New SAT Reading : New SAT

Study concepts, example questions & explanations for New SAT Reading

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Example Questions

Example Question #182 : New Sat Math Calculator

Convert the following expression to radians:

 

\(\displaystyle \frac{45^{\circ}+30^{\circ}}{45-30}\)

Possible Answers:

\(\displaystyle \frac{5\pi}{36}\)

\(\displaystyle \frac{\pi}{36}\)

\(\displaystyle \frac{\pi}{30}\)

\(\displaystyle \frac{\pi}{12}\)

\(\displaystyle \frac{7\pi}{36}\)

Correct answer:

\(\displaystyle \frac{\pi}{36}\)

Explanation:

First we need to simplify the expression:

 

\(\displaystyle \frac{45^{\circ}+30^{\circ}}{45-30}=\frac{75^{\circ}}{15}=5^{\circ}\)

 

In order to change degrees to radians, we need to multiply by \(\displaystyle \frac{\pi}{180^{\circ}}\):

 

\(\displaystyle 5^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{36}\)

Example Question #581 : New Sat

Change \(\displaystyle 270^{\circ}\)  to radians.

 

Possible Answers:

\(\displaystyle 3\pi\)

\(\displaystyle \pi\)

\(\displaystyle 1.5\pi\)

\(\displaystyle 2\pi\)

\(\displaystyle 2.5\pi\)

Correct answer:

\(\displaystyle 1.5\pi\)

Explanation:

In order to change degrees to radians we need to multiply degrees by \(\displaystyle \frac{\pi}{180^{\circ}}\):

 

\(\displaystyle 270^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{3\pi}{2}=1.5\pi\)

Example Question #582 : New Sat

Convert one radian to degrees.

Possible Answers:

\(\displaystyle 47.3^{\circ}\)

\(\displaystyle 67.3^{\circ}\)

\(\displaystyle 57.3^{\circ}\)

\(\displaystyle 60^{\circ}\)

\(\displaystyle 50^{\circ}\)

Correct answer:

\(\displaystyle 57.3^{\circ}\)

Explanation:

In order to change radians to degrees we need to multiply radians by \(\displaystyle \frac{180^{\circ}}{\pi}\):

 

\(\displaystyle 1\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{\pi}\approx 57.3^{\circ}\)

Example Question #583 : New Sat

Convert one degree to radians.

Possible Answers:

\(\displaystyle \frac{\pi}{90}\)

\(\displaystyle \frac{\pi}{120}\)

\(\displaystyle \frac{\pi}{60}\)

\(\displaystyle \pi\)

\(\displaystyle \frac{\pi}{180}\)

Correct answer:

\(\displaystyle \frac{\pi}{180}\)

Explanation:

In order to change degrees to radians we need to multiply the degrees by \(\displaystyle \frac{\pi}{180^{\circ}}\):

 

\(\displaystyle 1^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{180}\)

Example Question #35 : Unit Circle And Radians

Simplify and give the followoing expression in degrees:

 

\(\displaystyle 2\pi-\frac{\pi}{4}\)

Possible Answers:

\(\displaystyle 285^{\circ}\)

\(\displaystyle 270^{\circ}\)

\(\displaystyle 300^{\circ}\)

\(\displaystyle 325^{\circ}\)

\(\displaystyle 315^{\circ}\)

Correct answer:

\(\displaystyle 315^{\circ}\)

Explanation:

First we need to simplify the expression:

 

\(\displaystyle 2\pi-\frac{\pi}{4}=\frac{8\pi-\pi}{4}=\frac{7\pi}{4}\)

Then multiply  by \(\displaystyle \frac{180^{\circ}}{\pi}\):

 

\(\displaystyle \frac{7\pi}{4}\times \frac{180^{\circ}}{\pi}=\frac{7\times 180^{\circ}}{4}=315^{\circ}\)

Example Question #21 : Circles

Simplify and give the followoing expression in degrees:

 

\(\displaystyle \frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}\)

Possible Answers:

\(\displaystyle 450^{\circ}\)

\(\displaystyle 380^{\circ}\)

\(\displaystyle 350^{\circ}\)

\(\displaystyle 480^{\circ}\)

\(\displaystyle 420^{\circ}\)

Correct answer:

\(\displaystyle 450^{\circ}\)

Explanation:

First we need to simplify the expression:

 

\(\displaystyle \frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}=\frac{\frac{4\pi+\pi}{14}}{\frac{1}{7}}=\frac{5\pi}{2}\)

Then multiply by \(\displaystyle \frac{180^{\circ}}{\pi}\):

 

\(\displaystyle \frac{5\pi}{2}\times \frac{180^{\circ}}{\pi}=\frac{5\times 180^{\circ}}{2}=450^{\circ}\)

Example Question #22 : Circles

Convert \(\displaystyle \frac{2\pi}{3}\) radians to degrees.

Possible Answers:

\(\displaystyle 250^\circ\)

\(\displaystyle 120^\circ\)

\(\displaystyle 60^\circ\)

\(\displaystyle 30^\circ\)

\(\displaystyle 150^\circ\)

Correct answer:

\(\displaystyle 120^\circ\)

Explanation:

Use the conversion \(\displaystyle \pi \textup{ radians}= 180\textup{ degrees}\).

Since we are converting radians to degrees, multiply by 180 degrees and divide by \(\displaystyle \pi\) radians.

\(\displaystyle \frac{2\pi}{3} \textup{ radians}\left(\frac{180 \textup{ degrees}}{\pi\textup{ radian}}\right)= 120\textup{ degrees}\)

Example Question #21 : Circles

How many degrees is 3 radians?

Possible Answers:

\(\displaystyle 172^{\circ}\)

\(\displaystyle 189^{\circ}\)

None of these other answers.

\(\displaystyle 150^{\circ}\)

\(\displaystyle 156^{\circ}\)

Correct answer:

\(\displaystyle 172^{\circ}\)

Explanation:

When going from radians to degrees one multiplies by the conversion factor 

\(\displaystyle \frac{180^{\circ}}{\pi rad}\).

The radians cancel and the answer is left in degrees.

\(\displaystyle 3\hspace{1mm}{\color{Red} rad}\cdot\frac{180^{\circ}}{\pi {\color{Red} rad}}=\frac{540^\circ}{\pi}=172^{\circ}\)

Example Question #22 : Circles

Convert to radians: \(\displaystyle 33^o\)

Possible Answers:

\(\displaystyle 0.183\)

\(\displaystyle 0.576\)

\(\displaystyle 0.058\)

\(\displaystyle 1.736\)

\(\displaystyle 0.189\)

Correct answer:

\(\displaystyle 0.576\)

Explanation:

To convert to radians, set up the ratio \(\displaystyle \frac{180}{\pi } = \frac{33} { x}\):

\(\displaystyle 180 x = 33 \pi\)

\(\displaystyle x = 33 \pi \div 180 \approx 0.576\)

Example Question #23 : Circles

Convert to degrees: \(\displaystyle \frac{2 \pi }{7}\)

Possible Answers:

\(\displaystyle 16.37^o\)

\(\displaystyle 51.43^o\)

\(\displaystyle 0.016^o\)

\(\displaystyle 147.58^o\)

Correct answer:

\(\displaystyle 51.43^o\)

Explanation:

To convert, divide by \(\displaystyle \pi\) and multiply by \(\displaystyle 180\):

\(\displaystyle \frac{2 \pi }{7 } \div \pi = \frac{2}{7}\)

\(\displaystyle \frac{2}{7} \cdot 180 \approx 51.47^o\)

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