ISEE Middle Level Math : Algebraic Concepts

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

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Example Questions

Example Question #2 : How To Add Variables

Possible Answers:

Correct answer:

Explanation:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable.  Therefore, you can group your problem as follows:

Now, just combine like terms:

Example Question #7 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

You should begin by distributing  through the whole group that it precedes:

Now, move your like variables next to each other:

Finally, combine the like terms:

Example Question #621 : Concepts

Simplify:

 

Possible Answers:

Correct answer:

Explanation:

First, group together your like variables:

The only like variables needing to be combined are the x-variables.  You can do this in steps or all at once:

Example Question #11 : How To Add Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

First, move the like terms to be next to each other:

Now, combine the x-variables and the y-variables:

Example Question #622 : Concepts

Simplify:

Possible Answers:

Correct answer:

Explanation:

Let's begin by moving the like terms toward each other.  Notice the following: zy is the same as yz.  (Recall the commutative property of multiplication.)

Now, all you have to do is combine the x-variables and the yz-terms:

Notice that you do not end up with any exponent changes.  That would only happen if you multiplied those variables.

Example Question #12 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Remember, when you have exponents like this, you will treat each exponented variable as though it were its own "type."  Likewise, pairs of variables are to be grouped together.  Therefore, group the problem as follows:

Notice that the only thing to be combined are the terms.

Therefore, your answer will be:

 

Example Question #34 : Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable.  Therefore, you can group your problem as follows:

Then, all you need to do is to combine the  terms:

Example Question #13 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by distributing the  through the parentheses:

Next, move the like terms next to each other.  Remember, treat  like it is its own, separate variable.

Finally, combine like terms:

Example Question #11 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Combine like terms:

Example Question #12 : Algebra

Simplify:

Possible Answers:

Correct answer:

Explanation:

Combine like terms:

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