Algebraic Relationships
In this assessment, you will encounter a number of different questions that will assess both your understanding of mathematics and your ability to reason quantitatively.
Instructions
(Click to Read)
Do not use a calculator in this assessment. You shouldn’t need one to answer these questions, and the extra practice with arithmetic (long division, multidigit multiplication, etc.) will just make you a better math student!
Once you input your answer, click on “Check” to see immediate feedback about the question, including an explanation. You can also skip the question and come back to it later.
You may encounter different types of questions:
 Multiple Choice
 You will see several answer choices, but only one will be correct.
 Select the correct answer choice.
 FreeResponse (OpenEnded)
 You will not see any answer choices, and only one answer is correct.
 Type your answer into the space provided.
 For fractions, input your answer as “#/#” without the quotation marks, replacing the # with numbers. For example:
 to input an answer of \(\frac{1}{2}\), type “1/2” without the quotation marks.
 For decimals less than 1, input your answer with a leading zero. For example:
 to input an answer of \(0.5\), type “0.5” without the quotation marks.
 For whole numbers, just type the number into the space provided. For example:
 to input an answer of \(5\), type “5” without quotation marks.
 ChecktheBox
 You will see several answer choices, but one or more may be correct.
 Select all correct answer choices.
Tips
(Click to Read)
 These aren’t basic math questions – they’re tricky! Read closely and make sure you know what’s being asked.
 Do calculations on paper with a pencil. You don’t get extra credit for answering in your head!
Assessment Summary
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 Answered
 Review

Question 1 of 20
1. Question
What is the value of \(x\), if \(x8=3+5\)?
CorrectIncorrect 
Question 2 of 20
2. Question
What is the value of \(x\), if \(3x9=x3\)?
CorrectIncorrect 
Question 3 of 20
3. Question
If \(x>0\) and \(8x^2y^3=2x^4y^3\), what is the value of \(x\)?
CorrectIncorrect 
Question 4 of 20
4. Question
What is the value of \(m\), if \(9x^2+3=mx^2+\frac{1}{3}m\)?
CorrectIncorrect 
Question 5 of 20
5. Question
What is the value of \(b\), if \(aā 0\) and \(\frac{12a}{ab}=\frac{1}{2}\)?
CorrectIncorrect 
Question 6 of 20
6. Question
What is the value of \(d+f\), if \(d+2e+f=15\) and \(2e=8\)?
CorrectIncorrect 
Question 7 of 20
7. Question
What is the value of \(y\), if \(ax^2+2xb+y=45\) and \(x(ax+2b)=40\)?
CorrectIncorrect 
Question 8 of 20
8. Question
What is the value of \(x^2y^2\), if \(x+y=9\) and \(xy=5\)?Ā
CorrectIncorrect 
Question 9 of 20
9. Question
What is the value of \(\frac{x}{y}\), if \(4x+12y=15x10y\)?
CorrectIncorrect 
Question 10 of 20
10. Question
What is the value of \(\frac{1}{2}x\), if \(x2y+4z=2w8\)?
CorrectIncorrect 
Question 11 of 20
11. Question
What is the value of \(a+b\), if \(a^2=b^2+16\) and \(ab=2\)?
CorrectIncorrect 
Question 12 of 20
12. Question
If \(d\) and \(f\) are consecutive integers less than \(0\), where \(d\lt f\), which of the following has the lowest value?
CorrectIncorrect 
Question 13 of 20
13. Question
Using the information given, compare the quantity in Column A to the quantity in Column B.
\(0\lt a\lt b\)
Column A
\(\frac{a}{b}\)Column B
\(\frac{b}{a}\)CorrectIncorrect 
Question 14 of 20
14. Question
Using the information given, compare the quantity in Column A to the quantity in Column B.
\(x\) and \(y\) are integers and \(x\lt y\lt 0\).
Column A
\(x^{2}\)Column B
\(y^{2}\)CorrectIncorrect 
Question 15 of 20
15. Question
If \((x+y)^{1}=9^{1}\) and \((xy)^{1}=3^{1}\), what is the value of \(x^{2}y^{2}\)?
CorrectIncorrect 
Question 16 of 20
16. Question
Using the information given, compare the quantity in Column A to the quantity in Column B.
\(a+b=3\)
Column A
\(2(a+b)\)Column B
\(3(a+b)\)CorrectIncorrect 
Question 17 of 20
17. Question
Using the information given, compare the quantity in Column A to the quantity in Column B.
\(xā 0\)
Column A
\(x\), if \(6x^{2}\timesĀ y=2x^{3}\times y\)
Column B
\(x\), if \(9xy^2=x^{3}y^2\)
CorrectIncorrect 
Question 18 of 20
18. Question
Using the information given, compare the quantity in Column A to the quantity in Column B.
\(1\lt a\lt 0\) and \(1\lt b\lt 0\)
Column A
\(a^2b^2\)Column B
\(a^{2}b^{2}\)CorrectIncorrect 
Question 19 of 20
19. Question
If \(x>0\), what is the of \(x\) in the equation \(3x^2+9=36\)?
CorrectIncorrect 
Question 20 of 20
20. Question
Using the information given, compare the quantity in Column A to the quantity in Column B.
\(x^38=19\)
Column A
\(x\)Column B
\(\frac{1}{x}\)CorrectIncorrect