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SAT Math : Algebra

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Example Questions

Example Question #1 : Exponential Ratios And Rational Numbers

Com_exp_1

Which of the following lists the above quantities from least to greatest?

Possible Answers:

I, IV, II, III

II, III, I, IV

I, IV, III, II

IV, III, II, I

I, III, II, IV

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

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Example Question #1 : How To Find A Rational Number From An Exponent

$Simplify: \frac{\sqrt[3]{81}}{\sqrt[3]{3}}$

Possible Answers:

$\frac{\sqrt[3]{9\star 9}}{\sqrt[3]{9}}= \sqrt[3]{9}$

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \frac{3}{1}= 3$

$\sqrt[3]{81\star 3}= \sqrt[3]{243} = 6.24$

$\frac{81}{3}= 27$

Correct answer:

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

Explanation:

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

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Example Question #2 : How To Find A Rational Number From An Exponent

Rationalize the denominator:

$\frac{1}{2-\sqrt{3}}$

Possible Answers:

$2+\sqrt{3}$

$\sqrt{3}$

$2-\sqrt{3}$

$\frac{2+\sqrt{3}}{7}$

Correct answer:

$2+\sqrt{3}$

Explanation:

The conjugate of $2-\sqrt{3}$ is $2+\sqrt{3}$ .

Now multiply both the numerator and the denominator by $2+\sqrt{3}$

and you get:

$\frac{2+\sqrt{3}}\left ({2-\sqrt{3}} \right )\left ( 2+\sqrt{3} \right )$

$\left ( 2-\sqrt{3} \right )\left ( 2+\sqrt{3} \right ) =2^{2}-\left ( \sqrt{3} \right )^{2} =4-3 = 1$

Hence we get

$\frac{2+\sqrt{3}}{1} = 2+\sqrt{3}$

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Example Question #1 : How To Find A Rational Number From An Exponent

Solve for :

$3^{x-5} = \frac{1}{27}$

Possible Answers:

Correct answer:

Explanation:

$3^{x-5}=\frac{1}{27}=3^{-3}$

x-5=-3

x=2

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Example Question #2 : How To Find A Rational Number From An Exponent

Solve for .

$\log _{5}x=2$

Possible Answers:

125

Correct answer:

Explanation:

$log_5{x} = 2$

$x = 5^{2} = 25$

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Example Question #3 : How To Find A Rational Number From An Exponent

If,

$log_a{120}= log_b{120}$

What does a=?

Possible Answers:

$\frac{a}{b}= 120$

a=10

b=10

a=b

ab=10

Correct answer:

a=b

Explanation:

If $log_a{x} = log_b{x}$ ,

then a=b .

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Example Question #4 : How To Find A Rational Number From An Exponent

$\sqrt{x+3} -x = 1$

Possible Answers:

x=1

x=9

x=4

x=13

x=0

Correct answer:

x=1

Explanation:

From the equation in the problem statement

$\sqrt{x+3} = x + 1$

Now squaring both sides we get

$x+3=x^{2}+2x+1$ this is a quadratic equation which equals

$x^{2}+x -2 = 0$

and the factors of this equation are

$\left ( x+2 \right )\left ( x-1 \right )$

This gives us $x=-2\ or\ x=1$ .

However, if we plug these solutions back into the original equation, does not create an equality. Therefore, x=-2 is an extraneous solution.

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Example Question #641 : Algebra

If 8〖(2)〗^x= 2^y, what is x in terms of y?

Possible Answers:

y – 3

y + 1

y – 1

y + 3

Correct answer:

y – 3

Explanation:

We replace 8 with 2³ so that each term has the same base, making the equation 2³ 2^x= 2^y. The terms on the left now have the same base, so we add the exponents to get 2^3+x= 2^y. Taking the log₂ of each side gives 3 + x = y, and therefore x = y – 3.

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Example Question #642 : Algebra

What is the number $\dpi{100} \small 256,000,000,000$ in scientific notation?

Possible Answers:

$\dpi{100} \small 2.56\times 10^{11}$

$\dpi{100} \small 2.56\times 10^{12}$

$\dpi{100} \small 2.56\times 10^{9}$

$\dpi{100} \small 2.56\times 10^{10}$

$\dpi{100} \small 2.56\times 10^{13}$

Correct answer:

$\dpi{100} \small 2.56\times 10^{11}$

Explanation:

$\dpi{100} \small 256,000,000,000 = 2.56\times 10^{11}$

The exponent is equal to the number of decimal points shifted.

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Example Question #643 : Algebra

Convert from scientific to decimal notation:

$2.3\times 10^{4}$

Possible Answers:

2300

230,000

0.00023

0.0023

23,000

Correct answer:

23,000

Explanation:

In this case the exponent is positive hence you have to move the decimal point 4 places to the right from where it is in the problem giving us

23,000

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SAT Math : Algebra

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Exponential Ratios And Rational Numbers

Example Question #1 : How To Find A Rational Number From An Exponent

Example Question #2 : How To Find A Rational Number From An Exponent

Example Question #1 : How To Find A Rational Number From An Exponent

Example Question #2 : How To Find A Rational Number From An Exponent

Example Question #3 : How To Find A Rational Number From An Exponent

Example Question #4 : How To Find A Rational Number From An Exponent

Example Question #641 : Algebra

Example Question #642 : Algebra

Example Question #643 : Algebra

All SAT Math Resources

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