Probability:
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1. In a fair deck of cards, find each probability:
A. A number smaller than 4
B. A red face card
C. A red or a queen
D. A red and a queen
E. A 7, 8, or jack
2. If 2 cards are drawn from the deck, find each probability:
A. With replacement: P(red, black)
B. Without replacement: P(face, diamond)
C. With replacement: P(number card, ace)
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Yellow / Red / Purple / Blue / TotalUnder 4 / 10 / 6 / 9 / 20
4-13 / 8 / 15 / 8 / 9
14 and over / 3 / 5 / 11 / 1
Total
3. What is the P ? 4. What is the P ?
5. What is the P (R or P)? 6. What is the P(red and under 4)?
7. Sixty percent of a company’s sales representatives have completed training seminars. Of these, 80% have had increased sales. Overall 56% of the representatives (whether trained or not) have had increased sales. Find the probability of increased sales given that a representative has not been trained.
Compute the values of the following:
8. 9P39. 10C810. 5P5
For problems 11 and 12, consider the following:
5 balls are drawn from an urn containing 10 red balls, 15 green balls, and 5 white balls. Find the probability that the balls are as described. First, write your answer using C notation; then compute each answer as a percentage to 3 significant digits.
11. 2 reds and 3 whites12. 4 greens and 1 red
13. Expand:
14. Find the term that contains c4d5 in the binomial: .
15. Find the term that contains x8 in the binomial: .
16. Find the last three terms in the expansion of: .
17. The probability of a tennis player getting his first serve in is 0.78. Suppose that the player serves 10 more times:
a.) Find the probability that exactly 8 serves will be in.
b.) Find the probability that at least 1 of his serves will be in.
18. If 6 coins are tossed:
a.) What is the probability that exactly 3 heads will appear?
b.) What is the probability that at least 4 heads will appear?
19. In how many ways can the letters in the word PAPAYA be arranged?
20. In how many ways can 5 members be chosen from a team of 25 to represent the club at a convention?
21. In how many ways can a winner and runner up be selected from a pool of 30 contestants on a game show?
Statistics:
22. If scores are normally distributed with a mean of 30 and a standard deviation of 5, what percent of the scores is:
a.) greater than 30?
b.) greater than 37?
c.) between 28 and 34?
23. In a random telephone survey of 2,500 homeowners, 800 report that they have bought a new car within the past two years.
a.) What is the sample proportion?
b.) What is the margin of error?
c.) What interval (range) is likely to contain the true population proportion?
24. The lifespan of turtles in the Galapagos Islands are normally distributed with a mean age of 95 years and a standard deviation of 7 years.
a.) About what percent of the turtles live less than 88 years?
b.) About what percent of the turtles live between 95 and 109 years?
c.) In a colony of 500 turtles, about how many will live more than 102 years?
Solving Equations:
Find an equation in standard form of the lines containing the following points:
25. (7, 0) and (0, -4)26. (-3, -2) and (5, -2)27. (6, 1) and (0, -3)
Given the following information, find an equation of a line in standard form.
28. Passing through (0, -1), parallel to y = -3x + 4.
29. Passing through (2, 2), perpendicular to y = x + 5.
30. Passing through (4, 5), perpendicular to 2x + y = 6.
31. Passing through (0, 0), parallel to 2x – 5y = 10.
Solve the following inequalities and graph on the number line provided.
32. 33.
34. 35.
Exponents and Functions:
Simplify:
36. 37.
38. 39.
Solve for x.
40. 41.
For the following, let and Find:
42. f(g(2))43. g(f(-4))
44. f(g(a + 3))45. g-1(x)
46. (f – g)(x)47. (f•g)(x)
Systems:
Solve each system by elimination or substitution only.
48. 49.
50.
51. The indoor climbing gym is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 6 vans and 10 buses with 636 students. High School B rented and filled 9 vans and 9 buses with 612 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
52. Mike and John each improved their yards by planting grass sod and shrubs. They bought their supplies from the same store. Mike spent $70 on 10 sq. ft. of grass sod and 5 shrubs. John spent $44 on 5 sq. ft. of grass sod and 7 shrubs. What is the cost of one sq. ft. of grass sod and the cost of one shrub?
53. Graph:
Sequences and Series:
54. -22, -14, -6, 2, ... Find a38.55. -3, 9, -27, 81, ...Find a22.
56. 57.
Matrices:
Compute the following problems using the matrices below.
, , ,
58. 2D + B59. B – 6C
60. A-161. B∙A
62. 63.
Use matrices (Cramer’s Rule or Inverses) to solve the following systems.
64. 65.
66. Student Council is selling new Hatboro-Horsham hats, shirts, and sweatshirts. Hats cost $10, shirts $12, and sweatshirts $20. When sales were totaled, it was found that boys bought 26 hats, 30 shirts and 25 sweatshirts, while girls purchased 10 hats, 40 shirts and 20 sweatshirts. Display the following information in matrices, and then multiply to find the dollar amount spent by boys and girls.
Domain & Range
For the following graphs, state the domain and range, and determine if the graph represents a function.
67.
Domain: ______
Range: ______
Function? ______
68.
Domain: ______
Range: ______
Function? ______
Rational Expressions
Simplify the each and state the domain restrictions.
69. 70.
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