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New SAT Math - Calculator : New SAT Math - Calculator

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2 Diagnostic Tests 27 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #1 : How To Find The Amount Of Sales Tax

Jenny buys a blouse that is priced at $45. She pays a total of $48.15, what is the rate of tax on the blouse?

Possible Answers:

$.07\%$

$8\%$

$7\%$

$5\%$

$13\%$

Correct answer:

$7\%$

Explanation:

The purpose of this question is to calculate tax rates using dollar amounts.

First, the amount of tax payed must be determined. This is done by finding the difference between the amount paid and the listed price

48.15-45=3.15 ,

which equals $3.15.

Then, that must be translated into a percentage of $45.

Therefore,

$\frac{3.15}{45}=.07$ , yielding .07 of 1. This is a 7% tax rate.

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Example Question #141 : Probability

The image above represents a spinner with 10 regions. The 6 larger sectors have a radius that is twice that of the smaller sectors.

If spun, what is the probability that the spinner will stop while pointing to a green sector?

Possible Answers:

$\frac{2}{5}$

$\frac{5}{1 4}$

$\frac{1}{3}$

$\frac{3}{8}$

$\frac{5}{12}$

Correct answer:

$\frac{5}{12}$

Explanation:

The probability that the spinner will stop in a particular sector depends on the angle of the sector, not on the size of the sector. The radii of the sectors is therefore irrelevant.

The two larger green sectors are each one third of a quarter circle, and each is a sector of measure

$\frac{1}{3} \cdot \frac{1}{4} \cdot 360 ^{\circ } = 30 ^{\circ }$ .

The two smaller ones are each a half of a quarter circle, and each is a sector of measure

$\frac{1}{2} \cdot \frac{1}{4} \cdot 360 ^{\circ } = 45 ^{\circ }$ .

Therefore, the total angle measure of the green sectors is

$2 \cdot 30 ^{\circ } + 2 \cdot 45 ^{\circ }= 60 ^{\circ }+ 90 ^{\circ } = 150 ^{\circ }$ .

The probability that the spinner will stop in a green sector is found by taking this out of a total of $360 ^{\circ }$ :

$\frac{150 ^{\circ }}{360 ^{\circ }} = \frac{5}{12}$

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Example Question #261 : New Sat

The given table reports the average high and low temperatures over four years. What is the average rate of change for the high temperature during the four years?

Note: The temperature is in degrees Fahrenheit.

$\begin{tabular}{||c c c ||} \hline Year & Avg. High Temp. & Avg. Low Temp. \\ [0.5ex] \hline\hline 2002 & 76 & 34 \\ \hline 2003 & 78 & 40 \\ \hline 2004 & 79 & 38 \\ \hline 2005 & 82 & 45 \\ [1ex] \hline\hline \end{tabular}$

Possible Answers:

$4^\circ\text{F}$

$6^\circ\text{F}$

$3^\circ\text{F}$

$1^\circ\text{F}$

$2^\circ\text{F}$

Correct answer:

$2^\circ\text{F}$

Explanation:

The given table reports the average high and low temperatures over four years. The question asks to calculate the average rate of change for the high temperature over the four years depicted.

To calculate average rate of change use the following formula.

$\text{Avg. Rate of Change}=\frac{\text{Ending Year High Temp.}-\text{Beginning Year High Temp.}}{\text{Ending Year}-\text{Beginning Year}}$

$\\\text{Ending High Temp.}= 82 \\\text{Beginning High Temp.}=76 \\\text{Ending Year}=2005 \\\text{Beginning Year}=2002$

Substitute these values into the formula looks as follows.

$\text{Avg. Rate of Change}=\frac{\text{Ending Year High Temp.}-\text{Beginning Year High Temp.}}{\text{Ending Year}-\text{Beginning Year}}$

$\text{Avg. Rate of Change}=\frac{82-76}{2005-2002}$

$\text{Avg. Rate of Change}=\frac{6}{3}=2$

Therefore, the average rate of change for the high temperature from 2002 to 2005 is 2 degrees Fahrenheit.

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Example Question #141 : Probability

The given table reports the average high and low temperatures over four years. What is the fraction of average low temperatures in 2002 to 2005?

Note: The temperature is in degrees Fahrenheit.

Possible Answers:

$\frac{42}{30}$

$\frac{30}{42}$

$\frac{5}{7}$

$\frac{34}{45}$

$\frac{45}{34}$

Correct answer:

$\frac{34}{45}$

Explanation:

The table reports the average high and low temperatures over four years. To calculate the fraction of average low temperatures in 2002 to 2005 first identify the average low temperature in 2002 and in 2005.

Examining the table,

Average low temperature in 2002: 34 degrees Fahrenheit.

Average low temperature in 2005: 45 degrees Fahrenheit.

From here, to find the fraction of average low temperatures during this time period, use the following formula.

$\text{Fraction of Low Temperatures}=\frac{\text{Beginning Year Low Temp}}{\text{Ending Year Low Temp}}$

$\text{Fraction}=\frac{34}{45}$

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Example Question #11 : Circles

What is the equation of a circle with center (1,1) and a radius of 10?

Possible Answers:

(x-1)^2+(y-1)^2=100

(x-1)+(y-1)=100

x^2 + y^2 = 100

(x+1)^2+(y+1)^2=100

x^2 + y^2 = 10

Correct answer:

(x-1)^2+(y-1)^2=100

Explanation:

The general equation for a circle with center (h, k) and radius r is given by

(x-h)^2+(y-k)^2=r^2 .

In our case, our h-value is 1 and our k-value is 1. Our r-value is 10.

Substituting each of these values into the equation for a circle gives us

(x-1)^2+(y-1)^2=100

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Example Question #341 : Equations / Inequalities

Tommy throws a rock off a 10 meter ledge at a speed of 3 meters/second. Calculate when the rock hits the ground.

To solve use the equation

s(t)=-gt^2+v_0(t)+h_0

where

$\\g=4.9 \\v_0=\text{speed} \\h_0=\text{starting height}$

Possible Answers:

$1.75\text{ seconds}$

$1.5\text{ seconds}$

$1.3\text{ seconds}$

$1.25\text{ seconds}$

$2\text{ seconds}$

Correct answer:

$1.75\text{ seconds}$

Explanation:

Tommy throws a rock off a 10 meter ledge at a speed of 3 meters/second. To calculate when the rock hits the ground first identify what is known.

Using the equation

s(t)=-gt^2+v_0(t)+h_0

where

$\\g=4.9 \\v_0=\text{speed} \\h_0=\text{starting height}$

it is known that,

$v_0=3\frac{ \text{ m}}{\text{ s}}$

$h_0=10 \text{ m}$

Substituting the given values into the position s(t) equation looks as follows.

s(t)=-4.9t^2+3(t)+10

Now to calculate when the rock hits the ground, find the value that results in s(t)=0 .

0=-4.9t^2+3t+10

Use graphing technology to graph s(t) .

Screen shot 2016 02 11 at 8.18.52 am

It appears that the rock hits the ground approximately 1.75 seconds after Tommy throws it.

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Example Question #1 : Fractions And Percentage

A family with 6 children, aged 4, 4, 5, 7, 12, and 13 are moving to a new home. They all want the same bedroom, so the parents have a lottery. Each child places their name in once for every year of age (the four year olds each put their name in 4 times, the seven year old puts his name in 7 times, etc.) What is the probability of the chosen child being 4 years old?

Possible Answers:

$17.\overline{7}\%$

$20\%$

None of the available answers

$8.\overline{8}\%$

It is most likely that the chosen child will be the oldest child.

Correct answer:

$17.\overline{7}\%$

Explanation:

First, we will determine the total number of ballots:

$4+4+5+7+12+13=45\hspace{1 mm}ballots$

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

$\frac{4+4}{45}=\frac{8}{45}=0.1\overline{7}=17.\overline{7}\%$

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Example Question #131 : Probability

Use the following table to answer the question.

Table2

What class did Craig have the highest grade in?

Possible Answers:

$\text{Art}$

$\text{Math}$

$\text{There is not enough information to answer the question.}$

$\text{}$ $\text{Science}$

Correct answer:

$\text{}$ $\text{Science}$

Explanation:

Let's look at the table.

Table2

We can see the first column lists all the students. The next column shows all of the classes. And the last column shows the grade they received in those classes.

Now, to find which class Craig received the highest grade, we must first locate Craig. We can see all of Craig's classes are at the very bottom of the table.

Now, we will look at the grade he got in each class by following along the rows with Craig's name.

We can see Craig's first class is Math. He received a B.

Craig's second class is Science. He received an A.

Craig's third class is Art. He received a B.

Knowing this, we can see the highest grade Craig received was an A. The class where he received an A was Science.

Therefore, the class that Craig received the highest grade was Science.

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Example Question #671 : Sat Mathematics

The parabolas of the functions f(x) and g(x) on the coordinate plane have the same vertex.

If we define $f(x) = \frac{4}{5}(x-9)^{2}+ 6$ , which of the following is a possible equation for g(x) ?

Screen shot 2016 02 10 at 12.25.12 pm

Possible Answers:

$g(x) = \frac{4}{5}(x-7)^{2}+ 6$

$g(x) = \frac{4}{5}(x-9)^{2}-2$

None of the other responses gives a correct answer.

$g(x) = \frac{8}{5}(x-18)^{2}+ 12$

$g(x) = \frac{3}{5}(x-9)^{2}+ 6$

Correct answer:

$g(x) = \frac{3}{5}(x-9)^{2}+ 6$

Explanation:

The eqiatopm of f(x) is given in the vertex form

$f(x) =a(x-h)^{2}+ k$ ,

so the vertex of its parabola is (h,k ) . The graphs of f(x) and g(x) are parabolas with the same vertex, so they must have the same values for and .

For the function $f(x) = \frac{4}{5}(x-9)^{2}+ 6$ , h = 9 and k = 6 .

Screen shot 2016 02 10 at 12.25.12 pm

Of the five choices, the only equation of g(x) that has these same values, and that therefore has a parabola with the same vertex, is $g(x) = \frac{3}{5}(x-9)^{2}+ 6$ .

Screen shot 2016 02 10 at 12.27.19 pm

To verify, graph both functions on the same grid.

Screen shot 2016 02 10 at 12.28.14 pm

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Example Question #1741 : Sat Mathematics

Janet can pick between 10 and 20 tomatoes in an hour. What is a possible amount of time for Janet to pick 120 tomatoes?

Possible Answers:

$4\text{ hours}$

$20\text{ hours}$

$16\text{ hours}$

$5\text{ hours}$

$6\text{ hours}$

Correct answer:

$6\text{ hours}$

Explanation:

Since Janet can pick between 10 and 20 tomatoes in an hour, there is a range for which she can pick 120 tomatoes. Therefore, to find the possible amount of time it will take Janet to pick 120 tomatoes set up two fractions.

$\text{Time}_1=\frac{\text{Total Tomatoes Picked}}{\text{Rate}_1}$

The first fraction will use the rate of 10 tomatoes an hour.

Therefore, identifying the variables are as follows.

$\\\text{Total Tomatoes}=120 \\\text{Rate}_1=10$

Substituting these into the fraction results in a possible time

$\text{Time}_1=\frac{120}{10}=\frac{12\times 10}{10}=12\text{ hours}$

The second fraction will use the rate of 20 tomatoes an hour.

$\text{Time}_2=\frac{\text{Total Tomatoes Picked}}{\text{Rate}_2}$

Therefore, identifying the variables are as follows.

$\\\text{Total Tomatoes}=120 \\\text{Rate}_2=20$

Substituting these into the fraction results in a possible time

$\text{Time}_1=\frac{120}{20}=\frac{6\times 20}{20}=6\text{ hours}$

Of the answer selections 6 hours would be the correct answer.

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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 #1 : How To Find The Amount Of Sales Tax

Example Question #141 : Probability

Example Question #261 : New Sat

Example Question #141 : Probability

Example Question #11 : Circles

Example Question #341 : Equations / Inequalities

Example Question #1 : Fractions And Percentage

Example Question #131 : Probability

Example Question #671 : Sat Mathematics

Example Question #1741 : Sat Mathematics

All New SAT Math - Calculator Resources

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