SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #1 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate: .

Possible Answers:

None of the other responses is correct.

The expression is undefined.

Correct answer:

Explanation:

, or, equivalently,

Example Question #1 : How To Find Absolute Value

Define .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

, or, equivalently,

Example Question #11 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #11 : How To Find Absolute Value

Define .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #61 : New Sat Math No Calculator

Define an operation  as follows:

For all real numbers ,

Evaluate 

Possible Answers:

Both  and 

Correct answer:

Explanation:

Example Question #11 : How To Find Absolute Value

Given:  are distinct integers such that:

Which of the following could be the least of the three?

Possible Answers:

, or 

 or  only

 or  only

 or  only

 only

Correct answer:

 or  only

Explanation:

, which means that  must be positive. 

If  is nonnegative, then . If  is negative, then it follows that . Either way, . Therefore,  cannot be the least. 

We now show that we cannot eliminate  or  as the least.

 

For example, if , then  is the least;  we test both statements:

, which is true.

 

, which is also true.

 

If , then  is the least; we test both statements:

, which is true.

 

, which is also true.

 

Therefore, the correct response is  or  only.

Example Question #11 : Absolute Value

, and  are distinct integers.  and . Which of the following could be the greatest of the three?

Possible Answers:

 only

 only

None of the other responses is correct.

, or 

 only

Correct answer:

 only

Explanation:

, so  must be positive. Therefore, since , equivalently, , so  must be positive, and

If  is negative or zero, it is the least of the three. If  is positive, then the statement becomes

,

and  is still the least of the three. Therefore,  must be the greatest of the three.

Example Question #32 : Algebra

Give the solution set:

Possible Answers:

Correct answer:

Explanation:

If , then either  or . Solve separately:

or 

The solution set, in interval notation, is .

Example Question #12 : Absolute Value

Define an operation  on the real numbers as follows:

If , then 

If , then 

If , then 

If , and 

then which of the following is a true statement?

Possible Answers:

Correct answer:

Explanation:

Since , evaluate

, setting  :

 

Since , then select the pattern

 

Since , evaluate

, setting :

 

, so the correct choice is that .

 

 

 

Example Question #12 : How To Find Absolute Value

Given:  are distinct integers such that:

Which of the following could be the least of the three?

Possible Answers:

 or  only

 only

 only

, or 

 only

Correct answer:

 only

Explanation:

, which means that  must be positive. 

If  is nonnegative, then . If  is negative, then it follows that . Either way, . Therefore,  cannot be the least. 

Now examine the statemtn . If , then  - but we are given that  and  are distinct. Therefore,  is nonzero, , and 

and

.

 cannot be the least either.

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