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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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

Example Questions

Example Question #5071 : Algebra Ii

Solve the following using properties of fractions:

$\frac{3\times2}{2\times2}=$

Possible Answers:

$\frac{3}{2}$

$\frac{6}{4}$

$1\tfrac{1}{2}$

All answers are correct.

Correct answer:

All answers are correct.

Explanation:

$\frac{3\times2}{2\times2}=\frac{6}{4}=\frac{3}{2}$

Every answer choice is equivalent to this, so they are all correct.

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Example Question #5072 : Algebra Ii

Solve the following using properties of fractions:

$\frac{7}{9}\div \frac{1}{2}=$

Possible Answers:

$\frac{9}{10}$

$\frac{8}{11}$

$\frac{7}{18}$

$\frac{14}{9}$

Correct answer:

$\frac{14}{9}$

Explanation:

When dividing fractions, remember to multiply the first fraction by the reciprocal of the second, as illustrated by the following identity:

$\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$

$\frac{7}{9}\div \frac{1}{2}=\frac{7}{9}\times\frac{2}{1}=\frac{7\times2}{9\times1}=\frac{14}{9}$

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Example Question #5073 : Algebra Ii

Find the equivalent of the following:

$\frac{x}{y}=\frac{m}{n}$

Possible Answers:

x+n=y+m

x+m=y+n

xn=ym

xm=yn

Correct answer:

xn=ym

Explanation:

One of the properties of fractions states that if $\frac{a}{b}=\frac{c}{d}$ , then ad=bc .

It follows that if $\frac{x}{y}=\frac{m}{n}$ , then xn=ym .

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Example Question #19 : Number Theory

Which of the following is a NOT a real number?

Possible Answers:

$\frac{1}{8}$

$\sqrt{4}$

$\sqrt{2}$

3.2

$\sqrt{-4}$

Correct answer:

$\sqrt{-4}$

Explanation:

By definition, a real number is one that is NOT imaginary. Imaginary numbers are numbers that, when squared, give a negative result.

So, the correct answer choice for the above question must be one that is, in fact, an imaginary number.

Using the above defintion, we are able to identify only one of the answer choices as a number that, when squared, gives a negative result. This is $\sqrt{-4}$ . When we take the square of $\sqrt{-4}$ , we get , ultimately, satisfying our definition of an imaginary number, and giving us the correct answer choice.

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Example Question #5075 : Algebra Ii

Which is NOT a real number?

$\sqrt{36}, \, \sqrt{49}, \, \sqrt{81}, \, \sqrt{-4}$

Possible Answers:

$\sqrt{36}$

$\sqrt{49}$

$\sqrt{-4}$

$\sqrt{81}$

Correct answer:

$\sqrt{-4}$

Explanation:

The mathematics a real number is any integer, irrational, or rational number. The set of real numbers does not include imaginary numbers.

If we look at the possible answers we see that three out of the four are real numbers because they are integers.

$\sqrt{49} = 7$

$\sqrt{36} = 6$

$\sqrt{81} = 9$

7, 6, and 9 are all Real Numbers.

The answer is $\sqrt{-4}$ because when a negative number is under a radical sign it creates an imaginary number which is not included in the set of real numbers.

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Example Question #21 : Real Numbers

Which of the following are NOT real numbers?

Possible Answers:

$\frac{\pi}{e}$

$\textup{All of the answers are real numbers.}$

i^4

$\sqrt{30}$

Correct answer:

$\textup{All of the answers are real numbers.}$

Explanation:

Real numbers may include positive and negative integers, rational numbers, and also irrational numbers.

Rational numbers are terms that can be expressed as ratios of numbers, such as $\frac{3}{7}$ .

Real numbers cannot include infinity or imaginary numbers, such as $i=\sqrt{-1}$ .

However, the imaginary term provided in the answer choice is not fully simplified.

$i^4 = i^2\cdot i^2 = (-1)(-1) = 1$

This value is a real number.

The term $\frac{\pi}{e}$ is an irrational number, and is considered a real number.

The term $\sqrt{30}$ is also irrational, and is a real number.

The correct answer is: $\textup{All of the answers are real numbers.}$

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Example Question #1 : Types Of Numbers

Which of the following describes the number $\pi$ ?

Possible Answers:

real, rational

real, natural

imaginary, irrational

real, irrational

Correct answer:

real, irrational

Explanation:

$\pi$ is a real number, because you can represent it on the Cartesian coordinate plane, but it is irrational because it cannot be represented by a fraction of two integers. Natural numbers are integers greater than 0.

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Example Question #5074 : Algebra Ii

Which of the following sets of numbers contain only natural numbers.

Possible Answers:

3, 5, 2, 1

$\sqrt{2}$ , 1, 5, 6

1.3, 2, 5, 7.9

-1, 3, 4, 100

Correct answer:

3, 5, 2, 1

Explanation:

Natural numbers are simply whole, non-negative numbers.

Using this definition, we see only one set of numbers within our answer choices containing only whole, non-negative numbers. Any set containing decimals or negative numbers, will violate our defintion of natural numbers and thus be an incorrect answer.

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Example Question #2 : Types Of Numbers

What is the value of i^6 ?

Possible Answers:

Correct answer:

Explanation:

There is a repeating pattern of four exponent values of i: i^1=i, i^2=-1, i^3=-1, i^4=1 .

i^6 is the same as i^2 .

$i^6=i^2\cdot i^2 \cdot i^2=(-1)(-1)(-1)=-1$

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Example Question #3 : Types Of Numbers

Simplify (i-4)(2i+2) .

Possible Answers:

-6i-6

-6i-10

6i+4

Correct answer:

-6i-10

Explanation:

Multiplying out using FOIL (First, Inner, Outer, Last) results in,

2i^2-8i+2i-8 .

Remember that i^2=-1

2(-1)-8i+2i-8=-6i-10

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #5071 : Algebra Ii

Example Question #5072 : Algebra Ii

Example Question #5073 : Algebra Ii

Example Question #19 : Number Theory

Example Question #5075 : Algebra Ii

Example Question #21 : Real Numbers

Example Question #1 : Types Of Numbers

Example Question #5074 : Algebra Ii

Example Question #2 : Types Of Numbers

Example Question #3 : Types Of Numbers

All Algebra II Resources

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