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New SAT Math - Calculator : New SAT Math - Calculator

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Example Questions

Example Question #2882 : Sat Mathematics

Screen shot 2016 02 11 at 3.40.03 pm

Approximate the Average Yearly change in the number of PhD's.

Possible Answers:

$\frac{4}{17}$

$\frac{2}{17}$

$-\frac{2}{17}$

$-\frac{4}{17}$

$\frac{1}{4}$

Correct answer:

$-\frac{4}{17}$

Explanation:

What this question is asking for is to approximate the slope of the line of best fit. To calculate the slope, we need to find find two points on the line. The best points to pick out is (18,9) , and (1,13) . Now we can find the rate of change by using the following equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where (x_1,y_1), (x_2,y_2) are points on the line.

$\text{Slope}=\frac{13-9}{1-18}=-\frac{4}{17}$

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Example Question #3051 : Sat Mathematics

The table below shows the number of college graduates per 2 months

$\begin{tabular}{ccccccc} ~&1&2&3&4&5&6\\ \hline MidWest& 10 & 30 &40 & 60 & 100 &24\\ South& 11&45&54&65&90&34\\ East Coast& 56& 23 & 32 & 99 & 10 &56 \end{tabular}$

Which 2 month period had the most college graduates?

Possible Answers:

$4^{\text{th}}$

$6^{\text{th}}$

$1^{\text{st}}$

$5^{\text{th}}$

$3^{\text{rd}}$

Correct answer:

$4^{\text{th}}$

Explanation:

In order to answer this question, we need to add each column up and see what column is the largest.

$\begin{tabular}{ccccccc} ~&1&2&3&4&5&6\\ \hline MidWest& 10 & 30 &40 & 60 & 100 &24\\ South& 11&45&54&65&90&34\\ East Coast& 56& 23 & 32 & 99 & 10 &56\\ \hline Totals& 77&98& 126&224& 200& 114 \end{tabular}$

It looks like that the $4^{\text{th}}$ 2 month period has the most college graduates.

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Example Question #5 : How To Graph A Line

The equation 3x + 2y = 6 represents a line. This line does NOT pass through which of the four quadrants?

Possible Answers:

III

Cannot be determined

Correct answer:

III

Explanation:

Plug in for to find a point on the line:

3(0) + 2y = 6

y = 3

Thus, (0,3) is a point on the line.

Plug in for to find a second point on the line:

3x + 2(0) = 6

x = 2

(2,0) is another point on the line.

Now we know that the line passes through the points (2,0) and (0,3) .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

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Example Question #11 : How To Find The Volume Of A Cylinder

A vase needs to be filled with water. If the vase is a cylinder that is $\dpi{100} \small 12{}''$ tall with a $\dpi{100} \small 2{}''$ radius, how much water is needed to fill the vase?

Possible Answers:

$\dpi{100} \small 12\pi$

$\dpi{100} \small 48\pi$

$\dpi{100} \small 96\pi$

$\dpi{100} \small 24\pi$

$\dpi{100} \small 64\pi$

Correct answer:

$\dpi{100} \small 48\pi$

Explanation:

Cylinder

$\dpi{100} \small V = \pi r^{2}h$

$\dpi{100} \small V = \pi (2)^{2}\times 12$

$\dpi{100} \small V = 4\times 12\pi$

$\dpi{100} \small V = 48\pi$

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Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Solve for x

$\small 3x+7 \geq -2x+4$

Possible Answers:

$\small x \leq \frac{3}{5}$

$\small x \geq -\frac{3}{5}$

$\small x \leq -\frac{3}{5}$

$\small x \geq \frac{3}{5}$

Correct answer:

$\small x \geq -\frac{3}{5}$

Explanation:

$\small 3x+7 \geq -2x+4$

$\small 3x \geq -2x-3$

$\small 5x \geq -3$

$\small x\geq -\frac{3}{5}$

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Example Question #2 : How To Use The Quadratic Function

f(x)=2(x-3)^2+5

What is the focus of the above quadratic equation?

Possible Answers:

$\left(-3, \frac{41}{8}\right)$

$\left(-3, -\frac{41}{8}\right)$

$\left(3, 5\right)$

$\left(3, \frac{1}{8}\right)$

$\left(3, \frac{41}{8}\right)$

Correct answer:

$\left(3, \frac{41}{8}\right)$

Explanation:

The focus is solved by using the following formula (x,y+p) , where x,y are the coordinates of the vertex, and is the distance from the vertex. To solve for , we use

$a=\frac{1}{4p}$ , where is the coefficient in front of the x^2 term and is the focus.

Since a=2 , we can substitute in to get,

$2=\frac{1}{4p}$

$2p=\frac{1}{4}$

$p=\frac{1}{4}\cdot\frac{1}{2}=\frac{1}{8}$

Now we need to find the vertex of the equation.

Since our equation is in vertex form, we can deduce that the vertex is at (3,5)

So the focus is at $\left( 3,5+\frac{1}{8}\right)=\left( 3,\frac{41}{8}\right)$

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Example Question #91 : Data Analysis

Screen shot 2016 02 12 at 9.39.26 am

The bar chart shows the number of consecutive heads for a fair coin. How many more 4 Heads were there compared to 3 Heads?

Possible Answers:

Correct answer:

Explanation:

To figure this out, we need to go to the y-axis and find the number of 4 heads and 3 Heads there were. $4\: \text{Heads}=5$ , $3\:\text{Heads}=3$ . Now we find the difference between them, which is simply 5-3=2 .

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Example Question #92 : Data Analysis

Screen shot 2016 02 12 at 9.39.26 am

Find the average rate of change between 3 Heads and 5 Heads

Possible Answers:

$\frac{1}{2}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

The average rate of change is calculated by the following.

$\text{Average Rate of Change}=\frac{f(b)-f(a)}{b-a}$

So we simply do the following,

$\text{3\:Heads}=3$

$\text{5\:Heads}=6$

$\text{Average Rate of Change}=\frac{6-3}{5-3}=\frac{3}{2}=1.5$

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Example Question #3063 : Sat Mathematics

Week 1 Homework Time Week 2 Homework Time

$\vline\begin{tabular}{cccc} \hline Monday & 4\\ Tuesday & 5\\ Wednesday & 3\\ Thursday & 2\\ Friday & 1\\ Saturday & 6\\ Sunday & 3\\ \hline \end{tabular}\vline$ $\vline\begin{tabular}{cccc} \hline Monday & 2\\ Tuesday & 3\\ Wednesday & 4\\ Thursday & 1\\ Friday & 3\\ Saturday & 1\\ Sunday & 6\\ \hline \end{tabular}\vline$

The above tables show how much time Amanda spent doing homework during the first 2 weeks of school. Which week has the largest standard deviation?

Possible Answers:

$S_{w_2}$

$S_{w_1}$

Correct answer:

$S_{w_2}$

Explanation:

The first step is to calculate the mean for each table.

$\bar{w_1}=\frac{4+5+3+2+1+6+3}{7}=\frac{24}{7}$

$\bar{w_2}=\frac{2+3+4+1+3+1+6}{7}=\frac{20}{7}$

Recall how to find the standard deviation

$S=\sqrt{\frac{1}{n-1}\sum_{i=0}^{n} (x_i-\bar{x})^2}$

Now we will apply this to each table.

$S_{w_1}=\sqrt{\frac{\left(4-\frac{24}{7}\right)^2+\left(5-\frac{24}{7}\right)^2+\left(3-\frac{24}{7}\right)^2+\left(2-\frac{24}{7}\right)^2+\left(1-\frac{24}{7}\right)^2+\left(6-\frac{24}{7}\right)^2+\left(3-\frac{24}{7}\right)^2}{6}}$

$S_{w_1}=1.71825$

$S_{w_2}=\sqrt{\frac{\left(2-\frac{20}{7}\right)^2+\left(3-\frac{20}{7}\right)^2+\left(4-\frac{20}{7}\right)^2+\left(1-\frac{20}{7}\right)^2+\left(3-\frac{20}{7}\right)^2+\left(1-\frac{20}{7}\right)^2+\left(6-\frac{20}{7}\right)^2}{6}}$

$S_{w_2}=1.7728$

Since $S_{w_2}>S_{w_1}$ , $S_{w_2}$ is our answer

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Example Question #361 : Sat Mathematics

Tangents

In the above diagram, $\overarc {TU}$ has length $30 \pi$ . Give the radius of the circle to the nearest whole number.

Possible Answers:

The question cannot be answered with the information given.

102

Correct answer:

Explanation:

Call $t = m \overarc {TU}$ . The measure of the corresponding major arc is $360 ^{\circ } - m \overarc {TU}= 360 ^{\circ } -t$

If two tangents are drawn to a circle from a point outside the circle, the measure of the angle they form is equal to half the difference of the measures of their intercepted arcs; therefore

$\frac{1}{2} \left (360 ^{\circ } -t -t \right ) = m \angle BNT$

Substituting:

$\frac{1}{2} \left (360 ^{\circ } -2t\right ) = 66 ^{\circ }$

$180 ^{\circ } -t = 66 ^{\circ }$

$180 ^{\circ } -t + t - 66 ^{\circ } = 66 ^{\circ } + t - 66 ^{\circ }$

$114 ^{\circ } = t$

Therefore, $m \overarc {TU} = 114 ^{\circ }$ . Since $\overarc {TU}$ has length $30 \pi$ , it follows that if is the circumference of the circle,

$\frac{C}{360^{\circ }} = \frac{30 \pi }{m \overarc{TU}}$

$\frac{C}{360^{\circ }} = \frac{30 \pi }{114^{\circ }}$

$C= \frac{30 \pi }{114^{\circ }} \cdot 360^{\circ }$

$C = 94\frac{14}{19} \pi$

Divide the circumference by $2 \pi$ to obtain the radius:

$r = \frac{C}{2 \pi} = \frac{94 \frac{14}{19}\pi }{2 \pi} = 47 \frac{7}{19}$ .

This makes 47 the correct choice.

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New SAT Math - Calculator : New SAT Math - Calculator

Study concepts, example questions & explanations for New SAT Math - Calculator

All New SAT Math - Calculator Resources

Example Questions

Example Question #2882 : Sat Mathematics

Example Question #3051 : Sat Mathematics

Example Question #5 : How To Graph A Line

Example Question #11 : How To Find The Volume Of A Cylinder

Example Question #2 : How To Find The Solution To An Inequality With Multiplication

Example Question #2 : How To Use The Quadratic Function

Example Question #91 : Data Analysis

Example Question #92 : Data Analysis

Example Question #3063 : Sat Mathematics

Example Question #361 : Sat Mathematics

All New SAT Math - Calculator Resources

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