Los Angeles Mission College



Fall 2012 Math 125 Practice Final

1. Solve [pic]

You need to multiply by the LCD to clear the fractions. The LCD is 24.

[pic]

2. John bought a briefcase at a 30% discount sale for $75. What is the original price of the briefcase?

3. A total of $4000 was invested, part of it at 5% interest and the remainder at 6%. If the total yearly interest amounted to $230, how much was invested at each rate? Use a system of linear equations to solve.

We did this problem in class.

4. A car leaves a town at 60 miles per hour. How long will it take a second car, traveling at 75 miles per hour, to catch the first car if it leaves 1 hour later?

5. Solve [pic] for [pic]

6. Solve [pic]

We did this problem in class.

7. Solve [pic]

We did this problem in class.

8. Solve[pic]. Express your answer in interval notation.

9. Find the product [pic]

10. Factor completely [pic]

11. Factor [pic]-( there was a mistake here…it’s 64 not 16

12. Solve [pic]

13. Solve [pic]

14. Solve [pic]

This is a quadratic equation…How would you solve it…. You can try to factor, complete the square, or use the quadratic formula

15. Solve [pic]

We went over this in class. To solve distribute and take 182 to the other side

[pic]-> I would use the quadratic formula to solve…

For 16- 20, perform the indicated operations, and express your answer in simplest form.

16. [pic] -> cancel

17. [pic]

18. [pic]

Did in class

19. [pic]

Did in class

20. [pic]

21. Simplify the complex fraction [pic]

Did in class

For 22 to 24, solve the equation.

22. [pic]

You need to multiply by the LCD to clear the fraction: LCD=(x-2)(x-1)….

23. [pic]

Multiply by the LCD=3x to clear the fraction [pic]

24. [pic]

25. A car travels 180 miles in the same time that a truck travels 120 miles. If the car’s speed is 20 miles per hour faster than the truck’s, find the car’s speed and the truck’s speed.

26. John can paint the house in 3 hours. His friend Blake can paint the same house in 7 hours. How long will it take them to paint the house if they work together?

27. Evaluate the numerical expression [pic]

For 12 and 13, simplify and express the final result using positive exponents.

28. [pic]

Solution: [pic]

29. [pic]

30. Express the radical in simplest radical form. Assume the variable represent positive real numbers[pic]

31. Subtract [pic][pic]

32. Rationalize the denominator [pic]

Multiply the numerator and the denominator by the conjugate of the denominator which is [pic]: [pic]

For 33 and 34, solve the equation

33. [pic]

Did in class

34. [pic]

Isolate one radical on one side of the equation:[pic]

Now square both sides and solve…

35. Simplify [pic]

[pic]

36. Simplify [pic]

For 37 - 38, write the expression using positive rational exponents.

37. [pic]

38. [pic]

39. Simplify and express the final result using positive exponents

[pic]

40. perform the indicated operation and express the answer in simplest radical form [pic]

For 41 -46 perform the indicated operations and simplify : Review also dividing complex fractions.

41. [pic]

42. [pic]

43. [pic]

44. [pic]

45. [pic]

46. [pic]

47. Solve [pic]

Done in class. The best way to solve this equation is by using the square root property: [pic]

48. Solve by completing the square [pic]

49. Solve [pic]

Done in class on Thursday

50. Graph [pic]

51. Find the slope and the y-intercept. Graph [pic]

52. Graph the line that has the indicated slope and contains the indicated point [pic]

53. Find the equation of the line that is perpendicular to the line [pic]and contains the point (3, -4). Express the equation in standard form.

Done in class on Thursday

54. The Rent-Me Car Rental charges $35 per day plus $0.32 per mile to rent a car. Determine a linear function that can be used to calculate daily car rentals. Then use that function to determine the cost of renting a car for a day and driving 150 miles.

Equation: [pic]

[pic]

We did many of these problems in class. We used points in the examples in class.

55. On a 335- mile car trip, John averaged 5 miles per hour faster for the first 200 miles than he did for the last 135 miles. The entire trip took 7 hours. Find the rate for the first 200 miles.

56. A pharmacist stocks a 10% solution of acid and a 22% solution of acid. How many liters of each should be mixed to produce 20 liters of an 18% solution of acid?

57. Specify the domain

a) [pic]

b) [pic]

58. If [pic], find [pic]

We have done problems like these a lot in class. Make sure you review them. The Solution:

[pic]

[pic]

[pic]

59. If [pic] and [pic], determine [pic]

Solution: [pic]

60. If [pic] and [pic], find [pic]

61. Find the inverse of the given function [pic]

Solution: [pic]

[pic]

So [pic]

62. If y varies directly as x, and if y=28 when x=5, find y when x=16

For 63 and 64, use the concepts of translation and/or reflection to describe how the curve can be obtained. What is the basic function? state each translation clearly. Graph

63. [pic]

This is a parabola: basic function is [pic]

Horizontal shift: moved to the left 3 units

Vertical Shift: moved down 3 units

Reflection: about the x-axis

64. [pic]

This is a parabola: basic function is [pic]

Horizontal shift: moved to the right 3 units

Vertical Shift: moved down 2 units

No Reflection about the x-axis

65. Evaluate the expression [pic]

66. Evaluate the expression [pic]

67. Solve the equation without using your calculator [pic]

Did problems like these on Wednesday: Take the log on both sides then bring down the variable: [pic]

68. Solve the equation [pic]

Did problems like these on Wednesday. Go over the group activity we did.

69. Solve the equation [pic]

70. Solve the equation [pic]

71. Expand [pic]

72. Suppose that $3000 is invested at 5% interest compounded quarterly. How much money has accumulated at the end of 10 years?

P=3000, r=0.05, n=4, t=4,….Use the formula: [pic]

[pic]

We did many of these problems. In this problem, you are asked to find A. In other problems, they give you A. For example, they might tell you Amount after 3 years is 2500. So A=2500 and t=3. Review these problems.

For 73 and 74, solve the equation without using your calculator

73. [pic]

Did problems like these on Wednesday

74. [pic]

Did problems like these on Wednesday

75. The number of bacteria present in a certain culture after t hours is given by [pic], where [pic]represents the initial number of bacteria. How long will it take 400 bacteria to increase to 2400 bacteria? Express your answer to the nearest tenth of an hour. Do we have exponential growth or decay? Justify your answer.

For 76 and 77, find the vertex of the parabola. State whether the parabola opens upward or downward. Do you have x-intercepts? y-intercept?

76. [pic]

77. [pic]

78. Write the equation of the circle center [pic] and radius [pic]

For problems 79-82, name the graph of the equation. Explain your reasoning. Then graph.

79. [pic]

80. [pic]

Did problems like these on Monday. That is a circle…Now complete the square so you know the center and the radius of the circle.

When you complete the square you get: [pic]

The center is (2,-1) and the radius is 3. Now you can graph.

81. [pic]

82. [pic]

83. Solve the system using the method of your choice (you should know how to solve the system using all 3 methods) [pic]

84. The perimeter of a rectangle is 90 inches. The length of the rectangle is 5 inches less than the width of the rectangle. Find the dimensions of the rectangle.

You can set a system of linear equations:

[pic] -> the perimeter is 90 inches

[pic]

You can solve using the substitution method.

85. Graph the solution set for the system [pic]

We reviewed this on Monday. Graph each line, in this case it’s going to be dashed lines not solid lines. Shade the region for each line. The common shaded region is the solution. Make sure you clearly state that in the final.

86. Solve the system of equations [pic]

For 87-89, solve each system. Then Graph.

87. [pic]

88. [pic]

This is a system of nonlinear equations. You can use the substitution method. From equation 2, you get: [pic]

Substitute x-2 for y in the first equation: [pic]

You get a quadratic equation. Notice it does not factor. I would use the quadratic formula.

89. [pic]

We also did this on Monday. You can use the substitution method or the elimination method.

It’s best to use the elimination method. You can multiply the second equation by -1 ( in order to clear the variable y)

[pic] Adding the 2 equations you will get [pic]

When x=2, solve for y: Using the original second equation:

[pic] So one of the solution is (2,0)

When x=-2, solve for y…….That would be your second solution

90. Divide [pic]by [pic]

We did this in class on Thursday. You will need to use long division. Remember one of the terms is missing: [pic]

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