ISEE Upper Level Math : How to add exponential variables

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

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Example Questions

Example Question #1 : How To Add Exponential Variables

Rewrite the polynomial in standard form:

Possible Answers:

Correct answer:

Explanation:

The degree of a term of a polynomial with one variable is the exponent of that variable. The terms of a polynomial in standard form are written in descending order of degree. Therefore, we rearrange the terms by their exponent, from 5 down to 0, noting that we can rewrite the  and constant terms with exponents 1 and 0, respectively:

Example Question #2 : How To Add Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : How To Add Exponential Variables

Assume that . Simplify:

Possible Answers:

Correct answer:

Explanation:

 

Example Question #4 : How To Add Exponential Variables

If , simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : How To Add Exponential Variables

If , simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #6 : How To Add Exponential Variables

Define  

What is  ?

Possible Answers:

Correct answer:

Explanation:

Substitute  for  in the definition:

Example Question #7 : How To Add Exponential Variables

Add:

Possible Answers:

Correct answer:

Explanation:

Example Question #8 : How To Add Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

We can expand the first term using FOIL:

Reorder the expression to group like-terms together.

Simplify by combining like-terms.

Example Question #9 : How To Add Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Expand each term by using FOIL:

Rearrange to group like-terms together.

Simplify by combining like-terms.

Example Question #10 : How To Add Exponential Variables

Simplify:

Possible Answers:

The expression can not be simplified further

Correct answer:

Explanation:

Start by reordering the expression to group like-terms together.

Combine like-terms to simplify.

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