ISEE Upper Level Math : Numbers and Operations

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

varsity tutors app store varsity tutors android store

Example Questions

Example Question #8 : Exponents

Define  as follows:

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : Exponents

Simplify the expresseion:

Possible Answers:

The expression is already simplified.

Correct answer:

The expression is already simplified.

Explanation:

Variable terms can be combined by adding and subtracting if and only of they are like - that is, if each exponent of each variable is the same. In the given expression, no two exponents are the same. The terms cannot be combined, and the expression is already simplified.

Example Question #10 : Exponents

Define a function  as follows:

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #61 : Numbers And Operations

Define a function .

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Example Question #62 : Numbers And Operations

Define  and .

Evaluate .

Possible Answers:

Undefined

Correct answer:

Explanation:

, by definition, so

Evaluate  and  separately:

 

 

 

Example Question #63 : Numbers And Operations

Define  as follows:

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #64 : Numbers And Operations

\dpi{100} (7-4)^{3}=

Possible Answers:

\dpi{100} 4

\dpi{100} 9

\dpi{100} 3

\dpi{100} 27

Correct answer:

\dpi{100} 27

Explanation:

Subtract the numbers inside the parentheses first.  This leaves you with 3, which you then raise to the 3rd power:

\dpi{100} 3\times 3\times 3=27

Example Question #65 : Numbers And Operations

Evaluate:

Possible Answers:

The expression is undefined.

Correct answer:

Explanation:

Any nonzero number taken to the power of 0 is equal to 1, so

Example Question #66 : Numbers And Operations

Multiply:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method:

Example Question #67 : Numbers And Operations

Evaluate:

 

Possible Answers:

Correct answer:

Explanation:

Based on the power rule for exponents we can write:

 

 

That means; to raise a power to a power we need to multiply the exponents. In addition, based on the product rule for exponents in order to multiply two exponential terms with the same base, we need to add their exponents:

 

 

So we can write:

 

Learning Tools by Varsity Tutors