ISEE Middle Level Math : Algebraic Concepts

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

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Example Questions

Example Question #114 : Ssat Middle Level Quantitative (Math)

Joey's teacher takes off 5 points from student essays each day the essay is late. The essays are scored out of 100 points. If Joey's essay got a score of 68, but he turned it in 3 days late, what would his score have been if he had turned the essay in on time?

Possible Answers:

Correct answer:

Explanation:

Given that Joey's essay was 3 days late, he lost 15 points. This is because he loses 5 points for each day that it is late, and having turned it in 3 days late, lost 15 points. 

Joey's final score (68) will be equal to his original grade, minus the penalty.

If we add 15 to the score that ultimately received, the sum is 83.

If Joey had turned his essay in on time, he would have earned a score of 83. 

Example Question #115 : Ssat Middle Level Quantitative (Math)

Write in base ten:

Possible Answers:

Correct answer:

Explanation:

In base five, each place value is a power of five, starting with 1 at the right, then, going to the left, 

 can be calculated in base ten as

.

 

 

Example Question #171 : Algebraic Concepts

Annie ran  miles on Wednesday. She ran  more miles on Thursday than she did on Wednesday. On Friday, she ran a distance in miles that was  longer than the distance she ran on Wednesday. On Saturday, she ran a distance in miles that was  longer than the distance she ran on Thursday. What is the total number of miles that Annie ran, Wednesday through Saturday?

Possible Answers:

Correct answer:

Explanation:

On Wednesday, Annie ran  miles.

She ran  more miles on Thursday than she did on Wednesday. Therefore, she ran  miles on Thursday.

On Friday, she ran a distance in miles that was  longer than the distance she ran on Wednesday.  of  miles is  mile. (You can figure this out by realizing that since  of  is  and  is half of  of  must be half of , which is .) , so Annie ran  miles on Friday.

On Saturday, she ran a distance in miles that was  longer than the distance she ran on Thursday. of  is . , so Annie ran  miles on Saturday. 

The sum of these distances is equal to

Annie ran  miles in total Wednesday through Saturday.

Example Question #172 : Algebraic Concepts

Bob and Anita drove cross country together. If Bob drove  miles on the trip, and Anita drove twice as many miles as Bob, how many miles total did they drive together?

Possible Answers:

Correct answer:

Explanation:

If Bob drove  miles, and Anita drove twice as many miles as Bob, then Anita drove  miles; therefore, the sum of the miles that they drove together would be 3J. 

Thus, the correct answer is

Example Question #1 : Expressions & Equations

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 #33 : 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 #1 : Expressions & Equations

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 #31 : How To Add Variables

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.

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