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New SAT Math - No Calculator : New SAT

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3 Diagnostic Tests 1 Practice Test Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Pattern Behaviors In Exponents

Jack has $\$15$ , 000 to invest. If he invests two-thirds of it into a high-yield savings account with an annual interest rate of $8\%$ , compounded quarterly, and the other third in a regular savings account at $6\%$ simple interest, how much does Jack earn after one year?

Possible Answers:

$\$1081.98$

$\$1051.32$

$\$1124.32$

$\$1128.75$

$\$901.43$

Correct answer:

$\$1124.32$

Explanation:

First, break the problem into two segments: the amount Jack invests in the high-yield savings, and the amount Jack invests in the simple interest account (10,000 and 5,000 respectively).

Now let's work with the high-yield savings account. $10,000 is invested at an annual rate of 8%, compounded quarterly. We can use the compound interest formula to solve:

$\text{Final Balance}=\text{ Principal} \cdot \bigg(1+\frac{\text{Interest Rate}}{c}\bigg)^{(\text{Time})(c)}$

Plug in the values given:

$=10,000\cdot \bigg(1+\frac{.08}{4}\bigg)^{(1)(4)}$

$=10,000 \cdot (1.02)^{4}$

=10,824.32

Therefore, Jack makes $824.32 off his high-yield savings account. Now let's calculate the other interest:

$\text{Interest}=\text{Principal} \cdot \text{ Interest Rate} \cdot \text{ Time}$

$=5,000 \cdot (0.06)\cdot (1)$

=300

Add the two together, and we see that Jack makes a total of, $\$1124.32$ off of his investments.

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Example Question #291 : New Sat

Screen shot 2016 02 11 at 3.40.03 pm

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

Possible Answers:

$\frac{4}{17}$

$-\frac{2}{17}$

$\frac{1}{4}$

$\frac{2}{17}$

$-\frac{4}{17}$

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 #292 : New Sat

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:

$5^{\text{th}}$

$3^{\text{rd}}$

$4^{\text{th}}$

$6^{\text{th}}$

$1^{\text{st}}$

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 #671 : Sat Mathematics

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 #131 : Solid Geometry

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:

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

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

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

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

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

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 #3 : How To Find The Solution To An Inequality With Multiplication

Solve for x

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

Possible Answers:

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

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

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

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

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 #3 : How To Use The Quadratic Function

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

What is the focus of the above quadratic equation?

Possible Answers:

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

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

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

$\left(3, 5\right)$

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

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 #63 : Arithmetic Mean

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 #64 : Arithmetic Mean

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 #293 : New Sat

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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New SAT Math - No Calculator : New SAT

Study concepts, example questions & explanations for New SAT Math - No Calculator

All New SAT Math - No Calculator Resources

Example Questions

Example Question #2 : Pattern Behaviors In Exponents

Example Question #291 : New Sat

Example Question #292 : New Sat

Example Question #671 : Sat Mathematics

Example Question #131 : Solid Geometry

Example Question #3 : How To Find The Solution To An Inequality With Multiplication

Example Question #3 : How To Use The Quadratic Function

Example Question #63 : Arithmetic Mean

Example Question #64 : Arithmetic Mean

Example Question #293 : New Sat

All New SAT Math - No Calculator Resources

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