Download Final Exam Review – Part 4

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Algebra 2
Final Exam Review – Part 4
UNIT 6: SYSTEMS AND MATRICES – Use your calculator according to the directions for each
question.
41. At a fair, a frozen yogurt stand sells large cones for $2.50 and small cones for $2.00. Suppose the stand
sells 250 cones and makes $565.00. How many cones of each type were sold?
a. Define the variables and write a system of equations.
b. Solve the system using a non-matrix method: either substitution or elimination (linear combinations).
Don’t use RREF on calc.
c. Now check your work to part b by using RREF on the calculator. Show your original matrix, the
reduced matrix from the calculator, and then clearly state what your variables are equal to.
42. Solve with substitution:
x + 3y = 13
2x – 5y = -18
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Algebra 2
43. Solve with elimination:
2x + 3y = 1
-3x + 2y = 5
44. Solve using row operation by hand. (MATRIX ELIMINATION) Write down symbols to show what
row operations you are doing.
2x - 2y = -2
3x + y = 17
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Algebra 2
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UNIT 7: COUNTING AND PROBABILITY -- NO CALCULATOR
45. An elementary school with 200 students was gathering data about which of their students played
basketball and which played soccer. The school found that 85 of the students played basketball, 93
played soccer, and 54 played neither.
a. Create a Venn diagram for this situation.
b. Suppose a student was picked at random from the school. What is the probability that the student
plays basketball?
c. Suppose a student was picked at random from the school. What is the probability that the student
plays both basketball and soccer?
46. A jar contains 7 green balls and 10 red balls. Two balls are drawn from the jar (one at a time without
replacement).
a. Draw a tree diagram to represent the probabilities in this problem.
b. What is the probability that both of the balls will be red?
c. What is the probability that both of the balls will be the same color?
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47. Perform each of the following calculations. Remember: You can’t use your calculator on this section.
a. Find 5!
b. Find 10 P3
c. Find 7 C3
48. Suppose A and B are events with the following probabilities: P( A) = 0.3 and P(B) = 0.2.
a. If A and B are independent, find P( A and B).
b. If A and B are mutually exclusive, find P( A and B).
49. Ms. Knecht is making invitation cards for her daughter’s graduation party and she has some choices to
make. The options for size are small, medium, or large, and the options for color are violet, yellow, blue,
or magenta. She must also decide whether to use print or cursive.
How many possibilities are there for Ms. Knetcht’s invitations?
50. Make Pascal’s triangle. Go to the seventh row.
51. Write the sum 16 C5 + 16 C6 as a single combination number. Hint: Think about a pattern from Pascal’s
triangle. You don’t need to compute the numerical values.
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UNIT 7: COUNTING AND PROBABILITY – CALCULATORS ALLOWED
52. You are flipping 7 coins. Let H represent heads. Let T represent tails.
Algebra 2
a. What is the probability of flipping HHTTTTT?
b. What is the probability of flipping two heads and 5 tails in any order?
53. There are 2000 students at LHS. 600 students watch Real House Wives of Orange County. 800 students
watch Real House Wives of NJ. 1000 watch neither show.
What is the probability that a random student chosen watches BOTH shows?
Show a diagram or a calculation that supports your answer.
54. There are five positions in basketball: point guard, shooting guard, small forward, power forward and
center.
a. Suppose a coach has five players on her team. How many ways can she assign the five players to the
five positions?
b. Suppose instead that the coach has twelve players on her team. Five of the players will be assigned
positions and seven must sit on the bench. How many ways can this be done?
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55. The math club has 15 members and must pick 4 representatives for a competition. How many ways can
this be done?
56. There are 10 different pairs of jeans in my closet: 6 are skinny jeans, 4 are flared.
a. I am going on vacation and need to bring 2 pairs of jeans. How many different ways can I choose 2
pairs of jeans randomly from my closet?
b. What is the probability that the 2 pairs of jeans I choose are both skinny jeans?
57. In a deck of 52 playing cards, 13 cards are diamonds and 39 cards are a different suit.
a. How many ways can you be dealt a hand of 4 cards from the whole deck?
b. What is the probability that all 4 cards you are dealt are diamonds?
c. Suppose there’s a casino game where the player is dealt a hand of 4 cards. It costs $10 to play this
game. If all 4 of the cards are diamonds, the player wins $100. Calculate the expected value of a play
of this game. [Hint: The two options are winning or losing. Figure out the probability of both
options. Then, find the expected value.]
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58. A standard deck includes 52 cards. (13 hearts, 13 diamonds, 13 clubs, and 13 spades).
a. If three cards are drawn from the deck without replacement, what is the probability that all three will
be hearts?
b. If three cards are drawn from the deck without replacement, what is the probability that none of the
three will be hearts?
c. If a single card is drawn from the deck, what is the probability that the card will be either a heart or
an ace (but not both)?
d. A six sided die is rolled and then a card is drawn from the deck. What is the probability of getting a
4 followed by an ace?
59. A jar contains 7 green balls and 10 red balls. Two balls are drawn from the jar (one at a time without
replacement).
a. What is the probability that both of the balls will be red?
b. What is the probability that both of the balls will be the same color?
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Algebra 2
60. Consider a population of 10,000 people. A certain disease infects 2% of the population. 97% of people
who have the disease will test positive for it, while 94% of people who do not have the disease will test
negative.
a. Make a table to represent this situation.
(
)
b. Find P positive test disease .
c. Suppose a person tests positive for this disease. What is the probability that this person actually has
the disease?
d. What is the probability that the test gives an accurate positive result?
e. What is the probability that the test gives a false positive result?
f. What is the probability that the test result is inaccurate?
g. What is the probability that a person tests positive?
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Algebra 2
61. Events A and B are mutually exclusive. P( A) = .45 and P(B) = .95. Find P( A and B).
62. How many different ways can you arrange the first six letters of the alphabet?
63. The combination for a lock is based on three numbers in a fixed order. (Note: 32-12-17 and 12-17-32 are
considered different combinations). The numbers go from 1 to 40 and no number may be used twice).
How many combinations are possible?
64. A pizza shop offers 9 topics. A pizza may have no topics, all nine topics, or anything in between.
a. How many different pizzas are possible?
b. How many 4 topping pizzas are possible?
c. Suppose sausage is one of the topics. How many 4 topping pizzas are possible that include sausage?
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Algebra 2
Answers:
41 a. L = # of large cones. S = # of small cones, L + S = 250, 2.5L + 2S = 565. b. L =130, S =120.
42 (1, 4)
43 (-1, 1)
44 (4, 5)
85 c. 32
45 a. 32 play both, 53 only play basketball, 61 only play soccer, and 54 play neither. b. 200
200
æ10 öæ 9 ö 90
æ10 öæ 9 ö æ 7 öæ 6 ö 132
46 b. ç ÷ç ÷ =
c.
ç ÷ç ÷ + ç ÷ç ÷ =
è17 øè16 ø 272
è17 øè16 ø è17 øè16 ø 272
47 a. 120 b. 720 c. 35
48 a. .06
b. 0
49 24
50 Check this in class if you have questions
51 17 C6
7
7
1
21
52 a. ( 12 ) = 128
b. 7 C2 × ( 12 ) = 128
= 0.0078
= 0.164
400
53
2000
54 a. 120 b. 95040
55 15C4 1365
15 1
6 C2



56 a. 10 C2  45
b.
45 3
10 C 2
C

57 a. 52C4  270725 b. 13 4  0.002641 c. -9.71 (player loses $9.71 on average)
52 C4

æ 1 öæ 4 ö
4
C
C
12 3
58 a. 13 3 = 0.0129
b. 39 3 = 0.4135
c.
d. ç ÷ç ÷ =
+
= .288
è 6 øè 52 ø 312
52 52
52 C3
52 C3


10  9  90
10  9   7  6  132
59 a.   
b.
     
17 16  272
17 16  17 16  272
60 b. 0.97 c. 0.248 d. 0.0194 e. 0.0585 f. 0.0594 g. 0.0782
61 P A and B  0
62 6! = 720


63 40× 39× 38 = 59,280


64 a. 29 = 512
b.
9
C4 =126
c.
8
C3 = 56