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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #112 : Data Properties

The average score on a test that Sarah was absent for was . What must Sarah score on test to bring the average up to , if there are other students in the class?

Possible Answers:

100

Correct answer:

Explanation:

Set equal to the sum of the tests of the first students.

$\frac{x}{14}=82, x=1148.$

Now set up an equation to solve for Sarah's test score:

$\frac{1148+y}{15}=83, y=97$

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Example Question #113 : Data Properties

In the Olympics gymnastics time trials, Sally's scores were $\textup{9.3, 9.6, 8.7, 9.1}$ . The highest score Sally can earn is a . Suppose she has one more opportunity to earn a qualifying score of 9.5 to be on a team. Which of the following statements is TRUE?

Possible Answers:

Sally will make the team if she earns a $\textup{ 9.5.}$

Sally will make the team if she earns a $\textup{ 9.925.}$

Sally will only make the team if she makes a perfect ten.

Sally will make the team if she earns a $\textup{ 9.825.}$

Sally will not make the team.

Correct answer:

Sally will not make the team.

Explanation:

In order to determine whether Sally will qualify for the last time trial, set up an equation to find the mean. Out of the five scores, one of the scores is unknown, and Sally's final score must be 9.5 or higher. Let the unknown score be .

Write the equation to solve for the mean.

$\frac{9.3+9.6+8.7+9.1+x}{5}=9.5$

9.3+9.6+8.7+9.1+x=47.5

36.7+x=47.5

x=10.8

Unfortunately, Sally cannot make the gymnastics team because she needs to earn a 10.8, which is not possible on the score limit.

The correct answer is:

$\textup{Sally will not make the team.}$

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Example Question #13 : Mean

Find the mean of the following set of numbers: , , , , , and .

Possible Answers:

Correct answer:

Explanation:

The mean is also the average of a set of numbers. To find the mean, add all of the numbers in the set: , , , , , and . Then, divide your answer by the number of terms present within the set, in this case .

3+6+9+34+12+2=66

In this case, the sum of all the numbers is . Divide by the size of the set: .

$\frac{66}{6}=11$

This will give you an average or mean of .

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Example Question #114 : Data Properties

The average of the class on the most recent exam was an 84.1. The 2 lowest scores of the class were 71 and 73. If the teacher decides to removed the 2 lowest scores from the class average and there are 10 students in the class, what is the new class average?

Possible Answers:

87.1

84.9

69.7

99.6

89.1

Correct answer:

87.1

Explanation:

To get the total combined score of everyone in the class, multiply the average of the class by the number of students.

84.1*10=841 . Since the teacher decided to drop the lowest 2 scores, let's subtract those 2 scores from the total.

841-71-73=697 .

Now the new total is 697. To find the new average, divide this new total by the new number of grades to be averaged in, which is 8. Remember that the teacher dropped 2 grades so there are less grades to take into account.

$\frac{697}{8}=87.1$

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Example Question #21 : Mean

Find the mean for the set:

10, 10, 11, 11, 11, 12, 12, 15, 27, 39

Possible Answers:

15.8

16.3

15.1

Correct answer:

15.8

Explanation:

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are ten numbers so we add them up and divide by ten:

$\frac{10+10+11+11+11+12+12+15+27+39}{10}=15.8$

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Example Question #22 : Mean

Find the mean of the set:

76, 78, 82, 83, 84, 84, 88, 89, 89, 89, 91, 91, 93, 97, 100, 100

Possible Answers:

88.4

87.9

89.2

88.7

Correct answer:

88.4

Explanation:

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are 16 numbers in the set, so we add the numbers together and divide by 16 to find the mean:

76+78+82+83+84+84+88+89+89+89+91+91+93+97+100+100

$=1414\rightarrow \frac{1414}{16}=88.4$

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Example Question #23 : Mean

Find the mean of the set:

32, 33, 33, 34, 35, 37, 38, 41, 42, 45, 47

Possible Answers:

35.7

37.1

37.9

39.1

Correct answer:

37.9

Explanation:

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are 11 numbers in the set, so we add the numbers together and divide by 11 to find the mean:

$\frac{32+33+33+34+35+37+38+41+42+45+47}{11}=37.9$

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Example Question #24 : Mean

Find the mean of the set:

7, 10, 16, 16, 16, 16, 17, 23, 25, 27, 30, 31, 41, 57, 57, 58

Possible Answers:

28.1

27.2

27.9

26.7

Correct answer:

27.9

Explanation:

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are 16 numbers in the set, so we add the numbers together and divide by 16 to find the mean:

7+10+16+16+16+16+17+23+25+27+30+31+41+57+57+58

$=447\rightarrow \frac{447}{16}=27.9$

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Example Question #25 : Mean

Find the mean of the set:

11, 13, 17, 22, 22, 22, 23, 23, 26, 28, 47, 49

Possible Answers:

24.4

25.8

24.9

25.3

Correct answer:

25.3

Explanation:

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are 12 numbers in the set, so we add the numbers together and divide by 12 to find the mean:

$\frac{11+13+17+22+22+22+23+23+26+28+47+49}{12}=25.3$

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Example Question #26 : Mean

Find the mean of the set:

4, 5, 6, 12, 15, 18, 19, 23, 26, 27, 31, 39, 41

Possible Answers:

21.5

20.5

Correct answer:

20.5

Explanation:

To find the mean, there are two steps:

1. Add all of the numbers in the set together.

2. Divide that number by the amount of numbers are in the set.

For this problem there are 13 numbers in the set, so we add the numbers together and divide by 13 to find the mean:

4+5+6+12+15+18+19+23+26+27+31+39+41

$=266\rightarrow \frac{266}{13}=20.5$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #112 : Data Properties

Example Question #113 : Data Properties

Example Question #13 : Mean

Example Question #114 : Data Properties

Example Question #21 : Mean

Example Question #22 : Mean

Example Question #23 : Mean

Example Question #24 : Mean

Example Question #25 : Mean

Example Question #26 : Mean

All Algebra II Resources

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