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ISEE Middle Level Math : Variables

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Algebraic Concepts

$6^{3} \div (11-5)=$ $\displaystyle 6^{3} \div (11-5)=$

Possible Answers:

13.5 $\displaystyle 13.5$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 36$

Correct answer:

$\displaystyle 36$

Explanation:

First find the exponent value: $6^{3}=216$ $\displaystyle 6^{3}=216$

Then find the value of $\left ( 11-5 \right )=6$ $\displaystyle \left ( 11-5 \right )=6$

Finally, solve the entire expression with the known values: $216\div 6=36$ $\displaystyle 216\div 6=36$

The answer is 36.

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Example Question #1 : Algebraic Concepts

Simplify:

$\displaystyle 4 (2x + 7) - 4$

Possible Answers:

8x + 3 $\displaystyle 8x + 3$

8x + 24 $\displaystyle 8x + 24$

4x + 12 $\displaystyle 4x + 12$

8x + 12 $\displaystyle 8x + 12$

4x + 24 $\displaystyle 4x + 24$

Correct answer:

8x + 24 $\displaystyle 8x + 24$

Explanation:

$\displaystyle 4 (2x + 7) - 4$

$=4 \cdot 2x + 4 \cdot 7 - 4$ $\displaystyle =4 \cdot 2x + 4 \cdot 7 - 4$

$\displaystyle =8x + 28 - 4$

$\displaystyle =8x + 24$

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Example Question #3 : Multiplying And Dividing Polynomials

Multiply:

$\displaystyle 4x(3x-2)$

Possible Answers:

$\displaystyle 12x^2+8x$

$\displaystyle 12x^2-8x$

12x+8 $\displaystyle 12x+8$

12x-8 $\displaystyle 12x-8$

Correct answer:

$\displaystyle 12x^2-8x$

Explanation:

Use the distributive property:

$4x(3x-2)=(4x\times3x)-(4x\times2)=12x^2-8x$ $\displaystyle 4x(3x-2)=(4x\times3x)-(4x\times2)=12x^2-8x$

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Example Question #2 : Algebraic Concepts

$14s \cdot 3s=$ $\displaystyle 14s \cdot 3s=$

Possible Answers:

48s $\displaystyle 48s$

13s $\displaystyle 13s$

17s $\displaystyle 17s$

$42s^{2}$ $\displaystyle 42s^{2}$

Correct answer:

$42s^{2}$ $\displaystyle 42s^{2}$

Explanation:

Multiply the numbers and multiply the variables:

$14\cdot 3\cdot s\cdot s=42s^{2}$ $\displaystyle 14\cdot 3\cdot s\cdot s=42s^{2}$

Answer: $42s^{2}$ $\displaystyle 42s^{2}$

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Example Question #641 : Concepts

Simplify:

$-8 (-2y^{2}+ 7y - 9)$ $\displaystyle -8 (-2y^{2}+ 7y - 9)$

Possible Answers:

$16y^{2} -56y+72$ $\displaystyle 16y^{2} -56y+72$

$16y^{2} +7y-9$ $\displaystyle 16y^{2} +7y-9$

$16y^{2} -7y+9$ $\displaystyle 16y^{2} -7y+9$

$16y^{2} -56y-72$ $\displaystyle 16y^{2} -56y-72$

Correct answer:

$16y^{2} -56y+72$ $\displaystyle 16y^{2} -56y+72$

Explanation:

$-8 (-2y^{2}+ 7y - 9)$ $\displaystyle -8 (-2y^{2}+ 7y - 9)$

$= -8\cdot (-2y^{2} ) +\left ( -8 \right ) \cdot 7y -\left ( - 8\right ) \cdot 9$ $\displaystyle = -8\cdot (-2y^{2} ) +\left ( -8 \right ) \cdot 7y -\left ( - 8\right ) \cdot 9$

$= 16y^{2} -56y+72$ $\displaystyle = 16y^{2} -56y+72$

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Example Question #1 : Algebraic Concepts

Multiply:

$\displaystyle -4x(x+3)$

Possible Answers:

$\displaystyle -4x^2-12x$

$\displaystyle 4x^2-12x$

$\displaystyle -4x^2+12x$

$\displaystyle 4x^2+12x$

Correct answer:

$\displaystyle -4x^2-12x$

Explanation:

$\displaystyle -4x(x+3)=(-4x)(x)+(-4x)3=-4x^2+(-12x)$

$\displaystyle =-4x^2-12x$

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Example Question #3 : Algebraic Concepts

67h*3h= $\displaystyle 67h*3h=$

Possible Answers:

200h $\displaystyle 200h$

201h $\displaystyle 201h$

$201h^{2}$ $\displaystyle 201h^{2}$

$200h^{2}$ $\displaystyle 200h^{2}$

Correct answer:

$201h^{2}$ $\displaystyle 201h^{2}$

Explanation:

Multiply the whole numbers and add an exponent to the variable totaling the number of exponents in the equation:

$67h*3h=201h^{2}$ $\displaystyle 67h*3h=201h^{2}$

Answer: $201h^{2}$ $\displaystyle 201h^{2}$

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Example Question #3 : Algebraic Concepts

$602k*3k^{3}=$ $\displaystyle 602k*3k^{3}=$

Possible Answers:

$1204k^{4}$ $\displaystyle 1204k^{4}$

$1806k^{3}$ $\displaystyle 1806k^{3}$

$1806k^{4}$ $\displaystyle 1806k^{4}$

1806k $\displaystyle 1806k$

Correct answer:

$1806k^{4}$ $\displaystyle 1806k^{4}$

Explanation:

Multiply the whole numbers and add an exponent to the variable totaling the number of exponents in the equation:

$602k*3k^{3}=1806k^{4}$ $\displaystyle 602k*3k^{3}=1806k^{4}$

Answer: $1806k^{4}$ $\displaystyle 1806k^{4}$

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Example Question #2 : How To Multiply Variables

$45n^{2}*5n^{2}=$ $\displaystyle 45n^{2}*5n^{2}=$

Possible Answers:

$45n^{4}$ $\displaystyle 45n^{4}$

452n $\displaystyle 452n$

$225n^{4}$ $\displaystyle 225n^{4}$

90n $\displaystyle 90n$

Correct answer:

$225n^{4}$ $\displaystyle 225n^{4}$

Explanation:

Multiply the whole numbers and add an exponent to the variable totaling the number of exponents in the equation:

$45n^{2}*5n^{2}=225n^{4}$ $\displaystyle 45n^{2}*5n^{2}=225n^{4}$

Answer: $225n^{4}$ $\displaystyle 225n^{4}$

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Example Question #3 : How To Multiply Variables

$\displaystyle 33d*11d=$

Possible Answers:

$363d^{3}$ $\displaystyle 363d^{3}$

$363d^{2}$ $\displaystyle 363d^{2}$

363d $\displaystyle 363d$

$3311d^{2}$ $\displaystyle 3311d^{2}$

Correct answer:

$363d^{2}$ $\displaystyle 363d^{2}$

Explanation:

Multiply the constants and add an exponent to the variable totaling the number of variables in the equation:

$33d*11d=363d^{2}$ $\displaystyle 33d*11d=363d^{2}$

Answer: $363d^{2}$ $\displaystyle 363d^{2}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Variables

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : Algebraic Concepts

Example Question #1 : Algebraic Concepts

Example Question #3 : Multiplying And Dividing Polynomials

Example Question #2 : Algebraic Concepts

Example Question #641 : Concepts

Example Question #1 : Algebraic Concepts

Example Question #3 : Algebraic Concepts

Example Question #3 : Algebraic Concepts

Example Question #2 : How To Multiply Variables

Example Question #3 : How To Multiply Variables

All ISEE Middle Level Math Resources

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