GRE Subject Test: Math

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GRE Quantitative Reasoning › GRE Subject Test: Math

Questions 1 - 10

Which of the following is not a subset of Set A:{ }

{}

Explanation

Step 1: A subset of a set must have elements in Set A. If any number in the subset is not in the original set, then that subset is not a subset of that set.

{} is not a subset because is not in Set A.

What is the range of the set of numbers: ?

Explanation

Step 1: Arrange the numbers in the set from smallest to largest:

After we arrange, we get: .

Step 2: To find the range, subtract the largest number from the smallest number.

The range of the data set is .

Daisy wants to arrange four vases in a row outside of her garden. She has eight vases to choose from. How many vase arrangements can she make?

Explanation

For this problem, since the order of the vases matters (red blue yellow is different than blue red yellow), we're dealing with permutations.

With selections made from potential options, the total number of possible permutations(order matters) is:

$P(n,k)=\frac{n!}{(n-k)!}$

$P(8,4)=\frac{8!}{(8-4)!}=1680$

Find one possible value of , given the following equation:

$343=7^{15t-12}$

Cannot be determined from the information given.

Explanation

We begin with the following:

$343=7^{15t-12}$

This can be rewritten as

$7^3=7^{15t-12}$

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

Solve this to get t.

Expand: .

Explanation

Step 1: Evaluate .

Step 2. Evaluate

From the previous step, we already know what is.

is just multiplying by another

Step 3: Evaluate .

The expansion of is

What is the slope and y-intercept of this line: ?

$Slope=\frac {3}{4},y-intercept=3$

$Slope=\frac {3}{4},y-intercept=2$

$Slope=\frac {-3}{4},y-intercept=3$

$Slope=\frac {4}{3},y-intercept=3$

Explanation

Step 1: Move the y-term to the other side. We will add 4y.

$\rightarrow 3x=12+4y$

Step 2: Move the constant to the other side. We will subtract 12.

$\rightarrow 3x-12=4y$

Step 3: Divide by the coefficient in front of the y term. In this question, we divide all terms by 4.

$\frac {3x-12}{4}=\frac {4y}{4}\rightarrow\frac {3}{4}x+\frac {-12}{4}=y$

$\rightarrow y=\frac {3}{4}x-3$

Step 4: Identify the slope and the y-intercept. The slope is the number that is in front of the x term, and the y-intercept is the number that comes after the x-term.

In this question, the slope is $\frac {3}{4}$ and the y-intercept is .

For which of the following functions can the Maclaurin series representation be expressed in four or fewer non-zero terms?

$f(x)= \frac{x^{5}}{3}+2$

$f(x)= x^{2}+\sqrt{x}+1$

$f(x)=x+3\sin(x)$

$f(x)=\ln|x+3|$

Explanation

Recall the Maclaurin series formula:

$f(x)=\sum_{n=0}^{\infty}\frac{f^n(0)}{n!}x^n$

$=f(0)+f'(0)x+\frac{f''(0)}{2!}x^2+\frac{f'''(0)}{3!}x^3+...$

Despite being a 5th degree polynomial recall that the Maclaurin series for any polynomial is just the polynomial itself, so this function's Taylor series is identical to itself with two non-zero terms.

The only function that has four or fewer terms is $f(x)= \frac{x^{5}}{3}+2$ as its Maclaurin series is $2+\frac{1}{3}x^5$ .

What is the vector form of ?

$\left \langle 10,-1,10\right \rangle$

$\left \langle 10,10,-1\right \rangle$

$\left \langle -1,10,10\right \rangle$

$\left \langle 10,1,10\right \rangle$

$\left \langle 10,10,1\right \rangle$

Explanation

In order to derive the vector form, we must map the , , -coordinates to their corresponding , , and coefficients.

That is, given $a_{1}i+a_{2}j+a_{3}k$ , the vector form is $a=\left \langle a_{1},a_{2},a_{3}\right \rangle$ .

So for , we can derive the vector form $\left \langle 10,-1,10\right \rangle$ .

What is the mean of:

Explanation

Step 1: Take the sum of all numbers in the set...

Step 2: Count how many elements are in the set...

There are numbers

Step 3: To find the mean, divide the sum by the number of elements..

$\frac {57}{10}=5.7$

The mean is

$Simplify: \sqrt{-72}$

$6i{\sqrt{2}}$

$-6i\sqrt{2}$

$-6{\sqrt{2}}$

$6{\sqrt{-2}}$

Explanation

$When\ reducing\ the\ square\ root\ of\ a\ negative\ number\ -\ we\ must\ first\$

$i=\sqrt{-1}$

$\sqrt{-72}=\sqrt{-1}\sqrt{72}=i\sqrt{72}$

$Once\ we\ have\ taken\ out\ the\ i,\ then\ we\ can\ simply\ break\ down$ $the\ number\ under\ the\ radical\ by\ finding\ the\ largest\ perfect\ square\ that\ will go\ into\ it.$