is twice as long as the shortest side, and the third side is 2 inches longer than the shortest side. What are the three sides? a. b. c. d. 4, 10, 12 4, 8, 14 6, 8, 10 6, 8, 12 ____ 40. If 3 books are chosen from a list of 10, how many ways can a student choose a book if the books are all different? a. b. c. d. ____ 41. Which is the graph of the system: a. b. c. d. ____ 42. Solve for x: log x a. b. –3 c. d. 3 = −2 ____ 43. Find the solution set of this linear system: a. b. c. d. (2, 0) (0, 2) no solution (0, −2) ? ____ 44. Let z1 = −1 – 3i and z2 = 4 + 5i. Find | z2 |. a. b. c. d. ____ 45. 4 – 5i –4 – 5i –4 + 5i Use this system to find the determinant: . a. b. c. d. ____ 46. Find the common difference in the arithmetic sequence: 1, 7, 13, 19, 25, 31, … a. b. c. d. ____ 47. 6 −6 5 13 Find the value of the sum a. b. c. d. . 20 1024 30 384 ____ 48. Use the elimination method to find the solution for x: a. b. c. d. 3 2 1 0 ____ 49. Solve for x: 162x = 8x + 1 a. b. c. d. 5 3 . ____ 50. Find the value of a for this series: a. b. c. d. 3 Carefully review your answers on this progress test 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 the online test submission page in the presence of your proctor. The University of Nebraska is an equal opportunity educator and employer. ©2018, The Board of Regents of the University of Nebraska. All rights reserved.
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