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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #52 : Squaring / Square Roots / Radicals

Evaluate:

$i^{-31}$

Possible Answers:

The expression is undefined

Correct answer:

Explanation:

$a^{-m}$ is defined to be equal to $\frac{1}{a^{m}}$ for any real or imaginary and for any real ; therefore,

$i^{-31} = \frac{1}{i^{31}}$

To evaluate a positive power of , divide the power by 4 and note the remainder:

$31 \div 4= 7 \textrm{ R }3$

Therefore,

$i ^{31} = i ^{3} = -i$

Substituting,

$i^{-31} = \frac{1}{-i}$

Rationalizing the denominator by multiplying both numerator and denominator by :

$i^{-31} = \frac{1 \cdot i}{-i \cdot i }= \frac{ i}{-i ^{2}}= \frac{ i}{-(-1)}= \frac{ i}{1}= i$

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Example Question #1 : Exponents And Rational Numbers

Solve for .

$2^{x}= 64$

Possible Answers:

x=-6

x=6

x=5

$x=64^{2}$

x=64

Correct answer:

x=6

Explanation:

Since $2^{x}= 2^{6}$

Hence x=6

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Example Question #222 : Exponents

Simplify:

$\sqrt[3]{x^{10}y^{8}z^{9}}$

Possible Answers:

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

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

$\sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}^{\sqrt[3]{xyz}}$

$x^{3}y^{2}z^{3}$

Correct answer:

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Explanation:

$\sqrt[3]{x^{9}xy^{6}y^{2}z^{9}}=x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

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Example Question #2 : Exponents And Rational Numbers

Solve for :

$\sqrt{x} -1= 4$

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

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Example Question #224 : Exponents

Evaluate:

$\log 0.1=$

Possible Answers:

$\frac{1}{10}$

Correct answer:

Explanation:

$0.1= 10^{-1}$

$\log 0.1=-1$

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Example Question #225 : Exponents

Solve for .

$\log_{2}x=4$

Possible Answers:

Correct answer:

Explanation:

$x= 2^4{}= 16$

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Example Question #3 : Exponents And Rational Numbers

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

Possible Answers:

$a^{2}$

a+b

$b^{2}$

Correct answer:

a+b

Explanation:

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is a+b .

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Example Question #4 : Exponents And Rational Numbers

Solve for .

$\log (x+3)+\log x=1$

Possible Answers:

$5\ or\ -2$

$-5\ or\ 2$

Correct answer:

Explanation:

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence, $x(x+3)=10^{1}$

$x^{2}+3x=10$

x^2+3x-10=0

By fatoring we get (x+5)(x-2)=0

Hence $x=-5\ or\ 2$ .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

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Example Question #5 : Exponents And Rational Numbers

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

Possible Answers:

125

Correct answer:

Explanation:

The answer is 3³ = 27

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Example Question #6 : Exponents And Rational Numbers

Solve for .

$\log _{9}x=\frac{1}{2}$

Possible Answers:

Correct answer:

Explanation:

$\log _{9}x=\frac{1}{2}$

$x = 9^{\frac{1}{2}}= 3$

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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #52 : Squaring / Square Roots / Radicals

Example Question #1 : Exponents And Rational Numbers

Example Question #222 : Exponents

Example Question #2 : Exponents And Rational Numbers

Example Question #224 : Exponents

Example Question #225 : Exponents

Example Question #3 : Exponents And Rational Numbers

Example Question #4 : Exponents And Rational Numbers

Example Question #5 : Exponents And Rational Numbers

Example Question #6 : Exponents And Rational Numbers

All SAT Math Resources

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