Final Exam Review PDF AQA 2024

## Final Exam Review ### Assignment: Final Exam Review **11/22/24, 11:33 AM** **Student:** **Date:** **Instructor:** Michelle Armstrong **Course:** MTH 1108 Fall 2024 (1) 1. **Solve the equation.** 4 + 8n = 6n + 8 Select the correct choice below and fill in any answer boxes in your c...

## Final Exam Review ### Assignment: Final Exam Review **11/22/24, 11:33 AM** **Student:** **Date:** **Instructor:** Michelle Armstrong **Course:** MTH 1108 Fall 2024 (1) 1. **Solve the equation.** 4 + 8n = 6n + 8 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is (Simplify your answer.) B. There is no solution. 2. **Solve the equation.** 9x - (5x + 5) = 7x - 41 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is (Simplify your answer.) B. There is no solution. 3. **Solve the equation.** 3/7 * -x - 2 = -x 4x - 2 = 0 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is (Simplify your answer.) B. There is no solution. 4. **Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set.** -6x + 8 ≤ 38 Express the solution using set-builder notation. The solution set is {x | }. (Use integers or fractions for any numbers in the expression.) Express the solution using interval notation. The solution set is . (Use integers or fractions for any numbers in the expression.) Choose the correct graph of the inequality below. A. -10 -8 -6 -4 -2 0 2 B. -10 -8 -6 -4 -2 0 2 C. 0 2 4 6 8 10 D. -10 -8 -6 -4 -2 0 2 E. -10 -8 -6 -4 -2 0 2 F. -10 -8 -6 -4 -2 0 2 5. **Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set.** -4(x + 2) < 16 The solution is expressed in set notation as {x| }. The solution is expressed in interval notation as . Choose the correct graph of the solution set below. A. -10 -8 -6 -4 -2 0 2 4 6 8 10 B. -10 -8 -6 -4 -2 0 2 4 6 8 10 C. -10 -8 -6 -4 -2 0 2 4 6 8 10 D. -10 -8 -6 -4 -2 0 2 4 6 8 10 6. **Solve the inequality. Express your answer using set notation and interval notation. Graph the solution set.** 0.5x - 15 ≤ 6 The solution is expressed in set notation as {x| }. The solution is expressed in interval notation as . Choose the correct graph of the solution set below. A. -10 -8 -6 -4 -2 0 2 4 6 8 10 B. -10 -8 -6 -4 -2 0 2 4 6 8 10 C. -10 -8 -6 -4 -2 0 2 4 6 8 10 D. -10 -8 -6 -4 -2 0 2 4 6 8 10 7. **How much pure acid should be mixed with 6 gallons of a 60% acid solution in order to get a 70% acid solution?** To get a 70% acid solution, you need gallon(s) of pure acid. 8. **The manager of a coffee shop has one type of coffee that sells for $10 per pound and another type that sells for $13 per pound. The manager wishes to mix 90 pounds of the $13 coffee to get a mixture that will sell for $12 per pound. How many pounds of the $10 coffee should be used?** A. 22.5 lb B. 135 lb C. 45 lb D. 67.5 lb 9. **The manager of a candy shop sells chocolate covered peanuts for $5 per pound and chocolate covered cashews for $9 per pound. The manager wishes to mix 30 pounds of the cashews to get a cashew - peanut mixture that will sell for $8 per pound. How many pounds of peanuts should be used?** A. 40 lb B. 10 lb C. 20 lb D. 5 lb 10. **Verify that the values of the variables listed are solutions of the system of equations.** { 3x + y = 15 4x + 3y = 30 x = 3, y = 6 solution not a solution 11. **Verify that the values of the variables listed are solutions of the system of equations.** { 4x + y = -3 3x + 4y = 14 x = -2, y = -5 solution not a solution 12. **Find the distance d(P1,P2) between the points P₁ and P2.** P₁ = (3,3); P2 = (3, -5) A. -8 B. 8 C. 9 D. 7 13. **Find the midpoint of the line segment joining the points P₁ and P2.** P₁ = (-6,6); P2 = (-9,-6) A. (-3/2, 6) B. (3, 12) C. (-15, 0) D. (-15/2, 0) 14. **Find the midpoint of the line segment joining the points P₁ and P2.** P₁ = (7,1); P2 = (-16,-16) A. (9/2, 15/2) B. (9, 15) C. (-9, -15) D. (23/2, 17 /2) 15. **Determine whether the given point is on the graph of the equation.** Equation: x² - y² = 64 Point: (8, 8) No Yes 16. **List the intercepts and type(s) of symmetry, if any.** y² = x + 1 A. intercepts: (1,0), (0,1), (0, -1) symmetric with respect to x-axis B. intercepts: (0,1), (1,0), (-1,0) symmetric with respect to y-axis C. intercepts: (0,1), (1,0), (-1,0) symmetric with respect to y-axis D. intercepts: (-1,0), (0,1), (0, -1) symmetric with respect to x-axis 17. **List the intercepts and type(s) of symmetry, if any.** 16x² + y² = 16 A. intercepts: (1,0), (-1,0), (0,4), (0,-4) symmetric with respect to x-axis, y-axis, and origin B. intercepts: (1,0), (-1,0), (0,4), (0,-4) symmetric with respect to x-axis and y-axis C. intercepts: (4,0), (-4,0), (0,1), (0, -1) symmetric with respect to x-axis and y-axis D. intercepts: (4,0), (-4,0), (0,1), (0, -1) symmetric with respect to the origin 18. **Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.** x² + y - 1 = 0 A. y-axis B. x-axis C. origin D. x-axis, y-axis, origin E. none 19. **Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.** 16x² + y² = 16 A. origin B. x-axis C. y-axis D. x-axis, y-axis, origin E. none 20. **Determine whether the given points are on the graph of the equation.** Equation y² = x² + 256 Points (0,16), (16,0), (-16,0) Which points are on the graph of the equation y² = x² + 256? Select all that apply. A. (16,0) B. (0,16) C. (-16,0) D. None of the points are on the graph. 21. **Determine which of the given points are on the graph of the equation.** Equation: x² + y² = 4 Points: (2,0), (-2,2), (√2,√2) Which of these points are on the graph of the equation? Select all that apply. A. (2,0) B. (√2,√2) C. (-2,2) D. None of the points are on the graph. 22. **Plot the point. Then plot the point that is symmetric to it with respect to (a) the x-axis, (b) the y-axis, (c) the origin.** (-2, 3) Plot the point (-2,3). (a) Plot the point that is symmetric to (-2,3) with respect to the x-axis. (b) Plot the point that is symmetric to (-2,3) with respect to the y-axis. (c) Plot the point that is symmetric to (-2,3) with respect to the origin. 23. **Plot the point. Then plot the point that is symmetric to with respect to (a) the x-axis; (b) the y-axis; (c) the origin.** (6, -2) Plot the point (6, -2). (a) Plot the point that is symmetric to (6, -2) with respect to the x-axis. (b) Plot the point that is symmetric to (6, -2) with respect to the y-axis. (c) Plot the point that is symmetric to (6, -2) with respect to the origin. 24. **For the given equation, list the intercepts and test for symmetry.** x² + y - 144 = 0 What is/are the intercept(s)? Select the correct choice and, if necessary, fill in the answer box within your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts. Is the graph of the equation symmetric with respect to the x-axis? Yes No Is the graph of the equation symmetric with respect to the y-axis? Yes No Is the graph of the equation symmetric with respect to the origin? Yes No 25. **For the given equation, list the intercepts and test for symmetry.** y = x²-x-42 What is/are the intercept(s)? Select the correct choice and, if necessary, fill in the answer box within your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts. Is the graph of the equation symmetric with respect to the x-axis? Yes No Is the graph of the equation symmetric with respect to the y-axis? Yes No Is the graph of the equation symmetric with respect to the origin? Yes No 26. **Find the slope of the line.** A. -1 B. -7 C. 7 D. 1 27. **Find the slope of the line containing the two points.** (8, -5); (-8, -4) A. -16/1 B. 1/16 C. 1/16 D. 16 28. **Graph the line containing the point P and having slope m.** P = (4, -2); m = 6 A. B. C. D. 29. **Find the slope and y-intercept of the line.** x + y = -3 A. slope = 1; y-intercept = -3 B. slope = -1; y-intercept = -3 C. slope = 1; y-intercept = 3 D. slope = 0; y-intercept = -3 30. **Find the slope and y-intercept of the line.** 10x - 3y = 30 A. slope = 10/3; y-intercept = -10 B. slope = 10/3; y-intercept = 3 C. slope = 10/3; y-intercept = 30 D. slope = 10/3; y-intercept = 10 31. **Find an equation for the line with the given properties.** Slope undefined; containing the point (-4,4) A. y = 4 B. x = -4 C. y = - 4 D. x = 4 32. **Find the slope-intercept form of the equation of the line with the given properties.** Slope = 3; y-intercept = -10 A. y = -10x + 3 B. y = 3x + 10 C. y = 3x - 10 D. y = 10x - 3 33. **Find an equation for the line, in the indicated form, with the given properties.** Containing the points (-8, 0) and (3, 5); general form A. -8x - 2y = 14 B. 8x + 2y = 14 C. 5x - 11y = -40 D. -5x - 11y = -40 34. **Find an equation for the line with the given properties.** Parallel to the line -3x - y = 3; containing the point (0,0) A. y = -1/3x B. y = -3x C. y = 1/3x + 3 D. y = 1/3x 35. **Find an equation for the line with the given properties.** Perpendicular to the line y = 1/3x + 2; containing the point (2,-5) A. y = -3x - 1 B. y = -3x + 1 C. y =3x - 1 D. y = -1/3x - 11/3 36. **A point on a line and its slope are given. Find the point-slope form of the equation of the line.** P = (4, 2); m = 3/4 The point-slope form of the equation of the line is . (Use integers or fractions for any numbers in the equation.) 37. **A point on a line and its slope are given. Find the point-slope form of the equation of the line.** P = (-6, 4); m =0 The point-slope form of the equation of the line is . (Simplify your answer. Use integers or fractions for any numbers in the equation.) 38. **Find the slope and y-intercept of the given line. Then graph the line** y = 1/6x + 4 Determine the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is . (Type an integer or a simplified fraction.) B. The slope is undefined. Determine the y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept of the line is . (Type an integer or a simplified fraction.) B. There is no y-intercept. Use the graphing tool to graph the line. 39. **Find the slope and y-intercept of the line. Graph the line.** x + 6y = 30 Determine the slope. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is . (Type an integer or a simplified fraction.) B. The slope is undefined. Determine the y-intercept. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept of the line is . (Type an integer or a simplified fraction.) B. There is no y-intercept. Use the graphing tool to graph the line. 40. **Write the standard form of the equation of the circle with radius r and center (h,k).** r =12; (h,k) = (2, -2) A. (x-2)² + (y + 2)² = 12 B. (x - 2)² + (y + 2)² = 144 C. (x + 2)² + (y - 2)² = 144 D. (x + 2)² + (y - 2)² = 12 41. **Write the standard form of the equation of the circle with radius r and center (h,k).** r = √2; (h,k) = (0, 3) A. x² + (y - 3)² = 2 B. (x + 3)² + y² = 4 C. x² + (y + 3)² = 2 D. (x - 3)² + y² =4 42. **Find the center (h,k) and radius r of the circle with the given equation.** x² + y² - 14x + 8y + 65 = 81 A. (h,k) = (-7, 4); r = 81 B. (h,k) = (7, -4); r = 9 C. (h,k) = (4, -7); r = 81 D. (h, k) = (-4, 7); r = 9 43. **Find the center (h,k) and radius r of the circle with the given equation.** x² + y² - 10x -12y = 3 A. (h,k) = (-5, -6); r = 64 B. (h, k) = (5, 6); r = 8 C. (h,k) = (-6, -5); r = 64 D. (h,k) = (6, 5); r = 8 44. **Choose the equation of a circle with radius 8 and center (3, -5).** Choose the correct answer below. A. (x + 3)² + (y - 5)² = 8 B. (x -3)² + (y + 5)² = 8 C. (x - 3)² + (y + 5)² = 64 D. (x + 3)² + (y - 5)² = 64 45. **Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle.** r =1; (h,k) = (-1, 0) The standard form of the equation of this circle is . The general form of the equation of this circle is . (Simplify your answer.) Graph the circle. 46. **Write the standard form of the equation and the general form of the equation of the circle with radius r and center (h,k). Then graph the circle.** r = 10; (h,k) = (-6, 8) The standard form of the equation of this circle is . The general form of the equation of this circle is . (Simplify your answer.) Graph the circle. 47. **Find f(8) when f(x) = x² + 7x.** A. 113 B. √113 C. √713 D. √120 48. **Find - f(x) when f(x) = 3x² - 2x + 3.** A. 3x²- 2x - 3 B. -3x² + 2x - 3 C. -3x² + 2x +3 D. 3x² -2x + 3 49. **Find f(x - 1) when f(x) = 5x² - 3x + 3.** A. 5x² - 13x + 5 B. 5x² + 12x + 5 C. -13x² + 5x + 11 D. 5x² - 13x + 11 50. **Find f(2x) when f(x) = -3x² + 3x - 3.** A. -12x² + 6x - 3 B. -6x² + 6x - 3 C. -12x² + 6x - 6 D. -6x² + 6x - 6 51. **Find the domain of the function.** f(x) = √1/8-x A. {x|x= 8} B. {x|x ≤ 8} C. {x|x ≠ 8} D. {x|x ≥ 8} 52. **Find the domain of the function.** √(x-2) / x A. {x|x ≠ 2} B. {x|x > 2} C. {x|x ≥ 2} D. all real numbers 53. **Determine whether the relation represents a function. If it is a function, state the domain and range.** {(-3,11), (-2,6), (0,2), (2, 6), (4,18)} A. function domain: { -3, -2, 0, 2, 4} range: {11, 6, 2, 18} B. function domain: {11, 6, 2, 18} range: { -3, -2, 0, 2, 4} C. not a function 54. **Determine whether or not the equation defines y as a function of x.** y² = 9 - x² function not a function 55. **Determine whether or not the equation defines y as a function of x.** y² + x = 6 function not a function 56. **Determine whether or not the equation defines y as a function of x.** x - 5y = 9 function not a function 57. **For the given functions f and g, find f + g and state its domain.** f(x) = x - 6; g(x) = 7x² A. (f+g)(x) = 7x² - x + 6; all real numbers B. (f+g)(x) = 7x² + x - 6; {x|x=6} C. (f+g)(x) = -7x² + x - 6; all real numbers D. (f+g)(x) = 7x² + x - 6; all real numbers 58. **State the domain and range for the following relation. Then determine whether the relation represents a function.** |City |County| |:---|:---| |Ottawa |Canada| |Paris |France| |Beijing |China| |Lebu |Chile| |Arica | Choose the correct answer below. Domain: {Canada, France, China} Range: {Ottawa, Paris, Beijing} Domain: {Lebu, Arica} Range: {Chile} Domain: {Canada, France, China, Chile} Range: {Ottawa, Paris, Beijing, Lebu, Arica} Domain: {Ottawa, Paris, Beijing, Lebu, Arica} Range: {Canada, France, China, Chile} Does the relation represent a function? A. Yes, because each element in the first set corresponds to exactly one element in the second set. B. No, because an element in the second set corresponds to multiple elements in the first set. C. No, because each element in the first set does not correspond to exactly one element in the second set. D. Yes, because each element in the second set corresponds to exactly one element in the first set. 59. **State the domain and range for the following relation. Then determine whether the relation represents a function.** |Last name |First name| |:---|:---| |Hill |Kia| |Doe |John| |Marsha |Jan| |Brady |Jan| |Smith |Katie| Choose the correct answer. Domain: {John, Marsha, Jan, Katie, Kia} Range: {Doe, Brady, Smith, Hill} Domain: {Brady, Marsha, Jan} Range: {Doe, Smith, Hill, John, Katie, Kia} Domain: {Doe, Brady, Smith, Hill} Range: {John, Marsha, Jan, Katie, Kia} Domain: {Doe, Smith, Hill, John, Katie, Kia} Range: {Brady, Marsha, Jan} Does the relation represent a function? A. The relation in the figure is a function because each element in the domain corresponds to exactly one element in the range. B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain. C. The relation in the figure is not a function because the element "John" in the range corresponds to more than one element in the domain. D. The relation in the figure is not a function because the element "Doe" in the domain corresponds to more than one element in the range. 60. **Given the function f(x) = (x²-8) / (x-3), is the point (2,4) on the graph of f?** Yes No 61. **Match the graph to the function listed whose graph most resembles the one given.** A. square function B. cube root function C. square root function D. cube function 62. **Match the graph to the function listed whose graph most resembles the one given.** A. cube root function B. square root function C. cube function D. square function 63. **Match the graph to the function listed whose graph most resembles the one given.** A. absolute value function B. square function C. reciprocal function D. square root function 64. **Choose the function that matches the given graph.** The graph is a(n) (1) (1) absolute value function. square root function. cube function. constant function. square function. reciprocal function. identity function. cube root function. 65. **Match the correct function to the graph.** A. y= x-1 B. y= √ x-1 C. y = √x+1 D. y = √x 66. **Graph the function by starting with the graph of the basic function and the using the techniques of shifting, compressing, stretching, and/or reflecting.** f(x) = (x-5)² 67. **Graph the function by starting with the graph of the basic function and the using the techniques of shifting, compressing, stretching, and/or reflecting.** f(x) = (x + 4)² + 6 68. **Graph the function by starting with the graph of the basic function and the using the techniques of shifting, compressing, stretching, and/or reflecting.** f(x) = (x-2)³ - 2 69. **Graph the function by starting with the graph of the basic function and the using the techniques of shifting, compressing, stretching, and/or reflecting.** f(x) = √x - 4 - 5 70. **Graph the function by starting with the graph of the basic function and the using the techniques of shifting, compressing, stretching, and/or reflecting.** f(x) = - |x| 71. **Write the equation of a function that has the given characteristics.** The graph of y = √x, shifted 3 units to the right A. y = √x-3 B. y = √x + 3 C. y = √x - 3 D. y = √x + 3 72. **Write the equation that results in the desired transformation.** The graph of y = x², vertically stretched by a factor of 8 A. y = (x-8)² B. y = 8(x-8)x² C. y = 8x² D. y = -8x² 73. **Find the function that is finally graphed after the following transformations are applied to the graph of y = √x in the order listed. The graph is shifted up 4 units, reflected about the x-axis, and finally shifted left 8 units.** A. y = √x - 8 - 4 B. y = -√x - 8 + 4 C. y = √x + 8 +4 D. y = √x+ 8 - 4 74. **Find the function that is finally graphed after the following transformations are applied to the graph of y = √x in the order listed.** (1) Vertical stretch by a factor of 2 (2) Shift down 1 unit (3) Shift right 5 units 75. **Solve the equation by factoring.** x² - 81 = 0 A. {9, -9} B. {-9} C. {9} D. {81} 76. **Solve the equation by factoring.** x² - 5x + 6 = 0 A. {3, 2} B. {-3, -2} C. {-3, 2} D. {3, -2} 77. **Solve the equation by factoring.** 4x² +19x - 5 = 0 A. {1/4, -5} B. {-1/4, 5} C. {1/4, 5} D. {-1/4, -5} 78. **Solve the equation by completing the square.** x² + 12x + 27 = 0 A. {36, -9} B. {3, -1} C. {3, 9} D. {-3, -9} 79. **Solve the equation by completing the square.** x² + 4x - 3 = 0 A. {-4 -√7, -4 + √7} B. {2 + √7} C. {-2 -√7, -2 + √7} D. {-2 - 2√7, -2+ 2√7} 80. **Solve the equation by completing the square.** 7x² -2x - 4 = 0 A. {-1 -√29/7, -1 +√29/7} B. {1 - √29/7, 1 +√29/7} C. {-√29/7, √29/7} D. {-7 -√29/49, -7 +√29/49} 81. **Solve the following equation by completing the square.** x² + 2x = 3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { }. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution. 82. **Write the expression in the standard form a + bi.** (6 + 5i) - (-3 + i) A. 9 + 4i B. -9 - 4i C. 9 - 4i D. 3 + 6i 83. **Write the expression in the standard form a + bi.** (-5 - 8i)(3 + i) A. -7 + 19i B. 23 - 29i C. -7 - 29i D. -23 + 19i 84. **Write the expression in the standrad form a + bi.** (6 + 3i)(8 + 6i) A. 30 - 60i B. 18i² + 60i + 48 C. 66 - 12i D. 30 + 60i 85. **Write the