Expressions. Perform the Indicated Operation and Simplify

Math 125 Practice Final Exam pg.1

Math 125Practice Final Exam

Instructor: ButlerChapters 1 - 11

Expressions. Perform the indicated operation and simplify.

1. 2. 3.

4. 5. 6.

7. 8.

Simplify the complex fractions.

9. 10. 11.

Rationalize the denominators.

12. 13. 14.

Solving Equations. Solve for x.

15. 16. 17.

18. 19. 20.

21. 22. 23.

24. 25.

26. The width of a rectangle is 2 cm more than one-third of the length. The perimeter of the

rectangle is 44 cm. Find the length and width of the rectangle.

27. On a baseball diamond, the bases are 90 feet apart. Find to the nearest tenth of a foot the distance from home plate diagonally across the diamond to second base.

Functions.

28. Let . Find

29. Let .a). Find b) Find

30. Find the domain for the following.

a) b) c)

d) e) f)

31. Find the composition function and simplify your answer.

and

32. If and Then find and

33. Let . Find the inverse function

34. Let . Find the inverse function

35. If y is directly proportional to x, and y = 42 when x = 28 , find the value of y when x = 38.

Graphs. Label all points.

36. Graph and on the same set of axes.

37. Graph 38. Graph 39. Graph

40. Find the center and radius of the circle .

(First use completing the square to write it in standard form.)

41. Given the two points: and

a) Find the distance between the two points (simplify your radical, do not approximate)

b) Find the slope between the two points.

c) Write the equation of the line passing through the two points in slope-intercept form.

42. Given the two points: and

a) Find the distance between the two points. (simplify your radical, do not approximate)

b) Write the equation of the line passing through the two points in standard form.

43. Find the vertex of this parabola

44. Solve the system of equations using any method.

a) b)

45. Evaluate the determinant

Factor completely

46. 47.48.

49. 50.

51. Solve for 52. Solve the inequality

53. Solve 54. Solve

54. Simplify and express the answer using positive exponents

55. Find the equation of the line that is parallel to the line and contains the point .

56. Use the properties of Logarithms to expand as much as possible.

Evaluate log expressions where possible.

57. Evaluate58. Solve

59. Evaluate by using the change of base property. Approximate to 3 decimal places.

60. How long will it take $5000 to be worth $12,500 if it is invested at 7% compounded annually?

ANSWERS:

1. 2. 3. 4. 5. 6. 7.

8. 9. 10. 11. 12. 13.

14. 15. 16. empty set 17. 18. 19.

20. 21. 22. 23. 24. 25.

26. length = 15 cm, width = 7 cm 27. 127.3 feet 28. 29.a)

29.b) 30.a) 30.b) All positive Real Numbers 30.c) All Real Numbers

30.d) 30.e) 30.f) All positive Real Numbers 31.

32. 33.

34. 35. 37.

36.

38. 39.

40. center (-2,3) radius = 3 41. 42.

43. (1,7) 44.a) (7,0) 44.b) (-3,5) 45. 136 46. 47.

48. 49. 50. 51. or

52. 53. 54. 55. 55.

56. 57. 0 58. 38 59. 3.155 60. 13.5 years