12/11/2018 Algebra II - Semester 1 Review

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1 Name: Semester Review - Study Guide Score: 72 / 73 points (99%) Algebra II - Semester 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Name the property of real numbers illustrated by the equation. C 1. a. Closure Property b. Commutative Property of Multiplication c. Commutative Property of Addition d. Associative Property of Addition B C Which algebraic expression models the given word phrase? 2. 5 times the sum of a and b 3. You start with $15 and save $8 each week. What algebraic expression models the total amount you save? B 4. Evaluate the expression for the given value of the variable(s). a. b. c. d. B 5. ; x = 3 a. 3 b. 1 c. 11 d. 17 Combine like terms. What is a simpler form of each expression? B 6. a. b. c. d. B 7. Solve the equation. a. b. c. d. B 8. a. 14, 4 c. 14, 14 b. 4, 14 d. 4, 4 C 9. a. 8, 8 c. 0, 8 b. 8, 0 d. 0, 0 Solve the equation or formula for the indicated variable. D 10., for U a. b. c. d. Solve the inequality. Graph the solution set. C 11. 2r 9 ³ 6 a. r c. r ³ b. r ³ d. r Solve the compound inequality. Graph the solution. file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 1/10

2 A 12. 4x 5 < 17 or 5x + 6 > 31 a. x < 3 or x > 5 c. x < 3 or x > b. x < or x > d. x < or x > 5 B 13. Solve the absolute value equation. Graph the solution. a. x = or x = c. x = or x = b. x = or x = d. x = or x = Solve the equation. Check for extraneous solutions. C 14. ; a. x = or x = c. x = b. x = d. x = or x = A 15. Is the relation a function? a. yes b. no A 16. Use the vertical-line test to determine which graph represents a function. For each function, what is the output of the given input? B 17. For,. a. 2 b. 14 c. 16 d. 16 B 18. Specialty t-shirts are being sold online for $35 plus a one-time handling fee of $1.75. The total cost is a function of the number of t-shirts bought. What function rule models the cost of the t-shirts? Evaluate the function for 6 t-shirts. a. ; $ c. ; $45.5 b. ; $ d. ; $45.5 file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 2/10

3 What is the slope of the line that passes through the given points? A 19. ( 12, 12) and (2, 4) What is an equation of the line in slope intercept form? D 20. m = 10 and the y-intercept is (0, 7) C 21. Write the equation in slope-intercept form. What are the slope and y-intercept? a. ; c. ; slope: ; y-intercept: slope: ; y-intercept: b. ; d. slope: ; y-intercept: slope: ; y-intercept: B 22. What is the graph of the equation? Write an equation of the line, in point-slope form, that passes through the two given points. A 23. points:, What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? B 24. point: ; slope: A 25. What is the equation of the given line in standard form? Use integer coefficients. file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 3/10

4 C 26. What are the intercepts of the equation? Graph the equation. a. x-intercept: ( 4, 0) y-intercept: (0, 4) c. x-intercept: (4, 0) y-intercept: (0, 4) b. x-intercept: ( 4, 0) y-intercept: (0, 4) d. x-intercept: (4, 0) y-intercept: (0, 4) What is the equation of the line in slope-intercept form? B 27. the line parallel to through D 28. the line perpendicular to through What transformations change the graph of f(x) to the graph of g(x)? A 29. ; a. The graph of is the graph of translated to the right 9 units and down 6 units. b. The graph of is the graph of translated to the left 9 units and up 6 units. c. The graph of is the graph of translated to the down 9 units and right 6 units. d. The graph of is the graph of translated to the up 9 units and left 6 units. What is the graph of each inequality? B 30. 2x + 2y Solve the system by graphing. file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 4/10

5 D a. c. b. ( 2, 2) d. (2, 2) ( 2, 2) ( 2, 2) A 32. D 33. D 34. Solve the system by substitution. a. ( 5, 1) c. (1, 5) b. ( 1, 5) d. (5, 1) Solve the system using elimination. a. ( 2, 1) c. ( 1, 2) b. (2, 1) d. (1, 2) What are the solutions of the following systems? a. (5, 6) c. ( 5, 6) b. no solutions d. infinitely many solutions D 35. The length of a rectangle is 7.8 cm more than 4 times the width. If the perimeter of the rectangle is 94.6 cm, what are its dimensions? a. length = 7.9 cm; width = 39.4 cm c. length = 39.4 cm; width = 15.7 cm b. length = 23.8 cm; width = 15.7 cm d. length = 39.4 cm; width = 7.9 cm D 36. Solve the system of inequalities by graphing. What is the solution of the system? file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 5/10

6 What is the solution of the system? B 37. a. (2, 4) c. (2, 4) b. ( 2, 4) d. (4, 2) What is the graph of the function? A C 39. Suppose a parabola has vertex ( 8, 7) and also passes through the point ( 7, 4). Write the equation of the parabola in vertex form. What is the graph of the equation? D 40. C 41. What is the vertex form of the equation? file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 6/10

7 B 42. What is the expression in factored form? B 43. What is the expression in factored form? D 44. C 45. What are the solutions of the quadratic equation? A 46. a. 4, 7 c. 4, 7 b. 4, 7 d. 4, 7 D 47. = 0 a., c. 6, 3 b. 6, d. 6, D 48. = 0 a. 2, 4 c., b. 2, d. 2, B 49. What is the solution of each equation? b., d. B 50. a., c., b., d., B 51. The lengths of the sides of a rectangular window have the ratio 1.2 to 1. The area of the window is 1920 square inches. What are the dimensions of the window? a. 40 inches by 57.6 inches c. 40 inches by 80 inches b. 40 inches by 48 inches d inches by inches What value completes the square for the expression? D 52. a. 64 c. b. 8 d. POINTS: 0 / 1 Solve the quadratic equation by completing the square. D file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 7/10

8 A 54. D 55. Use the Quadratic Formula to solve the equation. C 56. B 57. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 155 square yards. The situation is modeled by the equation. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. a. 320 yards c yards b yards d yards What is the number of real solutions? C 58. a. one solution c. two solutions b. no real solutions d. cannot be determined B 59. a. one real solution c. no real solutions b. two real solutions d. cannot be determined A 60. a. one solution c. two solutions b. no real solutions d. cannot be determined Simplify the number using the imaginary unit i. C 61. a. 12 c. 12i 144i B 62. C 63. C 64. B 65. D 66. Simplify the expression. file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 8/10

9 D 67. What are the solutions? A 68. a. i, i c. i, i b. i, i d., A 69. C 70. Identify the vertex and the axis of symmetry of the graph of the function. a. vertex: ( 2, 4); b. vertex: (2, 4); c. vertex: ( 2, 4); d. vertex: (2, 4); A 71. Which is the graph of? C 72. What steps transform the graph of to? a. translate 3 units to the right, translate down 5 units b. translate 3 units to the left, translate up 5 units c. reflect across the x-axis, translate 3 units to the left, translate up 5 units d. reflect across the x-axis, translate 3 units to the right, translate down 5 units What are the vertex and the axis of symmetry of the equation? B 73. a. vertex: ( 4, 8) b. vertex: ( 4, 8) c. vertex: ( 4, 8) d. vertex: ( 4, 8) file:///f:/ /alg.%20ii/1st%20quarter/semeser_1_study_guide.htm 9/10

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