SAT II Math II : SAT Subject Test in Math II

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #1 : Radians And The Unit Circle

The degree angle  can be expressed as what in radians?

Possible Answers:

Correct answer:

Explanation:

In order to convert degrees to radians, we will need to know the conversion factor.

Set up a dimensional analysis to solve.

The answer is:  

Example Question #2 : Radians And The Unit Circle

Which of the following angles belong in the fourth quadrant?

Possible Answers:

Correct answer:

Explanation:

The fourth quadrant is in the positive x-axis and negative y-axis.  

The angle ranges are:

The only possible answer is:  

Example Question #3 : Radians And The Unit Circle

What degree measure is equivalent to ?

Possible Answers:

Correct answer:

Explanation:

Every pi radians is equal to 180 degrees.

Replace the pi term with 180 degrees and multiply.

The answer is:  

Example Question #1 : Law Of Cosines

A triangle has sides that measure 10, 12, and 16. What is the greatest measure of any of its angles (nearest tenth of a degree)?

Possible Answers:

Correct answer:

Explanation:

We are seeking the measure of the angle opposite the side of greatest length, 16.

We can use the Law of Cosines, setting , and solving for :

Example Question #2 : Law Of Cosines

A triangle has sides that measure 15, 17, and 30. What is the least measure of any of its angles (nearest tenth of a degree)?

Possible Answers:

Correct answer:

Explanation:

We are seeking the measure of the angle opposite the side of least length, 15.

We can use the Law of Cosines, setting , and solving for :

Example Question #1 : Law Of Cosines

Given : with .

Which of the following whole numbers is closest to ?

Possible Answers:

Correct answer:

Explanation:

Apply the Law of Cosines

setting  and solving for :

Of the five choices, 27 comes closest.

Example Question #2 : Law Of Cosines

Given : with .

Evaluate  to the nearest tenth.

Possible Answers:

The correct answer is not given among the other responses.

Correct answer:

Explanation:

Apply the Law of Cosines

setting  and solving for :

Example Question #5 : Law Of Cosines

In :

Evaluate the length of  to the nearest tenth of a unit.

Possible Answers:

Correct answer:

Explanation:

The figure referenced is below:

Triangle 2

By the Law of Cosines, given the lengths  and  of two sides of a triangle, and the measure  of their included angle, the length  of the third side can be calculated using the formula

Substituting , and , then evaluating:

Taking the square root of both sides:

Example Question #1 : Law Of Sines

Find the measure of angle .

2

Possible Answers:

Correct answer:

Explanation:

2

Start by using the Law of Sines to find the measure of angle .

Since the angles of a triangle must add up to ,

 

 

Example Question #1 : Law Of Sines

In 

Evaluate  (nearest degree)

Possible Answers:

Cannot be determined

Correct answer:

Cannot be determined

Explanation:

By the Law of Sines, if  and  are the lengths of two sides of a triangle, and  and  the measures of their respective opposite angles, 

 and  are opposite sides  and , so, setting , and :

However, the range of the sine function is , so there is no value of  for which this is true. Therefore, this triangle cannot exist.

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