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Algebra 8H Final Exam Review #4
Data and Probability
Frequency Table
Measures of Central Tendency
Box and Whisker Plot
Simple Probability
12.5 Compound Probability; Dependent and Independent Probability
12.4 Permutations and Combinations
Ch.5 – Solving Linear Inequalities
5.1 Solving Inequalities by Addition and Subtraction
5.2 Solving Inequalities by Multiplication and Division
5.3 Solving Multi-Step Inequalities
5.4 Solving Compound Inequalities
5.5 Inequalities Involving Absolut Value
5.6 Graphing Inequalities Variables
6.8 Graphing Systems of Inequalities
For all chapters, you should know the vocabulary at the end of each chapter and be able to define or describe the
words. I would also suggest you look at your previous quizzes and tests.
To review for mastery of a subject:
1. Complete this packet.
2. Review the quizzes and tests you have already taken and be sure that if you had the same test to take
today, you would get 100%.
3. Read the chapter summaries several times. Write down any ideas that are unclear.
4. Do the Chapter Test for each chapter – These should now be easy.
Data
1) This graph shows the number of slices of pizza sold each day during one week in the school cafeteria.
Each slide of pizza costs $0.50. What is the total amount of money the school cafeteria collected on the
sales of pizza for this week?
2) These box-and-whisker plots summarize the height of the boys and the height of the girls in an eighthgrade class.
Based on the data in these box-and-whisker plots, which statement is true?
A) The tallest student in the class is a girl.
B) The shortest student in the class is a boy.
C) The range of the boys’ heights is greater than the range of the girls’ heights.
D) The median height of the girls is greater than the median height of the boys.
Probability
1) A fair cube used in a game has 1 yellow side and 5 green sides. Gianna will win the game if the cube
lands on a green side on her next roll. Which statement best describes Gianna’s chance of winning the
game?
A) Certainly will win
B) Certainly will lose
C) Most likely will win
D) Most likely will lose
2) This table shows the number of marbles in a bag by color. If one marble is randomly selected from the
bag, what is the probability that it will be a blue or a red marble?
3) Erica has 5 blue pens, 3 black pens, and 6 red pens in her desk drawer. If she randomly picks a pen from
her drawer, what is the probability that she will pick a pen that is not black? Express your answer as a
fraction only.
4)
12.5 Compound Probability
1) Dina tosses a penny twice. What is the probability that it will land on heads both times?
2) Paula tosses a penny and then rolls a die. What is the probability that the penny will land on tails and the
die will land on a 4?
3) Julian is rolling a numbered cube with the numbers 1 to 6 on it. He rolls the cube twice. What is the
probability that the two rolls will have a sum of 8?
4) A spinner has four equal sectors: yellow, red, blue, and green. Sage spins the arrow three times. What is
the probability that the arrow will land on red the first time, yellow the second time, and blue the third
time?
5) Perry took a survey of his classmates to see how many siblings each had. The results are in the table.
a) Find the probability that a randomly chosen classmate will have 4 siblings.
b) Find the probability that a randomly chosen classmate will have less than 3 siblings.
6) A customer visiting a new car lot was looking for a convertible. The Buyers Co. lot had 8 black, 6 white,
4 silver, 5 red, and 7 green convertibles to consider.
a) Find the probability that a randomly chosen car will be silver.
b) Find the probability that a randomly chosen car will be red or black.
7) If you have drawn and kept the 8 of spades and the 7 of hearts from a standard deck of cards, what is the
chance you will draw another 7 or a spade next?
8) Nate has a shelf with 3 cans of green beans, 2 cans of corn, and 5 cans of peas and a shelf of 1 package
each of egg noodles, rice and ziti. In the freezer, her has 2 pounds of chicken and 3 pounds of beef. If he
randomly grabs one item from each area to put in a casserole, what is the probability that he makes a
chicken-corn-ziti casserole?
9) Ariel drew from a standard deck of cards and picked a king. He replaced the king and drew a second
card. What is the probability that he will pick a king again?
10) A bag contained four green balls, three red balls, and two purple balls. Jason removed one purple ball
from the bag and did not put the ball back in the bag. He then randomly removed another ball from the
bag. What is the probability that the second ball Jason removed was purple?
11) Andrew wants to buy a new car. His choices are a 2-door or a 4-door, a convertible top or a hard top,
and red, white, or black. How many options does he have?
12) Diana drew from a standard deck of cards wants to pick a king or a heart. What is the probability of
picking a king or a heart?
12.4 Permutations and Combinations
Determine whether each situation involves a permutation or combination. Explain your reasoning.
1) Three topping flavors for a sundae from ten topping choices
2) Selection and placement of four runners on a relay team from 8 runners
3) Five rides to ride at an amusement park with twelve rides
4) First, second, and third place winners for a 10K race
Evaluate each expression. You may use a calculator.
5) P(5, 2)
7) C(10, 2)
6) P(7, 7)
8) C(6, 5)
9) In a high school band, six girls and four boys play trumpets. Before auditions at the beginning of the
year, the new band director randomly assigns chairs to the students.
a. How man ways can the band director assign first chair, second chair, and third chair?
b. What is the probability that the first three chairs will be assigned to boys?
5.1 Solving Inequalities by Addition and Subtraction
Solve each inequality. Check your solution, and then graph it on a number line. (Sketch your own number line).
1) 𝑐 + 9 ≤ 3
2) 𝑑 − (−3) < 13
3) 2𝑥 − 3 ≥ 𝑥
4) 5𝑧 − 6 > 4𝑧
Define a variable, write an inequality, and solve each problem.
5) Jeff is buying a new car but owes 3000 on his old one. Jeff can spend no more than $18,000 to pay off
his old car and buy a new one. Write an inequality to show how much Jeff can spend on his new car.
Solve the inequality.
6) There are more than 10,000 varieties of tomatoes. One seed company produces seed packages for 200
varieties of tomatoes. For how many varieties do they not provide seeds? Write an inequality and solve.
5.2 Solving Inequalities by Multiplication and Division.
Solve each inequality. Check your solution, and then graph it on a number line. (Sketch your own number line).
𝑝
1) −5𝑗 < −60
2) 5 < 8
3)
2
𝑚 ≥ −22
3
7
4) − 9 𝑥 < 42
Define a variable, write an inequality, and solve each problem.
5) Negative one times a number is greater than -7.
6) Three fifths of a number is at least negative 10.
7) The dimensions of Lisle’s room are shown below. If the area of the room is at least 96 square feet, what
is the least width the room could have?
5.3 Solving Multi-Step Inequalities.
Solve each inequality. Check your solution.
1) 3𝑦 − 4 > −37
2) −5𝑞 + 9 > 24
3) −2𝑘 + 12 < 30
4) 15𝑥 − 4 > 11𝑥 − 16
5) 5𝑞 + 7 ≤ 3(𝑞 + 1)
6) −4𝑥 − 5 > 2𝑥 + 13
7)
𝑧
4
+ 7 ≥ −5
9) 9𝑚 + 7 < 2(4𝑚 − 1)
8) 8𝑐 − (𝑐 − 5) > 𝑐 + 17
10) 5𝑥 ≤ 10(3𝑥 + 4)
11) Ramone is ranking yards for $22 per yard to earn money for a car. So far he has $2150 saved. The car
that Ramone wants to buy costs at least $8290. Write an inequality to show how many more yards
Ramone still needs to rake to earn enough money to buy the car. Solve the inequality.
12) Avery High School holds a walk-a-thon each fall to raise money for charity. This year they want to raise
at least $375. Each student earns $0.75 for every half mile walked. How many miles will the students
need to walk?
13) A school buys 500 T-shirts. In addition to the price per shirt, there is a $45 set-up fee. The school can
afford to spend no more than $2295. Write an inequality to show the relationship. What must the price
be for the school to afford the shirts?
5.4 Solving Compound Inequalities.
Solve each compound inequality. Then graph the solution set.
1) 2 + 𝑥 < −5 𝑜𝑟 2 + 𝑥 > 5
2) 3 ≤ 2𝑔 + 7 𝑎𝑛𝑑 2𝑔 + 7 ≤ 15
3) 3𝑏 − 4 ≤ 7𝑏 + 12 𝑎𝑛𝑑 8𝑏 − 7 ≤ 25
4) 5𝑚 − 8 ≥ 10 − 𝑚 𝑜𝑟 5𝑚 + 11 < −9
5) 2ℎ − 2 ≤ 3ℎ ≤ 4ℎ − 1
6) 2𝑟 + 8 > 16 − 2𝑟 𝑎𝑛𝑑 7𝑟 + 21 < 𝑟 − 9
7) 2(𝑞 − 4) ≤ 3(𝑞 + 2) 𝑜𝑟 𝑞 − 8 ≤ 4 − 𝑞
8) 𝑛 − (6 − 𝑛) > 10 𝑜𝑟 − 3𝑛 − 1 > 20
9) The temperature in a fish tank must be at least 77°F and at most 83°F. Write a compound inequality that
describes acceptable temperatures for a fish tank.
5.5 Inequalities Involving Absolute Value
Solve each inequality. Then graph the solution set.
1) |𝑥 + 4| < 10
3) |3𝑥 + 2| > 8
2𝑥−3
2) |
|≥4
5
𝑦+4
4) |
5
|<4
5) When the temperature in the clouds is 7°F plus or minus 3°F, star-shaped crystals of snow form. At 14°F
plus or minus 4°F, plate-shaped crystals are formed.
a. Write an absolute value inequality to find the range of temperatures that produces star-shaped
crystals. The find the range.
b. Write an absolute value inequality to find the range of temperatures that produces plate-shaped
crystals. The find the range.
6.8 Systems of Inequalities
Solve each system of inequalities.
1) 𝑦 ≥ 𝑥
𝑦+𝑥 <2
2) 𝑦 < 3
𝑥+𝑦 ≤2