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SSAT Upper Level Math : Algebra

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Properties Of Exponents

$(-4)^{2} + (-4)^{3}$

Possible Answers:

-1,024

Correct answer:

Explanation:

$(-4)^{2} = -4 \cdot (-4) = +(4\cdot 4) = 16$

$(-4)^{3} = -4 \cdot (-4)\cdot (-4) = 16 \cdot (-4) = - (16 \cdot 4) = -64$

Therefore,

$(-4)^{2} + (-4)^{3} = 16 + (-64) = - (64-16) = -48$

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Example Question #61 : Algebra

Express 0.00000000000097 in scientific notation.

Possible Answers:

$0.97 \times 10 ^{-12}$

$97 \times 10 ^{-14}$

$0.97 \times 10 ^{-13}$

$9.7 \times 10 ^{-13}$

$9.7 \times 10 ^{-12}$

Correct answer:

$9.7 \times 10 ^{-13}$

Explanation:

To rewrite a very small number in scientific notation:

Write the number.

0.00000000000097

Move the decimal point right as many places as needed until it follows the first nonzero digit, which here is the nine. Count the number of places it is moved - here it will be thirteen places.

The number formed is 9.7 , which will be placed in front; , the negative of the number of places counted, will be the exponent. The number, in scientific notation, will be $9.7 \times 10 ^{-13}$ .

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Example Question #8 : How To Find The Properties Of An Exponent

Evaluate:

$\frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}}$

Possible Answers:

-6,250

$-\frac{2}{3,125}$

$-\frac{1}{6,250}$

The quantity is undefined.

Correct answer:

The quantity is undefined.

Explanation:

$5^{5} = 5 \times 5 \times 5 \times 5 \times 5 = 3,125$

$\left (-5 \right ) ^{5} = -\left ( 5^{5} \right ) = -3,125$

$\frac{\left ( -5\right ) ^{5} - 5^{5}}{\left ( -5\right ) ^{5} + 5^{5}} = \frac{-3,125 -3,125}{-3,125 + 3,125} =\frac{-6,250}{0}$

This is an undefined quantity.

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Example Question #9 : How To Find The Properties Of An Exponent

Evaluate:

$\frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} }$

Possible Answers:

$\frac{1}{2}$

The quantity is undefined.

$-\frac{1}{2}$

$\frac{1}{256}$

Correct answer:

$\frac{1}{2}$

Explanation:

$4^{4} = 4 \times 4 \times 4 \times 4 = 256$

$\left (- 4 \right ) ^{4} = \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) \times \left (- 4 \right ) = 256$

$\frac{4^{4}}{4^{4} +\left ( -4 \right ) ^{4} } = \frac{256 }{256 + 256} = \frac{256 }{512} =\frac{1 }{2}$

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Example Question #62 : Algebra

Evaluate:

$(100 - 4 \cdot 25) ^{100 \div 25 }$

Possible Answers:

The expression is undefined.

100

100,000,000

Correct answer:

Explanation:

$(100 - 4 \cdot 25) ^{100 \div 25 } = (100 - 100) ^{4} = 0 ^{4} =0$

as 0 taken to any positive power is equal to 0.

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Example Question #11 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Evaluate:

$(80 - 4 \cdot 25) ^{100 \div 25 }$

Possible Answers:

-16,000

16,000

-160,000

160,000

The expression is undefined.

Correct answer:

160,000

Explanation:

$(80 - 4 \cdot 25) ^{100 \div 25 }$

$= (80 - 100) ^{4 }$

$= (-20) ^{4 }$

= (-20) (-20) (-20) (-20) = 160,000

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Example Question #63 : Algebra

If $\dpi{100} x=\sqrt{34}$ then

Possible Answers:

x< 5

5< x< 6

x=4.56

6< x< 7

Correct answer:

5< x< 6

Explanation:

$\dpi{100} \sqrt{25}=5$

$\dpi{100} \sqrt{36}=6$

34 is between 25 and 36, thus its square root must be between the square roots of 25 and 36. x must be a number between 5 and 6.

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Example Question #64 : Algebra

Express the result in scientific notation:

$\left ( 3 \times 10 ^{4}\right )^{3}$

Possible Answers:

$9\times 10 ^{12}$

$27 \times 10 ^{12}$

$9\times 10 ^{7}$

$2.7 \times 10 ^{8}$

$2.7 \times 10 ^{13}$

Correct answer:

$2.7 \times 10 ^{13}$

Explanation:

Applying the power of a product property of exponents, then the power of a power property:

$\left ( 3 \times 10 ^{4}\right )^{3} = 3^{3}\times\left ( 10 ^{4}\right )^{3} = 27 \times 10 ^{4 \times3} = 27 \times 10 ^{12}$

This is not in scientific notation, so we adjust it as follows, applying the product of powers property:

$27 \times 10 ^{12} = 2.7 \times 10 ^{1} \times 10 ^{12} = 2.7 \times 10 ^{1+ 12} =2.7 \times 10 ^{13}$

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Example Question #67 : Algebra

Assume all variables to be nonzero.

Simplify: $4 \left ( xyz \right ) ^{3} (xyz) ^{0}$

Possible Answers:

$4 x^{3}y ^{3}z^{3}$

$12 x^{3}y ^{3}z^{3}$

$64 x^{3}y ^{3}z^{3}$

Correct answer:

$4 x^{3}y ^{3}z^{3}$

Explanation:

Since any nonzero expression taken to the power of 0 is equal to 1,

$4 \left ( xyz \right ) ^{3} (xyz) ^{0} = 4 \left ( xyz \right ) ^{3} \cdot 1 = 4 \left ( xyz \right ) ^{3}$

Using the power of a product property of exponents, this becomes

$4 \left ( xyz \right ) ^{3} = 4 x^{3}y^{3}z^{3}$

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Example Question #13 : How To Find The Properties Of An Exponent

Express the result in scientific notation:

$(2 \times 10^{3}) (3 \times 10^{4}) (5 \times 10^{5})$

Possible Answers:

$3 \times 10^{12}$

$3 \times 10^{61}$

$30 \times 10^{60}$

$3 \times 10^{13}$

$30 \times 10^{12}$

Correct answer:

$3 \times 10^{13}$

Explanation:

Apply the product of powers property:

$(2 \times 10^{3}) (3 \times 10^{4}) (5 \times 10^{5})$

$= 2 \times 3 \times 5 \times 10^{3} \times 10^{4} \times 10^{5}$

$= 30 \times 10^{3+4+5}$

$= 30 \times 10^{12}$

Since this is not in scientific notation, adjust as follows:

$30 \times 10^{12}$

$= 3 \times 10^{1} \times 10^{12}$

$= 3 \times 10^{1+12}$

$= 3 \times 10^{13}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Algebra

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #5 : Properties Of Exponents

Example Question #61 : Algebra

Example Question #8 : How To Find The Properties Of An Exponent

Example Question #9 : How To Find The Properties Of An Exponent

Example Question #62 : Algebra

Example Question #11 : Generate Equivalent Numerical Expressions: Ccss.Math.Content.8.Ee.A.1

Example Question #63 : Algebra

Example Question #64 : Algebra

Example Question #67 : Algebra

Example Question #13 : How To Find The Properties Of An Exponent

All SSAT Upper Level Math Resources

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