MAT 135 Midterm Review Dugopolski Sections 2.2,2.3,2.5,2.6,3.3,3.5,4.1,4.2,5.7,5.8,6.1,6.2,6.3
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1 Directions: Complete each problem and select the correct answer. NOTE: Not all topics on the midterm are represented in this review. For a complete set of review problems, please do the book-based midterm review. In addition, some of the review problems focus on the skills that are needed to complete the more complex problems that you will find on the midterm exam and are not representative of the actual exam problems. 1. Solve and write the solution in interval notation: ( ] ( ] ( ] ( ] 2. Given (, (, (, (, which of the following is true? Nothing can be determined from the given information. 3. What is the equation of the vertical line through the point (? 4. Solve and write the solution in interval notation: ] ] ( ] 5. A print shop charges plus per copy to print brochures. How many can be printed for? 6. Solve. 1
2 7. Assume that the model represents the cost, in hundreds of dollars, to produce items. How many items can be produced while keeping costs between and? 8. The table below represents the population of a city over time. What was the population of the city in? Year Population , , A local gym offers two plans for the use of its swimming pool. Plan A costs per month for unlimited use of the pool. Plan B costs per month, plus an additional per hour for the use of the pool. For what number of hours used per month will plan B be better? Plan B is better if the pool is used more than hours per month. Plan B is better if the pool is used fewer than hours per month. Plan B is better if the pool is used more than hours per month. Plan B is better if the pool is used fewer than hours per month. 10. Write the equation of the line that passes through ( and (. 11. Solve { } { } { } { } 12. Write the equation of a line passing through the point ( and parallel to. 2
3 13. If (, find (. ( ( ( ( 14. What is the equation of a line with an -intercept at and a -intercept at? 15. Solve and write the solution in interval notation:. ] ( ( 16. Solve and write the solution in interval notation:. ( ] ] ] 17. Solve for. 3
4 18. Solve. 19. What is true of two parallel lines? The product of the slopes of the two lines must equal The two lines have the same -intercept. The two lines always have the same slope. The two lines must go through the origin. 20. What is the -intercept of? ( ( ( ( 21. What is NOT true about the graph below? You may assume that each tick mark represents one unit. y x The slope of the line is negative. The -intercept of the graph is (. The point ( is on the graph. The -intercept of the graph is ( 4
5 22. Solve for. ( 23. If (, find ( 24. What are the domain and range of the data in the table at the below? { } { } { } { } { } { } This data do not represent a function so there is no domain and range. 25. Is the following relation a function: {( ( ( ( ( }? This is not a function This is a function. 26. Find the domain of (. ( ] ( Given (, which of the following is a factor? ( ( ( ( 5
6 28. A garage door measures feet by feet, where is the length of the sides of the square windows in the door. Write a polynomial expression that represents the area of the garage door. 29. Solve: {. ( ( ( 30. Which is a factor of ( ( ( ( 31. Factor completely:. ( ( ( ( ( ( ( ( 32. Factor completely: ( ( ( ( ( ( ( 33. Factor completely: ( ( ( ( ( ( ( ( 34. A vendor sells hot dogs and potato chips. A customer buys hot dogs and bags of potato chips for. Another customer buys hot dogs and bags of potato chips for. What is the cost of each item? It costs for a hot dog and for a bag of chips. It costs for a hot dog and for a bag of chips. It costs for a hot dog and for a bag of chips. It costs for a hot dog and for a bag of chips. 6
7 35. Solve: {. ( ) ( ) ( ) 36. Solve: { } { } { } { } 37. Which of the following statements is not true? ( ( ( ( ( ( 38. Evaluate ( if ( ( ( ( ( 39. A room is feet longer than it is wide. Its area is square feet. What are the dimensions of the room? The room is feet wide and feet long. The room is feet wide and feet long. The room is feet long and feet wide. The room is feet long and feet wide. 40. Divide and simplify:. 7
8 41. If ( and (, find ( (. ( ( 42. If ( and (, find ( ( ( ( ( ( ( ( 43. Divide and simplify: 44. What value(s) make the expression undefined:? 8
9 45. Express the perimeter of the triangle as a single rational expression. 46. Multiply and simplify:. ( ( 47. What is true of the function (? It is defined on ( (. It is defined on ( ( (. It is defined on ( (. It is defined for all real numbers. 9
10 48. Subtract and simplify:. ( ( ( ( ( ( ( 49. Simplify:. 50. Identify a factor of ( ( ( ( 51. Identify a factor of:. ( ( ( ( 10
11 Answer Key for Midterm Review 1. B 2. B 3. A 4. C 5. A 6. A 7. C 8. D 9. B 10. D 11. A 12. B 13. D 14. B 15. C 16. B 17. B 18. D 19. C 20. B 21. D 22. B 23. A 24. A 25. A 26. A 27. B 28. A 29. C 30. B 31. A 32. A 33. C 34. D 35. D 36. A 37. C 38. A 39. D 40. A 41. D 42. D 43. A 44. A 45. A 46. D 47. B 48. D 49. C 50. C 51. D 11
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