ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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Example Questions

Example Question #1 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

If  is added to  of another number, the result is . What is the other number?

Possible Answers:

Correct answer:

Explanation:

The first step is to translate the words, "if  is added to  of another number, the result is ," into an equation. This gives us:

Subtract  from each side. 

Multiply each side by

Therefore,  is the correct answer. 

Example Question #34 : How To Add Variables

Jack has a collection of coins. He gives Brett most of his collection, such that Brett now has twice as many coins as Jack. If there are 36 coins in the collection, how many coins does Jack now have?

Possible Answers:

Correct answer:

Explanation:

If Jack has a collection of 36 coins and gives Brett most of his collection, such that Brett now has twice as many coins as Jack, this problem can be solved by dividing the total into 3 equal parts, giving 2 of the parts to Brett and one of the parts to Jack

: this is Jack's part

: this is Brett's part

Example Question #34 : How To Add Variables

If , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

In solving for  the first step is to substitute  for , given that .

Next, the parentheses are solved for. 

This simplifies to , the correct answer. 

Example Question #2 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify the following expression: 

Possible Answers:

Cannot be computed

Correct answer:

Explanation:

When adding and subtracting variable, you can only combine like variables.  

That means all of the  variables are solved separately from the  variables.  

Then you just add and subtract the constants normally so  and .  

So the final answer is .

Example Question #124 : Ssat Middle Level Quantitative (Math)

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by distributing the  to its entire group:

Next, group the like terms:

Finally, combine the like terms:

Example Question #31 : How To Add Variables

When adding variables, we must add all of the like variables together but then combine them into one singular value at the end. True or False

Possible Answers:

False

True

Correct answer:

False

Explanation:

When adding variables, it is true that you must first add all of the like variables.  But then they are left separate to have an expression with the different variables differentiated.

Example Question #3 : Apply Properties Of Operations To Expand Linear Expressions With Rational Coefficients: Ccss.Math.Content.7.Ee.A.1

Simplify the followng:

Possible Answers:

Correct answer:

Explanation:

When adding variables together, you must first make sure you are combining the same variable.  So, in this case

we can see that both terms contain the variable a.  Therefore, we can combine them. 

Now, when we combine them, we can think of the variables as objects.  So, we can say were are combining an apple and 4 apples together.  So,

We can simplify our problem the same way.

Example Question #31 : How To Add Variables

Combine the following variables:

Possible Answers:

Correct answer:

Explanation:

Combine the following variables:

First, group the like terms. This means we will put terms with the same exponent next to each other. This will make it easier to be sure we are adding correctly.

Next, add the coefficients, but keep the exponents the same. Only combine terms with the same exponents. Notice that we have three different exponents (6,5 and 2) This means we will have three terms in our final answer.

So we get the following:

Example Question #181 : Variables

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will think of the variables as objects.  So, in the problem

let's think of the variable x as books.  So, we can look at the problem as we currently have 3 books.  We go to the library and borrow 7 more books.  How many books do we have now?  The answer is 10.  We now have 10 books.  

We can add the variables in the same way.  So,

Example Question #33 : How To Add Variables

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

To add variables, we will look at the variables as objects.  So, 

we can look at it as the following.  We have 6 dollars.  We do all of our chores, and we get 4 more dollars.  How many dollars do we have now?  We now have 10 dollars.  We add variables in the same way. So

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