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ISEE Middle Level Math : Algebraic Concepts

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All ISEE Middle Level Math Resources

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Example Questions

Example Question #1 : Algebraic Concepts

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

Possible Answers:

13.5

Correct answer:

Explanation:

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

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

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

The answer is 36.

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Example Question #2 : How To Multiply Variables

Simplify:

4 (2x + 7) - 4

Possible Answers:

8x + 12

4x + 24

8x + 3

8x + 24

4x + 12

Correct answer:

8x + 24

Explanation:

4 (2x + 7) - 4

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

=8x + 28 - 4

=8x + 24

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Example Question #1 : Multiplying And Dividing Polynomials

Multiply:

4x(3x-2)

Possible Answers:

12x^2-8x

12x+8

12x-8

12x^2+8x

Correct answer:

12x^2-8x

Explanation:

Use the distributive property:

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

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Example Question #1 : Algebraic Concepts

$14s \cdot 3s=$

Possible Answers:

13s

17s

$42s^{2}$

48s

Correct answer:

$42s^{2}$

Explanation:

Multiply the numbers and multiply the variables:

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

Answer: $42s^{2}$

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Example Question #2 : Algebraic Concepts

Simplify:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #2 : Algebraic Concepts

Multiply:

-4x(x+3)

Possible Answers:

4x^2-12x

-4x^2-12x

-4x^2+12x

4x^2+12x

Correct answer:

-4x^2-12x

Explanation:

-4x(x+3)=(-4x)(x)+(-4x)3=-4x^2+(-12x)

=-4x^2-12x

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Example Question #2 : Algebraic Concepts

67h*3h=

Possible Answers:

201h

$201h^{2}$

200h

$200h^{2}$

Correct answer:

$201h^{2}$

Explanation:

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

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

Answer: $201h^{2}$

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Example Question #6 : Operations

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

Possible Answers:

$1806k^{3}$

$1806k^{4}$

1806k

$1204k^{4}$

Correct answer:

$1806k^{4}$

Explanation:

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

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

Answer: $1806k^{4}$

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Example Question #5 : How To Multiply Variables

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

Possible Answers:

90n

452n

$225n^{4}$

$45n^{4}$

Correct answer:

$225n^{4}$

Explanation:

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

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

Answer: $225n^{4}$

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Example Question #6 : How To Multiply Variables

33d*11d=

Possible Answers:

363d

$363d^{3}$

$3311d^{2}$

$363d^{2}$

Correct answer:

$363d^{2}$

Explanation:

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

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

Answer: $363d^{2}$

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Algebraic Concepts

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 #2 : How To Multiply Variables

Example Question #1 : Multiplying And Dividing Polynomials

Example Question #1 : Algebraic Concepts

Example Question #2 : Algebraic Concepts

Example Question #2 : Algebraic Concepts

Example Question #2 : Algebraic Concepts

Example Question #6 : Operations

Example Question #5 : How To Multiply Variables

Example Question #6 : How To Multiply Variables

All ISEE Middle Level Math Resources

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