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Algebra II : Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Irrational Numbers

Which of the following is an irrational number?

Possible Answers:

$\frac{21}{5}$ $\displaystyle \frac{21}{5}$

$\pi$ $\displaystyle \pi$

$\sqrt{9}$ $\displaystyle \sqrt{9}$

5.75 $\displaystyle 5.75$

$0.\overline{3333}$ $\displaystyle 0.\overline{3333}$

Correct answer:

$\pi$ $\displaystyle \pi$

Explanation:

A rational number can be expressed as a fraction of integers, while an irrational number cannot.

$0.\overline{3333}$ $\displaystyle 0.\overline{3333}$ can be written as $\frac{1}{3}$ $\displaystyle \frac{1}{3}$.

$\sqrt{9}$ $\displaystyle \sqrt{9}$ is simply $\displaystyle 3$, which is a rational number.

The number 5.75 $\displaystyle 5.75$ can be rewritten as a fraction of whole numbers, $\frac{23}{4}$ $\displaystyle \frac{23}{4}$, which makes it a rational number.

$\frac{21}{5}$ $\displaystyle \frac{21}{5}$is also a rational number because it is a ratio of whole numbers.

The number, $\pi$ $\displaystyle \pi$, on the other hand, is irrational, since it has an irregular sequence of numbers ( 3.14159 $\displaystyle 3.14159$...) that cannot be written as a fraction.

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Example Question #5131 : Algebra Ii

If $A= \left \{ 10, 20, 30, 40, 50 \right \}$ $\displaystyle A= \left \{ 10, 20, 30, 40, 50 \right \}$, $B=\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60 \right \}$, and $C=\left \{ 20, 30, 40, 60 \right \}$ $\displaystyle C=\left \{ 20, 30, 40, 60 \right \}$, then find the following set:

$A\cup B$ $\displaystyle A\cup B$

Possible Answers:

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50 \right \}$

$\left \{ 10, 20, 40 \right \}$ $\displaystyle \left \{ 10, 20, 40 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle \left \{ 10, 20, 40, 60 \right \}$

$\left \{ 10, 20, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 40, 50, 60 \right \}$

Correct answer:

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

Explanation:

The union is the set that contains all the numbers from $A= \left \{ 10, 20, 30, 40, 50 \right \}$ $\displaystyle A= \left \{ 10, 20, 30, 40, 50 \right \}$ and $B=\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60 \right \}$. Therefore the union is $\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$.

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Example Question #2 : Number Sets

If $A= \left \{ 10, 20, 30, 40, 50 \right \}$ $\displaystyle A= \left \{ 10, 20, 30, 40, 50 \right \}$, $B=\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60 \right \}$, and $C=\left \{ 20, 30, 40, 60\right \}$ $\displaystyle C=\left \{ 20, 30, 40, 60\right \}$, find the following set:

$A\cap B\cap C$ $\displaystyle A\cap B\cap C$

Possible Answers:

$\left \{ 20, 40, 60 \right \}$ $\displaystyle \left \{ 20, 40, 60 \right \}$

$\left \{ 20, 40 \right \}$ $\displaystyle \left \{ 20, 40 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 20, 30, 40 \right \}$ $\displaystyle \left \{ 20, 30, 40 \right \}$

$\left \{ 40 \right \}$ $\displaystyle \left \{ 40 \right \}$

Correct answer:

$\left \{ 20, 40 \right \}$ $\displaystyle \left \{ 20, 40 \right \}$

Explanation:

The intersection is the set that contains only the numbers found in all three sets. Therefore the intersection is $\left \{ 20, 40 \right \}$ $\displaystyle \left \{ 20, 40 \right \}$.

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Example Question #1 : Number Sets

$B\cap C$ $\displaystyle B\cap C$

Possible Answers:

$\left \{ 20, 40, 60 \right \}$ $\displaystyle \left \{ 20, 40, 60 \right \}$

$\left \{ 20, 40 \right \}$ $\displaystyle \left \{ 20, 40 \right \}$

$\left \{ 40, 60 \right \}$ $\displaystyle \left \{ 40, 60 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle \left \{ 10, 20, 40, 60 \right \}$

$\left \{10, 20, 40 \right \}$ $\displaystyle \left \{10, 20, 40 \right \}$

Correct answer:

$\left \{ 20, 40, 60 \right \}$ $\displaystyle \left \{ 20, 40, 60 \right \}$

Explanation:

The intersection is the set that contains the numbers that appear in both $B=\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60 \right \}$ and $C=\left \{ 20, 30, 40, 60 \right \}$ $\displaystyle C=\left \{ 20, 30, 40, 60 \right \}$. Therefore the intersection is $\left \{ 20, 40, 60 \right \}$ $\displaystyle \left \{ 20, 40, 60 \right \}$.

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Example Question #3 : Number Sets

If $A=\left \{ 10, 20, 30, 40, 50\right \}$ $\displaystyle A=\left \{ 10, 20, 30, 40, 50\right \}$, $B=\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60 \right \}$, and $C=\left \{ 20, 30, 40, 60 \right \}$ $\displaystyle C=\left \{ 20, 30, 40, 60 \right \}$, find the following set:

$A\cap C$ $\displaystyle A\cap C$

Possible Answers:

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 30, 40 \right \}$ $\displaystyle \left \{ 30, 40 \right \}$

$\left \{ 20, 30, 40, 60 \right \}$ $\displaystyle \left \{ 20, 30, 40, 60 \right \}$

$\left \{ 20, 40 \right \}$ $\displaystyle \left \{ 20, 40 \right \}$

$\left \{ 20, 30, 40 \right \}$ $\displaystyle \left \{ 20, 30, 40 \right \}$

Correct answer:

$\left \{ 20, 30, 40 \right \}$ $\displaystyle \left \{ 20, 30, 40 \right \}$

Explanation:

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is $\left \{ 20, 30, 40 \right \}$ $\displaystyle \left \{ 20, 30, 40 \right \}$.

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Example Question #81 : Number Theory

If $A=\left \{ 10, 20, 30, 40, 50\right \}$ $\displaystyle A=\left \{ 10, 20, 30, 40, 50\right \}$, $B=\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60 \right \}$, and $C=\left \{ 20, 30, 40, 60\right \}$ $\displaystyle C=\left \{ 20, 30, 40, 60\right \}$, find the following set:

$A\cup B\cup C$ $\displaystyle A\cup B\cup C$

Possible Answers:

$\left \{ 20, 40, 60 \right \}$ $\displaystyle \left \{ 20, 40, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle \left \{ 10, 20, 40, 60 \right \}$

$\left \{ 40, 60 \right \}$ $\displaystyle \left \{ 40, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50 \right \}$

Correct answer:

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

Explanation:

The union is the set that contains all of the numbers found in all three sets. Therefore the union is $\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$. You do not need to re-write the numbers that appear more than once.

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Example Question #82 : Number Theory

If $A=\left \{ 10, 20, 30, 40, 50\right \}$ $\displaystyle A=\left \{ 10, 20, 30, 40, 50\right \}$, $B=\left \{ 10, 20, 40, 60\right \}$ $\displaystyle B=\left \{ 10, 20, 40, 60\right \}$, and $C=\left \{ 20, 30, 40, 60\right \}$ $\displaystyle C=\left \{ 20, 30, 40, 60\right \}$, find the following set:

$A\cap B$ $\displaystyle A\cap B$

Possible Answers:

$\left \{ 20, 40, 60 \right \}$ $\displaystyle \left \{ 20, 40, 60 \right \}$

$\left \{ 10, 20, 30, 40, 50, 60 \right \}$ $\displaystyle \left \{ 10, 20, 30, 40, 50, 60 \right \}$

$\left \{ 10, 20, 40, 60 \right \}$ $\displaystyle \left \{ 10, 20, 40, 60 \right \}$

$\left \{ 10, 20, 40 \right \}$ $\displaystyle \left \{ 10, 20, 40 \right \}$

$\left \{ 20, 40 \right \}$ $\displaystyle \left \{ 20, 40 \right \}$

Correct answer:

$\left \{ 10, 20, 40 \right \}$ $\displaystyle \left \{ 10, 20, 40 \right \}$

Explanation:

The intersection is the set that contains the numbers found in both sets. Therefore the intersection is $\left \{ 10, 20, 40 \right \}$ $\displaystyle \left \{ 10, 20, 40 \right \}$.

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Example Question #1 : Number Sets

Sets3

Which set of numbers represents the union of E and F?

Possible Answers:

70,15 $\displaystyle 70,15$

$\displaystyle 35,60,15,70,250$

$\displaystyle 60,15,75,140,250,70$

$\displaystyle 70,15,60,75$

$\displaystyle {35,70,15,60,75,250}$

Correct answer:

$\displaystyle {35,70,15,60,75,250}$

Explanation:

The union is the set of numbers that lie in set E or in set F.

. Sets3

In this problem set E contains terms $\displaystyle 35,60,15,70$, and set F contains terms $\displaystyle 250,70,15,75$. Therefore, the union of these two sets is $\displaystyle 35,60,15,70,75,250$.

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Example Question #3442 : Algebra 1

Express the following in Set Builder Notation:

$\left ( -\infty , -3\ \right )\cup \left ( -3, 1 \right )\cup \left ( 1, \infty \right )$ $\displaystyle \left ( -\infty , -3\ \right )\cup \left ( -3, 1 \right )\cup \left ( 1, \infty \right )$

Possible Answers:

$\left \{ x|-\infty < x< 1 \right \}$ $\displaystyle \left \{ x|-\infty < x< 1 \right \}$

$\left \{ x|-3< x< \infty \right \}$ $\displaystyle \left \{ x|-3< x< \infty \right \}$

$\left \{ x|-\infty < x< -3 \right \}$ $\displaystyle \left \{ x|-\infty < x< -3 \right \}$

$\left \{ x|-3< x< 1 \right \}$ $\displaystyle \left \{ x|-3< x< 1 \right \}$

$\left \{ x|-\infty< x< -3 \right\ OR\ -3< x< 1\ OR\ 1< x< \infty \}$ $\displaystyle \left \{ x|-\infty< x< -3 \right\ OR\ -3< x< 1\ OR\ 1< x< \infty \}$

Correct answer:

$\left \{ x|-\infty< x< -3 \right\ OR\ -3< x< 1\ OR\ 1< x< \infty \}$ $\displaystyle \left \{ x|-\infty< x< -3 \right\ OR\ -3< x< 1\ OR\ 1< x< \infty \}$

Explanation:

$\left ( -\infty , -3 \right ) = \left \{x| -\infty < x< -3 \right \}$ $\displaystyle \left ( -\infty , -3 \right ) = \left \{x| -\infty < x< -3 \right \}$

and $\cup$ $\displaystyle \cup$ stands for OR in Set Builder Notation

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Example Question #1 : Number Sets

Find the intersection of the two sets:

$A=\left \{ 1, 2, 3, 4, 5, 6, 7, 8 \right \}, B=\left \{ 2, 4, 6, 7, 9 \right \}$ $\displaystyle A=\left \{ 1, 2, 3, 4, 5, 6, 7, 8 \right \}, B=\left \{ 2, 4, 6, 7, 9 \right \}$

Possible Answers:

$\left \{ 2, 4, 6, 7 \right \}$ $\displaystyle \left \{ 2, 4, 6, 7 \right \}$

$\left \{ \right \}$ $\displaystyle \left \{ \right \}$

$\left \{ 1, 3, 5, 8, 9 \right \}$ $\displaystyle \left \{ 1, 3, 5, 8, 9 \right \}$

$\left \{ 1, 2, 3, 4, 5, 6, 7, 8,9 \right \}$ $\displaystyle \left \{ 1, 2, 3, 4, 5, 6, 7, 8,9 \right \}$

Correct answer:

$\left \{ 2, 4, 6, 7 \right \}$ $\displaystyle \left \{ 2, 4, 6, 7 \right \}$

Explanation:

To find the intersection of the two sets, $A\cap B$ $\displaystyle A\cap B$, we must find the elements that are shared by both sets:

$\left \{ 2, 4, 6, 7 \right \}$ $\displaystyle \left \{ 2, 4, 6, 7 \right \}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #5 : Irrational Numbers

Example Question #5131 : Algebra Ii

Example Question #2 : Number Sets

Example Question #1 : Number Sets

Example Question #3 : Number Sets

Example Question #81 : Number Theory

Example Question #82 : Number Theory

Example Question #1 : Number Sets

Example Question #3442 : Algebra 1

Example Question #1 : Number Sets

All Algebra II Resources

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