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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2021 : Algebra Ii

Evaluate the expression $x^{y}-z^{x}+x^{z}$ when x=2 , y=3 , and z=4 .

Possible Answers:

Correct answer:

Explanation:

First, substitute for , for , and for : $(2)^{3}-(4)^{2}+(2)^{4}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

8-16+16

Leaving you with,

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Example Question #131 : Expressions

Evaluate the expression $x(a+b)-x^{a}$ when a=2 , b=10 , and x=3 .

Possible Answers:

Correct answer:

Explanation:

First, substitute for , for , and for : $(3)(2+10)-(3)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

(3)(12)-(9)

36-9

Leaving you with,

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Example Question #2023 : Algebra Ii

Evaluate the expression $14-2c+d^{2}-c^{2}$ given c=12 and d=11 .

Possible Answers:

Correct answer:

Explanation:

First, substitute for and for : $14-2(12)+(11)^{2}-(12)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

14-2(12)+(121)-(144)

14-24+121-144

Leaving you with,

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Example Question #2024 : Algebra Ii

Evaluate the expression $5y+x^{2}(x-7)$ when x=8 and y=11 .

Possible Answers:

121

117

119

Correct answer:

119

Explanation:

First, substitute for and for : $5(11)+(8)^{2}((8)-7)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

5(11)+(64)(1)

55+64

Leaving you with,

119

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Example Question #2025 : Algebra Ii

Evaluate the expression $b^{4}+3a-9$ when a=6 and b=5 .

Possible Answers:

423

634

566

285

709

Correct answer:

634

Explanation:

First, you subsitute for and for : $(5)^{4}+3(6)-9$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

625+3(6)-9

625+18-9

Leaving you with,

634

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Example Question #2026 : Algebra Ii

If f(x)= 2x^2+1 and g(x)=x-3 , what is f(g(2)) ?

Possible Answers:

Correct answer:

Explanation:

To begin solving, first we would plug in to g(x) for every there is, making it:

g(2)=(2)-3

Solving, we get:

g(2)=-1

We would then put that solution into f(x) for every there is, making it:

$f(g(2))=2(-1)^{2}+1$

Following the order of operations, the first thing we do is square :

$-1 \times -1 = 1$

We can then solve the rest of the expression:

f(g(2))=2(1)+1

f(g(2))=3

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Example Question #2021 : Algebra Ii

Solve the expression: -6(x-6)^2-3x+2

Possible Answers:

-6x^2-69x+214

-6x^2+69x-214

-6x^2+69x-218

-6x^2-75x+218

-6x^2+69x-216

Correct answer:

-6x^2+69x-214

Explanation:

Evaluate the binomial squared first by order of operations.

(x-6)^2 = (x-6)(x-6)

= x(x)+(x)(-6)+(-6)(x)+(-6)(-6)

x^2-12x+36

The expression becomes:

-6(x^2-12x+36)-3x+2

Distribute the negative six through each term of the trinomial.

-6x^2+72x-216-3x+2

Combine like-terms.

The answer is: -6x^2+69x-214

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Example Question #2028 : Algebra Ii

Solve the expression if a=3 : 6a(a^2-a^3)

Possible Answers:

648

324

Correct answer:

Explanation:

Substitute the value of into the given expression.

6(3)((3)^2-(3)^3)

Simplify the parentheses by order of operations.

18(9-27) = 18(-18) = -324

The answer is:

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Example Question #2029 : Algebra Ii

If a=5 and b=6 , evaluate: $\frac{1}{b}-\frac{b}{a}$

Possible Answers:

$-\frac{19}{30}$

$-\frac{29}{30}$

$-\frac{31}{30}$

$-\frac{2}{5}$

$-\frac{41}{30}$

Correct answer:

$-\frac{31}{30}$

Explanation:

Substitute the assigned values into the expression.

$\frac{1}{b}-\frac{b}{a} = \frac{1}{6}-\frac{6}{5}$

Convert the fractions to a common denominator.

$\frac{1}{6}-\frac{6}{5} = \frac{1(5)}{6(5)}-\frac{6(6)}{5(6)} = \frac{5}{30}- \frac{36}{30}$

Now that the denominators are common, the numerators can be subtracted.

The answer is: $-\frac{31}{30}$

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Example Question #181 : Basic Single Variable Algebra

If a=4 and b=6 , determine: a(2-b)-a

Possible Answers:

Correct answer:

Explanation:

Substitute the values into the expression.

a(2-b)-a = 4(2-6)-4

Simplify the expression by distribution.

4(2-6)-4 = 4(-4)-4 = -16-4 = -20

The answer is:

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2021 : Algebra Ii

Example Question #131 : Expressions

Example Question #2023 : Algebra Ii

Example Question #2024 : Algebra Ii

Example Question #2025 : Algebra Ii

Example Question #2026 : Algebra Ii

Example Question #2021 : Algebra Ii

Example Question #2028 : Algebra Ii

Example Question #2029 : Algebra Ii

Example Question #181 : Basic Single Variable Algebra

All Algebra II Resources

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