SAT II Math II : Other Mathematical Relationships

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

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Example Questions

Example Question #147 : Sat Subject Test In Math Ii

Add in modulo 9:

Possible Answers:

Correct answer:

Explanation:

In modulo 9 arithmetic, a number is congruent to the remainder of its division by 9. 

Since 

and 

,

,

making "5" the correct response.

Example Question #2 : Other Mathematical Relationships

 varies directly as  and inversely as 

If  and , then .

To the nearest whole number, evaluate  if  and .

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

Explanation:

 varies directly as  and inversely as . This means that for some constant of variation ,

Alternatively, 

We can substitute the initial conditions for thevariables on the left side and the final conditions for those on the right side, then solve for :

Example Question #1 : Other Mathematical Relationships

 varies directly as both  and the square of .

If  and , then 

Evaluate  if  and .

Possible Answers:

Correct answer:

Explanation:

 varies directly as both  and the square of . This means that for some constant of variation ,

.

Alternatively stated,

.

We can substitute the initial conditions for the variables on the left side and the final conditions for those on the right side, then solve for :

Example Question #2 : Other Mathematical Relationships

 

Evaluate .

Possible Answers:

The system has no solution.

Correct answer:

Explanation:

Rewrite the two equations by setting  and  and substituting:

 

 

 

The result is a two-by-two linear system in terms of  and :

This can be solved, among other ways, using Gaussian elimination on an augmented matrix:

Perform row operations until the left two columns show identity matrix . One possible sequence:

 

 and . In the former equation, substitute  back for , and raise both sides to the power of 4:

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