MS Word Version of this document....

Simplify:

1.

2.

3. Multiply:

Factor:

4.

5.

6.

Factor:

7.

Solve:

8. = 25

9. = 15

10. Solve by completing the square: = 0

11. Write the expression in the form a + bi:

12. Simplify:

13. Write the standard form of the equation of the line passing through the point (1, –5) and perpendicular to the line .

14. Determine the domain and range:

15. Graph the parabola and find the vertex:

16. Determine the domain of the function

17. If f(x) = and g(x) = , find .

18.

19. ³ 18

Graph:

20.

21.

22. Solve: =

23. Write the equation in logarithmic form.

24. Write the equation in exponential form.

25. Evaluate:

26. Use the rules for logarithms of products, quotients, and powers to write as the sum or difference of logarithms:

27. Solve:

28. f(x) = and g(x) = , find .

29. A radioactive substance decays so that the amount A present at time t (years) is Find the half-life (time for half to decay) of this substance.

30. Find all real solutions of the following equation:

31. Graph f(x) =

32. Use synthetic division to find if .

33. Use the Remainder Theorem to find P(–4) if

34. List all of the potential rational zeros of the polynomial function. Do not attempt to find the zeros.

35. Use the Intermediate Value Theorem to show that the graph of the function has an x-intercept in the given interval. Approximate the x-intercept correct to two places.
;

36. Find a third-degree polynomial with real coefficients and with zeros –2 and 4 + i.

37. Find all the real and complex zeros of the polynomial .

Should be able to do this one, but probably too time-consuming for test. But synthetic division to break down a polynomial, given one of its zeros is well within the realm.

38. Find the rational roots of f . List any irrational roots correct to two decimal places.

f(x) =

Rational zeros and Descartes rule of signs are fair game.

39. Graph the parabola:

40. Graph:

41. Find the equation of the circle with center (5, –2) and radius of 2.

42. Find the vertex of the parabola y = .

43. Identify the following curve: =

44. Find the center and radius of the circle with the following equation:

45. Graph:

46.

47. If A = and B = , find .

48. Find the inverse of the matrix (if it exists) .

49. Write the augmented matrix for the system of equations.

50. Use matrices to solve the following system

51. Find the common difference for the arithmetic sequence: –8, 21, 50, ...

52. Give the first four terms of the arithmetic sequence for which = –38 and d = 3.

53. Write in summation notation:

54. – + – +

55. Write as an indicated sum:

56. Find the common ratio: , , , . . .

57. Find the sum of the geometric series: , , , , . . .

58. Let represent the statement:
4 + 12 + 20 + + =

Use the Principle of Mathematical Induction to show that is true for all integers n, .

59. Multiply:

This type will be bonus.

60. Evaluate: 7!

61. Prestige Builders has a development of new homes. There are five different floor plans, seven exterior colors, and an option of either a one-car or a two-car garage. How many choices are there for one home?

62. Eleven people are entered in a race. If there are no ties, in how many ways can the first two places come out?

63. How many subsets of two elements are contained in the set

64. How many different ways can 9 different runners finish in first, second, and third places in a race?

65. The probability of getting an A in Mrs. Ritchie's class in any semester is 19%. What is the probability of not getting an A?

66. Two urns each contain yellow balls and green balls. Urn I contains three yellow balls and four green balls and Urn II contains two yellow balls and four green balls. A ball is drawn from each urn. What is the probability that both balls are yellow?