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SAT II Math I : SAT Subject Test in Math I

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #51 : Sat Subject Test In Math I

How many elements are in a set that has exactly 128 subsets?

Possible Answers:

$\displaystyle 16$

None of the other responses is correct.

$\displaystyle 8$

$\displaystyle 7$

$\displaystyle 12$

Correct answer:

$\displaystyle 7$

Explanation:

A set with $\displaystyle N$ elements has $2 ^{N}$ $\displaystyle 2 ^{N}$ subsets.

Solve:

$2 ^{N} = 128$ $\displaystyle 2 ^{N} = 128$

$\ln 2 ^{N} = \ln 128$ $\displaystyle \ln 2 ^{N} = \ln 128$

$N \ln 2 = \ln 128$ $\displaystyle N \ln 2 = \ln 128$

$N = \frac{\ln 128}{\ln 2} = \frac{4.8520 }{0.6931} = 7$ $\displaystyle N = \frac{\ln 128}{\ln 2} = \frac{4.8520 }{0.6931} = 7$

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Example Question #1 : Mathematical Relationships

Rewrite as a single logarithmic expression:

$\ln x - 2 \ln (x + 2)$ $\displaystyle \ln x - 2 \ln (x + 2)$

Possible Answers:

$\ln \frac{1}{x^{2} +3x +4}$ $\displaystyle \ln \frac{1}{x^{2} +3x +4}$

$\ln \frac{x}{2x + 4}$ $\displaystyle \ln \frac{x}{2x + 4}$

$\ln \frac{1}{x +4}$ $\displaystyle \ln \frac{1}{x +4}$

$\ln \frac{x}{x^{2} +4x + 4}$ $\displaystyle \ln \frac{x}{x^{2} +4x + 4}$

$\ln \left (-x^{2} -3x -4 \right )$ $\displaystyle \ln \left (-x^{2} -3x -4 \right )$

Correct answer:

$\ln \frac{x}{x^{2} +4x + 4}$ $\displaystyle \ln \frac{x}{x^{2} +4x + 4}$

Explanation:

Using the properties of logarithms

$n \ln a = \ln a^{n}$ $\displaystyle n \ln a = \ln a^{n}$ and $\ln a - \ln b = \ln \frac{a}{b}$ $\displaystyle \ln a - \ln b = \ln \frac{a}{b}$,

we simplify as follows:

$\ln x - 2 \ln (x + 2)$ $\displaystyle \ln x - 2 \ln (x + 2)$

$= \ln x - \ln (x + 2)^{2}$ $\displaystyle = \ln x - \ln (x + 2)^{2}$

$= \ln x - \ln (x^{2} +4x + 4)$ $\displaystyle = \ln x - \ln (x^{2} +4x + 4)$

$= \ln \frac{x}{x^{2} +4x + 4}$ $\displaystyle = \ln \frac{x}{x^{2} +4x + 4}$

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Example Question #1 : Exponents And Logarithms

Solve: $log_{3}27$ $\displaystyle log_{3}27$

Possible Answers:

$\displaystyle 9$

$\displaystyle 27$

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

$\displaystyle 30$

$\displaystyle 3$

Correct answer:

$\displaystyle 3$

Explanation:

In order to solve this problem, covert 27 to the correct base and power.

$log_{3}27 = log_{3}\: 3^3$ $\displaystyle log_{3}27 = log_{3}\: 3^3$

Since $\displaystyle log_xx^n = n$, the correct answer is $\displaystyle 3$.

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Example Question #51 : Sat Subject Test In Math I

Simplify $(x^{-4})^7$ $\displaystyle (x^{-4})^7$

Possible Answers:

$x^{\frac{7}{4}}$ $\displaystyle x^{\frac{7}{4}}$

x^3 $\displaystyle x^3$

$x^{-11}$ $\displaystyle x^{-11}$

$x^{-47}$ $\displaystyle x^{-47}$

$x^{-28}$ $\displaystyle x^{-28}$

Correct answer:

$x^{-28}$ $\displaystyle x^{-28}$

Explanation:

When an exponent is raised by another exponent, we just multiply the powers.

$(x^{-4})^7=x^{-4*7}=x^{-28}$ $\displaystyle (x^{-4})^7=x^{-4*7}=x^{-28}$

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Example Question #2 : Exponents And Logarithms

Simplify:

$\displaystyle 3^9+3^9+3^9$

Possible Answers:

$3^{27}$ $\displaystyle 3^{27}$

9^9 $\displaystyle 9^9$

$9^{27}$ $\displaystyle 9^{27}$

$3^{10}$ $\displaystyle 3^{10}$

$27^{9}$ $\displaystyle 27^{9}$

Correct answer:

$3^{10}$ $\displaystyle 3^{10}$

Explanation:

When adding exponents, we don't add the exponents or multiply out the bases. Our goal is to see if we can factor anything. We do see three 3^9 $\displaystyle 3^9$. Let's factor.

$3^9+3^9+3^9=3^9(1+1+1)=3^9(3)=3^{10}$ $\displaystyle 3^9+3^9+3^9=3^9(1+1+1)=3^9(3)=3^{10}$ Remember when multiplying exponents, we just add the powers.

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Example Question #54 : Sat Subject Test In Math I

Solve and simplify.

$\sqrt[3]{125}$ $\displaystyle \sqrt[3]{125}$

Possible Answers:

$5\sqrt{5}$ $\displaystyle 5\sqrt{5}$

$\displaystyle 25$

$\displaystyle 5$

$5\sqrt[3]{5}$ $\displaystyle 5\sqrt[3]{5}$

$\displaystyle 3$

Correct answer:

$\displaystyle 5$

Explanation:

$\sqrt[3]{125}$ $\displaystyle \sqrt[3]{125}$ Another way to write this is x^3=125 $\displaystyle x^3=125$. The only number that makes 125 $\displaystyle 125$ is 5^3 $\displaystyle 5^3$.

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Example Question #55 : Sat Subject Test In Math I

Simplify:

$\log_3729$ $\displaystyle \log_3729$

Possible Answers:

$\displaystyle 6$

243 $\displaystyle 243$

$\displaystyle 9$

$3^{729}$ $\displaystyle 3^{729}$

3^9 $\displaystyle 3^9$

Correct answer:

$\displaystyle 6$

Explanation:

$\log_3729$ $\displaystyle \log_3729$ is the same as 3^x=729 $\displaystyle 3^x=729$. Let's factor out 729 $\displaystyle 729$. It's the same as 3^6 $\displaystyle 3^6$. Therefore x=6 $\displaystyle x=6$ which is the answer to our question.

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Example Question #52 : Sat Subject Test In Math I

Simplify:

$\log50-\log5$ $\displaystyle \log50-\log5$

Possible Answers:

$\log45$ $\displaystyle \log45$

$\log250$ $\displaystyle \log250$

$5\log50$ $\displaystyle 5\log50$

$\displaystyle 0$

$\displaystyle 1$

Correct answer:

$\displaystyle 1$

Explanation:

When dealing with subtraction in regards to logarithms, it's the same as dividing the numbers.

$\log50-\log5=\frac{\log50}{\log5}=\log \frac{50}{5}=\log10=1$ $\displaystyle \log50-\log5=\frac{\log50}{\log5}=\log \frac{50}{5}=\log10=1$

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Example Question #53 : Sat Subject Test In Math I

Simplify:

$\log_618+\log_672$ $\displaystyle \log_618+\log_672$

Possible Answers:

$\displaystyle 4$

$3\log_618$ $\displaystyle 3\log_618$

$6\log90$ $\displaystyle 6\log90$

$\log_690$ $\displaystyle \log_690$

$\displaystyle 6$

Correct answer:

$\displaystyle 4$

Explanation:

When dealing with addition in regards to logarithms, it's the same as multiplying the numbers.

$\log_618+\log_672=\log_6(18*72)=\log_61296=4$ $\displaystyle \log_618+\log_672=\log_6(18*72)=\log_61296=4$

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Example Question #58 : Sat Subject Test In Math I

Solve: $(x^{2})^{5}$ $\displaystyle (x^{2})^{5}$ when x=2 $\displaystyle x=2$.

Possible Answers:

1024 $\displaystyle 1024$

100 $\displaystyle 100$

1000 $\displaystyle 1000$

$\displaystyle 20$

$\displaystyle 64$

Correct answer:

1024 $\displaystyle 1024$

Explanation:

Power rule says when an exponent is raised to another exponent, you must multiply the exponents.

So 2*5=10 $\displaystyle 2*5=10$ and our expression is now $x^{10}$ $\displaystyle x^{10}$.

Plug in the given value to get

$2^{10}=1024$ $\displaystyle 2^{10}=1024$.

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SAT II Math I : SAT Subject Test in Math I

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #51 : Sat Subject Test In Math I

Example Question #1 : Mathematical Relationships

Example Question #1 : Exponents And Logarithms

Example Question #51 : Sat Subject Test In Math I

Example Question #2 : Exponents And Logarithms

Example Question #54 : Sat Subject Test In Math I

Example Question #55 : Sat Subject Test In Math I

Example Question #52 : Sat Subject Test In Math I

Example Question #53 : Sat Subject Test In Math I

Example Question #58 : Sat Subject Test In Math I

All SAT II Math I Resources

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