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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #2421 : Sat Mathematics

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 #2422 : Sat Mathematics

If,

$log_a{120}= log_b{120}$

What does a=?

Possible Answers:

b=10

ab=10

a=b

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

a=10

Correct answer:

a=b

Explanation:

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

then a=b .

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Example Question #6 : How To Find A Rational Number From An Exponent

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

Possible Answers:

x=0

x=1

x=13

x=9

x=4

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 #1 : How To Use Scientific Notation

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

Possible Answers:

y + 1

y – 3

y + 3

y – 1

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 #2421 : Sat Mathematics

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

Possible Answers:

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

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

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

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

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

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 #2 : How To Use Scientific Notation

Convert from scientific to decimal notation:

$2.3\times 10^{4}$

Possible Answers:

0.0023

230,000

2300

0.00023

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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Example Question #2422 : Sat Mathematics

Convert from decimal to scientific notation:

0.0000034

Possible Answers:

$3.4\times 10^{6}$

$3.4\times 10^{-4}$

$3.4\times 10^{7}$

$3.4\times 10^{-6}$

$3.4\times 10^{-5}$

Correct answer:

$3.4\times 10^{-6}$

Explanation:

In this case you have to move the decimal point 6 places to the right. When you move the decimal point to the right the exponent becomes negative. Similarly when you move the decimal point to the left the exponent is positive. Also, to the left of the decimal place there can be only one digit.

$3.4* 10^{-6}$

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Example Question #5 : Other Exponents

What is the result when , 678 , 732 is rounded to the nearest thousand and then put in scientific notation?

Possible Answers:

$5.679 \times 10^{3}$

$5.679 \times 10^{6}$

$5.679 \times 10^{-6}$

$5.678 \times 10^{6}$

$5.678 \times 10^{3}$

Correct answer:

$5.679 \times 10^{6}$

Explanation:

First, when we round to the nearest thousand we get 5, 679, 000 since we round up when the next digit is greater than 5.

Then, to put it in scientific notation, we arrange the digits so that a decimal point creates a number between 1 and 10. We get 5.679.

Then, we want the exponent of the 10 to be the number of times the decimal needs to move to the right. This is 6 times.

Thus, we get our answer. $5.679 \times 10^6$

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Example Question #6 : Other Exponents

What is 0.000000537 in scientific notation?

Possible Answers:

$5.37\times 10^6$

$5.37\times 10^{-7}$

$5.37\times 10^{7}$

$5.37\times 10^{-6}$

5.37

Correct answer:

$5.37\times 10^{-7}$

Explanation:

In order to write a number in scientific notation, you must shift the number of decimal places to get a number in the ones place.

Since the original number is a decimal, the exponent will need to be negative. This eliminates three answer choices.

In order to get 0.000000537 into scientific notation with '5' in the ones place, you must shift the decimal over seven places.

Therefore, the final answer in scientific notation is $5.37 \times 10^{-7}$ .

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Example Question #4 : How To Use Scientific Notation

Express 0.00000956 in scientific notation.

Possible Answers:

$95.6\cdot10^{-7}$

$956\cdot10^{-8}$

$0.956 \cdot 10^{-5}$

None of the given answers.

$9.56 \cdot 10^{-6}$

Correct answer:

$9.56 \cdot 10^{-6}$

Explanation:

In scientific notation, we want one digit in the unit's place, followed by a decimal point and subsequent digits.

The exponent of 10 is the number of units the decimal point has been shifted.

For 0.00000956, we want to move the decimal over so that we get the number 9.56 times 10 to some power. To do this, we must move the decimal over 6 places. Since 0.00000956 is obviously smaller than 9.56, that means that our exponent must be negative.

Therefore, our answer is $9.56 \cdot 10^{-6}$ .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2421 : Sat Mathematics

Example Question #2422 : Sat Mathematics

Example Question #6 : How To Find A Rational Number From An Exponent

Example Question #1 : How To Use Scientific Notation

Example Question #2421 : Sat Mathematics

Example Question #2 : How To Use Scientific Notation

Example Question #2422 : Sat Mathematics

Example Question #5 : Other Exponents

Example Question #6 : Other Exponents

Example Question #4 : How To Use Scientific Notation

All SAT Math Resources

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