ISEE Upper Level Math : Variables and Exponents

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

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Example Questions

Example Question #81 : Variables

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #81 : Variables

Evaluate .

Possible Answers:

Correct answer:

Explanation:

To solve for the variable isolate it on one side of the equation with all of constants on the other side.

First add one third to both sides.

Calculate a common denominator to add the two fractions.

Square both sides to solve for y.

Example Question #83 : Variables

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

Simplify the following:

Let's recall the rules for distributing exponents. 

We treat coefficients (like the 7) like regular numbers and raise them to the new exponent.

We deal with variables (like the t, h, and b) by multiplying their current exponent by the new exponent. 

Doing so yields:

Simplify to get:

Example Question #84 : Variables

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the Power of a Power Principle, 

So

Also, by the Power of a Product Principle, 

, so, substituting,

.

Example Question #85 : Variables

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the Power of a Product Principle, 

Also, by the Power of a Power Principle, 

Combining these ideas, then substituting:

Example Question #1 : How To Subtract Exponential Variables

Simplify the expression:

Possible Answers:

The expression cannot be simplified further.

Correct answer:

Explanation:

Group, then collect like terms:

Example Question #1 : How To Subtract Exponential Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #81 : Variables

Assume that . Which of the following expressions is equivalent to:

 ?

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Subtract Exponential Variables

If , simplify:

Possible Answers:

Correct answer:

Explanation:

Example Question #2 : How To Subtract Exponential Variables

If , simplify:

Possible Answers:

Correct answer:

Explanation:

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