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Algebra II : Mathematical Relationships and Basic Graphs

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Example Questions

Example Question #12 : Elementary Operations

Simplify the following expression:

$\displaystyle 117+(-33)-88$

Possible Answers:

$\displaystyle -104$

$\displaystyle -4$

$\displaystyle 4$

$\displaystyle 45$

Correct answer:

$\displaystyle -4$

Explanation:

Simplify the following expression:

$\displaystyle 117+(-33)-88$

Let's break this into parts.

First, realize that adding a negative number is the same as subtracting that number:

$\displaystyle 117-33=84$

Next, subtract the 88:

$\displaystyle 84-88=-4$

Our answer must be negative, because 88 is bigger than 84. Therefore our answer is -4

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Example Question #14 : Addition And Subtraction

If $f(x)=3x^{2}-4x+2$ $\displaystyle f(x)=3x^{2}-4x+2$ and $g(x)=2x^{2}+x+3$ $\displaystyle g(x)=2x^{2}+x+3$, what is $\displaystyle f(x)+g(x)$?

Possible Answers:

$2x^{2}+3x-5$ $\displaystyle 2x^{2}+3x-5$

$5x^{2}-3x+5$ $\displaystyle 5x^{2}-3x+5$

$x^{2}-5x-1$ $\displaystyle x^{2}-5x-1$

$6x^{4} -3x^{3}+2x^{2}-4x+6$ $\displaystyle 6x^{4} -3x^{3}+2x^{2}-4x+6$

$6x^{2}-4x+6$ $\displaystyle 6x^{2}-4x+6$

Correct answer:

$5x^{2}-3x+5$ $\displaystyle 5x^{2}-3x+5$

Explanation:

When we add the functions together, we can only add terms that have matching exponents. First, let's add the terms that are squared:

$3x^{2}+2x^{2}=5x^{2}$ $\displaystyle 3x^{2}+2x^{2}=5x^{2}$

Next, let's do the linear terms:

$\displaystyle -4x + x = -3x$

Finally, we add the constants:

$\displaystyle 2 + 3 = 5$

Then we collect all the terms back together:

$f(x)+g(x)=5x^{2}-3x+5$ $\displaystyle f(x)+g(x)=5x^{2}-3x+5$

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Example Question #2222 : Mathematical Relationships And Basic Graphs

Add the following numbers: $\displaystyle 973+287+188$

Possible Answers:

1458 $\displaystyle 1458$

1448 $\displaystyle 1448$

1428 $\displaystyle 1428$

1548 $\displaystyle 1548$

1568 $\displaystyle 1568$

Correct answer:

1448 $\displaystyle 1448$

Explanation:

Add the ones digits.

$\displaystyle 3+7+8 = 18$

The tens place is the carry over.

Add the tens digits with the carry over.

$\displaystyle 7+8+8+(1) = 24$

The tens place is the carry over for the next calculation.

Add the hundreds place with the carryover.

$\displaystyle 9+2+1+(2)= 14$

Combine this number with the ones digits of the previous calculations.

The answer is: 1448 $\displaystyle 1448$

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Example Question #4884 : Algebra Ii

Add the following numbers: $\displaystyle 3196+8541$

Possible Answers:

12737 $\displaystyle 12737$

11647 $\displaystyle 11647$

11637 $\displaystyle 11637$

11737 $\displaystyle 11737$

11727 $\displaystyle 11727$

Correct answer:

11737 $\displaystyle 11737$

Explanation:

Add the ones digits.

6+1=7 $\displaystyle 6+1=7$

Add the tens digits.

9+4=13 $\displaystyle 9+4=13$

The carryover is the tens digit.

Add the hundreds digits with the carryover.

$\displaystyle 1+5+(1)=7$

Add the thousands digits.

3+8=11 $\displaystyle 3+8=11$

Combine this number with the ones digits of the previous calculations.

The answer is: 11737 $\displaystyle 11737$

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Example Question #13 : Addition And Subtraction

Add the following numbers: $\displaystyle 2167+385+1473$

Possible Answers:

2825 $\displaystyle 2825$

3025 $\displaystyle 3025$

$\textup{The answer is not given.}$ $\displaystyle \textup{The answer is not given.}$

4025 $\displaystyle 4025$

2625 $\displaystyle 2625$

Correct answer:

4025 $\displaystyle 4025$

Explanation:

Add the ones digits.

$\displaystyle 7+5+3 = 15$

The carryover is the tens digit.

Add the tens digits with the carryover.

$\displaystyle 6+8+7+(1)=22$

The carryover is the tens digit.

Add the hundreds digits with the carryover.

$\displaystyle 1+3+4+(2)=10$

The carryover is the tens digit.

Add the thousands digits with the carryover. The thousands digit to 385 is zero.

$\displaystyle 2+0+1+(1)=4$

Combine all the ones digits from each calculation.

The answer is: 4025 $\displaystyle 4025$

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Example Question #18 : Elementary Operations

Solve: $\displaystyle 1874+381$

Possible Answers:

4694 $\displaystyle 4694$

2355 $\displaystyle 2355$

2265 $\displaystyle 2265$

2255 $\displaystyle 2255$

1255 $\displaystyle 1255$

Correct answer:

2255 $\displaystyle 2255$

Explanation:

Add the ones digits.

4+1=5 $\displaystyle 4+1=5$

Add the tens digits.

7+8=15 $\displaystyle 7+8=15$

The tens place will be the carryover.

Add the hundreds place with the carryover.

$\displaystyle 8+3+(1)= 12$

The tens place will be the carryover.

Add the thousands place with the carryover. The thousands place of 381 is zero.

$\displaystyle 1+0+(1)=2$

Combine all the ones digits from each calculation.

The answer is: 2255 $\displaystyle 2255$

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Example Question #15 : Addition And Subtraction

Add the numbers: $\displaystyle 1986+3218+3971$

Possible Answers:

8285 $\displaystyle 8285$

9185 $\displaystyle 9185$

9175 $\displaystyle 9175$

$\textup{The answer is not given.}$ $\displaystyle \textup{The answer is not given.}$

8175 $\displaystyle 8175$

Correct answer:

9175 $\displaystyle 9175$

Explanation:

Add the ones digits.

$\displaystyle 6+8+1= 15$

The carryover is the tens digit.

Add the tens digits with the carryover, one.

$\displaystyle 8+1+7+(1)=17$

The carryover is the tens digit.

Add the hundreds digits with the carryover, which is also one.

$\displaystyle 9+2+9+(1) = 21$

The carryover is the tens digit.

Add the thousands digits with the carryover, which is two.

$\displaystyle 1+3+3+2= 9$

Combine all the ones digits from the previous calculations.

The answer is: 9175 $\displaystyle 9175$

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Example Question #16 : Addition And Subtraction

Add the following numbers: $\displaystyle 1716+8946+1088$

Possible Answers:

11650 $\displaystyle 11650$

11850 $\displaystyle 11850$

11750 $\displaystyle 11750$

10650 $\displaystyle 10650$

10660 $\displaystyle 10660$

Correct answer:

11750 $\displaystyle 11750$

Explanation:

Add the ones digits.

$\displaystyle 6+6+8 = 20$

The two in the tens place is the carryover.

Add the tens digits with the carryover.

$\displaystyle 1+4+8+(2)=15$

The one in the tens place is the carryover.

Add the hundreds places with the carryover.

$\displaystyle 7+9+0+(1) =17$

The one in the tens place is the carryover.

Add the thousands places with the carryover.

$\displaystyle 1+8+1+(1) =11$

Combine this number with the ones digits from the previous calculations.

The answer is: 11750 $\displaystyle 11750$

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Example Question #4891 : Algebra Ii

Add the following numbers: $\displaystyle 1965+3979+2013$

Possible Answers:

7867 $\displaystyle 7867$

$\textup{The answer is not given.}$ $\displaystyle \textup{The answer is not given.}$

7797 $\displaystyle 7797$

7857 $\displaystyle 7857$

7957 $\displaystyle 7957$

Correct answer:

7957 $\displaystyle 7957$

Explanation:

Add the ones digits.

$\displaystyle 5+9+3=17$

The carryover is the tens place.

Add the tens digits with the carryover.

$\displaystyle 6+7+1+(1)= 15$

The carryover is the tens place.

Add the hundreds digits with the carryover.

$\displaystyle 9+9+0+(1)=19$

The carryover is the tens place.

Add the thousands digits with the carryover.

$\displaystyle 1+3+2+(1)=7$

The answer is: 7957 $\displaystyle 7957$

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Example Question #21 : Addition And Subtraction

Solve: $\displaystyle 117+981+318+996$

Possible Answers:

2412 $\displaystyle 2412$

1921 $\displaystyle 1921$

2411 $\displaystyle 2411$

2301 $\displaystyle 2301$

2392 $\displaystyle 2392$

Correct answer:

2412 $\displaystyle 2412$

Explanation:

Add the ones digits.

$\displaystyle 7+1+8+6 = 22$

The two in the tens digit is the carryover.

Add the tens digits with the carryover.

$\displaystyle 1+8+1+9+(2) = 21$

The two in the tens digit is the carryover.

Add the hundreds digits with the carryover.

$\displaystyle 1+9+3+9+(2) = 24$

Combine this number with the ones digits from the previous calculations.

The answer is: 2412 $\displaystyle 2412$

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #12 : Elementary Operations

Example Question #14 : Addition And Subtraction

Example Question #2222 : Mathematical Relationships And Basic Graphs

Example Question #4884 : Algebra Ii

Example Question #13 : Addition And Subtraction

Example Question #18 : Elementary Operations

Example Question #15 : Addition And Subtraction

Example Question #16 : Addition And Subtraction

Example Question #4891 : Algebra Ii

Example Question #21 : Addition And Subtraction

All Algebra II Resources

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