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ISEE Upper Level Math : Variables

Study concepts, example questions & explanations for ISEE Upper Level Math

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All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #31 : Operations

Divide:

$\frac{4x^{3}+8x^{2}-12x}{4x}$

Possible Answers:

$4x^{2}+8x-12$

$x^{2}+2x-3$

$x^{3}+2x^{2}-3x$

The expression cannot be simplified further.

$x^{4}+2x^{3}-3x^{2}$

Correct answer:

$x^{2}+2x-3$

Explanation:

To divide this problem we simplify it first. In this problem we can separate the big fraction into three smaller fractions.

$\frac{4x^{3}+8x^{2}-12x}{4x}=\frac{4x^{3}}{4x}+\frac{8x^{2}}{4x}-\frac{12x}{4x}$

Then from here, we can pull out a from both the numerator and denominator of each smaller fraction.

$\frac{4x(x^2)}{4x}+\frac{4x(2x)}{4x} - \frac{4x(3)}{4x}$

Now we cancel terms and get the following result:

x^2+2x-3

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Example Question #10 : How To Divide Variables

Simplify:

$\frac{2x^{4}+6x^{3}+8}{2x}$

Possible Answers:

$x^{3}+3x^{2}+4x$

$4x^{3}+12x^{2}+16x$

$4x^{3}+6x^{2}+16x$

$x^{3}+3x^{2}+4$

$x^{3}+3x^{2}+\frac{4}{x}$

Correct answer:

$x^{3}+3x^{2}+\frac{4}{x}$

Explanation:

To simplify this problem we first separate the large fraction into three smaller fractions.

$\frac{2x^{4}+6x^{3}+8}{2x}$

$=\frac{2x^{4}}{2x}+\frac{6x^{3}}{2x}+\frac{8}{2x}$

From here we can factor out from the numerator and denominator of the first two fractions.

$= \frac{2x(x^3)}{2x}+\frac{2x(3x^2)}{2x}+\frac{8}{2x}$

The can be canceled out in the first two fractions. From here we can factor out a from the numerator and denominator of the third fraction.

$=x^3+3x^2+\frac{2(4)}{2(x)}$

Thus becoming:

$=x^{3}+3x^{2}+\frac{4}{x}$

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Example Question #11 : How To Divide Variables

Divide:

$\frac{-4x^{4}-6x^{3}+8x^{2}}{2x^{2}}$

Possible Answers:

$-2x-3x^{2}+4$

$-2x^{3}-3x^{2}+4x$

$-2x^{2}-3x+4$

$-6x^{2}-8x+10$

$-2x^{2}-3x+8$

Correct answer:

$-2x^{2}-3x+4$

Explanation:

To divide this problem we start by simplify it. In this problem we can break the large fraction into three smaller fractions.

$\frac{-4x^{4}-6x^{3}+8x^{2}}{2x^{2}}=\frac{-4x^{4}}{2x^{2}}-\frac{6x^{3}}{2x^{2}}+\frac{8x^{2}}{2x^{2}}$

From here we can factor out a 2x^2 from the numerator and denominator of each fraction.

$\frac{2x^2(-2x^2)}{2x^2}- \frac{2x^2(3x)}{2x^2}+ \frac{2x^2(4)}{2x^2}$

Now we can cancel the 2x^2 terms and are left with the following result:

$-2x^{2}-3x+4$

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Example Question #32 : Operations

Simplify the following expression:

$\frac{343w^7}{49w^3}$

Possible Answers:

343w^4

$\frac{343w^4}{49}$

$\frac{49w^7}{w^3}$

7w^4

Correct answer:

7w^4

Explanation:

Simplify the following expression:

$\frac{343w^7}{49w^3}$

Let's begin by simplifying the coefficients

$\frac{343w^7}{49w^3}=\frac{49*7w^7}{49w^3}=\frac{7w^7}{w^3}$

Next, complete the question by subtracting the exponents:

$\frac{7w^7}{w^3}=7w^{7-3}=7w^4$

So, our answer is:

7w^4

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Example Question #33 : Operations

Simplify the following expression:

$\frac{49x^3y^5b^{12}}{7x^2y^6b^{8}}$

Possible Answers:

$\frac{49xb^4}{7y}$

$\frac{7xb^4}{y}$

7xb^4y

$\frac{7x^2b^4}{y}$

Correct answer:

$\frac{7xb^4}{y}$

Explanation:

Simplify the following expression:

$\frac{49x^3y^5b^{12}}{7x^2y^6b^{8}}$

Let's begin by simplifying the coefficients:

We have a 49 on top and a 7 on bottom. We can treat this just like a regular fraction:

$\frac{49}{7}=7$

Next, to deal with our variables, all we need to do is subtract the bottom exponent from the top exponent. If we get a negative number, we just put that number on the bottom.

$x^{3-2}=x^1=x$

$y^{5-6}=y^{-1}=\frac{1}{y}$

$b^{12-8}=b^4$

So our answer will look like this:

$\frac{7xb^4}{y}$

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Example Question #1 : How To Subtract Variables

Simplify:

5y + 4x + 8y - 12y

Possible Answers:

4x+y

9x-4y

4x-25y

9x+4y

4x-y

Correct answer:

4x+y

Explanation:

5y + 4x + 8y - 12y

= 4x + 5y+ 8y - 12y

$= 4x + \left ( 5+ 8 - 12 \right )y$

$= 4x + \left ( 13 - 12 \right )y$

= 4x + 1y

= 4x + y

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Example Question #921 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Simplify the expression:

18xy - 7y + 8xy + 8x

Possible Answers:

16x+ 11y

- 16x+ 11y

-8x - 7y +10 xy

27 xy

8x - 7y +26 xy

Correct answer:

8x - 7y +26 xy

Explanation:

Group and collect like terms:

18xy - 7y + 8xy + 8x

= 8x - 7y + 18xy + 8xy

$= 8x - 7y +\left ( 18 + 8 \right ) xy$

= 8x - 7y +26 xy

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Example Question #3 : How To Subtract Variables

Simplify:

10x - 5y + 8z -7y

Possible Answers:

The expression cannnot be simplified further.

5x -7y+ 8z

10x - 5y + z

10x - 12y + 8z

10x - 2y + 8z

Correct answer:

10x - 12y + 8z

Explanation:

Group and collect like terms:

10x - 5y + 8z -7y

=10x - 5y -7y + 8z

$=10x + \left (- 5 -7 \right )y + 8z$

$=10x + \left (- 12\right )y + 8z$

=10x - 12y + 8z

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Example Question #1 : How To Subtract Variables

x + y = 10

y+ z = 17

What is x - z ?

Possible Answers:

Insufficient information is given to answer this question.

Correct answer:

Explanation:

x -z = x + y - y + z = (x + y) - (y + z) = 10 - 17 = -7

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Example Question #31 : Operations

Simplify:

4x+3y+2x-5y

Possible Answers:

6x-2y

6x-8y

6x+8y

8x-3y

$6x^{2}-2y^{2}$

Correct answer:

6x-2y

Explanation:

To simplify this problem we need to combine like terms.

4x+3y+2x-5y

=4x+2x+3y-5y

=6x-2y

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : Variables

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #31 : Operations

Example Question #10 : How To Divide Variables

Example Question #11 : How To Divide Variables

Example Question #32 : Operations

Example Question #33 : Operations

Example Question #1 : How To Subtract Variables

Example Question #921 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #3 : How To Subtract Variables

Example Question #1 : How To Subtract Variables

Example Question #31 : Operations

All ISEE Upper Level Math Resources

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