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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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 #43 : Operations

Multiply:

$z\cdot z^{2}=$

Possible Answers:

$z^{2}$

$z^{4}$

$z^{3}$

Correct answer:

$z^{3}$

Explanation:

To solve add the exponents:

$z*z^{2}=z^{3}$

Answer: $z^{3}$

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Example Question #44 : Operations

Multiply:

$z^{3}\cdot z^{9}=$

Possible Answers:

$z^{36}$

$z^{6}$

$z^{13}$

$z^{12}$

Correct answer:

$z^{12}$

Explanation:

To solve add the exponents:

$z^{3}\cdot z^{9}=z^{12}$

Answer: $z^{12}$

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Example Question #45 : Operations

Multiply:

$y^{22}\cdot y^{3}=$

Possible Answers:

y+25

$y^{25}$

$y^{19}$

Correct answer:

$y^{25}$

Explanation:

To solve add the exponents:

$y^{22}\cdot y^{3}=y^{25}$

Answer: $y^{25}$

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Example Question #46 : Operations

Multiply:

$p^{14}\cdot p^{16}=$

Possible Answers:

$p^{2}$

$p^{1416}$

$p^{30}$

Correct answer:

$p^{30}$

Explanation:

To solve add the exponents:

$p^{14}\cdot p^{16}=p^{30}$

Answer: $p^{30}$

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Example Question #47 : Operations

Simplify:

(435.35)^0

Possible Answers:

435.35

$435^{35}$

The expression is undefined

Correct answer:

Explanation:

Any non-zero number raised to the power of zero is equal to .

(435.35)^0=1

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Example Question #48 : Operations

Simplify:

$(x^4)^{\frac{5}{2}}$

Possible Answers:

$x^{20}$

x^5

$x^{12}$

$x^{10}$

$x^{8}$

Correct answer:

$x^{10}$

Explanation:

We can apply the power of a power property:

$(x^4)^{\frac{5}{2}}=x^{(4\times \frac{5}{2})}=x^{10}$

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Example Question #51 : Algebraic Concepts

Simplify:

$(4x^2y^3)^{3}$

Possible Answers:

64x^3y^8

48x^6y^9

64x^4y^9

64x^6y^8

64x^6y^9

Correct answer:

64x^6y^9

Explanation:

We can first apply the power of a product rule and then apply the power of a power rule. So we can write:

$(4x^2y^3)^{3}=(4)^3\times (x^2)^3\times (y^3)^3=64\times x^{(2\times 3)}\times y^{(3\times 3)}=64x^6y^9$

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Example Question #82 : Algebra

Simplify:

$(\frac{1}{4}x-\frac{3}{4})^{2}$

Possible Answers:

$\frac{x^2}{8}-\frac{3}{8}x+\frac{9}{16}$

$\frac{x^2}{16}+\frac{3}{8}x+\frac{9}{16}$

None of these

$\frac{x^2}{16}-\frac{3}{16}x+\frac{9}{16}$

$\frac{x^2}{16}-\frac{3}{8}x+\frac{9}{16}$

Correct answer:

$\frac{x^2}{16}-\frac{3}{8}x+\frac{9}{16}$

Explanation:

We can solve it using the pattern for the square of a binominal or by using FOIL:

$(\frac{1}{4}x-\frac{3}{4})^{2}=(\frac{1}{4}x)^2-(2)( \frac{1}{4}x)( \frac{3}{4})+(\frac{3}{4})^2$

$=\frac{x^2}{16}-\frac{3}{8}x+\frac{9}{16}$

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Example Question #83 : Algebra

Simplify:

$(\frac{2}{5}x-\frac{1}{2})^{2}$

Possible Answers:

$\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{4}$

$\frac{4}{25}x^2+\frac{2}{5}x+\frac{1}{4}$

None of these

$\frac{4}{25}x^2-\frac{2}{5}x-\frac{1}{4}$

$\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{2}$

Correct answer:

$\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{4}$

Explanation:

We can solve it using the pattern for the square of a binominal or by using FOIL:

$(\frac{2}{5}x-\frac{1}{2})^{2}=(\frac{2}{5}x)^2-(2) (\frac{2}{5}x) (\frac{1}{2})+(\frac{1}{2})^2$

$=\frac{4}{25}x^2-\frac{2}{5}x+\frac{1}{4}$

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Example Question #52 : Algebraic Concepts

2 rabbits give birth to a litter of 8 rabbits. Each pair in that litter creates 4 rabbits. How many rabbits are there total, including the original 2 rabbits and their 8 children?

Possible Answers:

Correct answer:

Explanation:

If there are 8 rabbits, then that means there are 4 pairs of rabbits.

If each pair gives birth to 4 rabbits, that means there will be 16 rabbits produced by the litter ( $4\cdot4=16$ ).

Thus, the total number of rabbits is equal to 2+8+16=26 .

Thus, 26 is the correct answer.

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All ISEE Middle Level Math Resources

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

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ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #43 : Operations

Example Question #44 : Operations

Example Question #45 : Operations

Example Question #46 : Operations

Example Question #47 : Operations

Example Question #48 : Operations

Example Question #51 : Algebraic Concepts

Example Question #82 : Algebra

Example Question #83 : Algebra

Example Question #52 : Algebraic Concepts

All ISEE Middle Level Math Resources

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