All ISEE Lower Level Quantitative Resources
Example Questions
Example Question #1 : Equations
What is the value of x in the equation?
First, add .
Next, divide .
So
Example Question #2 : Algebraic Concepts
Simplify.
When simplifying an expression, you must combine like terms. There are two types of terms in this expression: “x’s” and whole numbers. Combine in two steps:
1) x’s: Â
2) whole numbers: Â Â
The simplified expression is: .
Example Question #3 : Algebraic Concepts
Solve, when .
To solve, insert  for each :
Simplify:
Â
*Common error: When solving this part of the equation  always remember the order of operations (PEMDAS) and square the number in the () BEFORE multiplying!
Example Question #4 : Algebraic Concepts
Solve for .
Example Question #5 : Algebraic Concepts
Use the equations to answer the question.Â
What is ?
First, you need to find what would make and true in their respective equations. equals 1 and equals 4. The next step is to add those together, which gives you 5.Â
Example Question #6 : Algebraic Concepts
What story best fits the expression ?
Nell bought 9 bags of candy with 3 pieces of candy in each bag.Â
Jonah had 3 baseball cards, but after his friend gave him some, he had 12.Â
Michelle had 3 stuffed animals and gave 1 away.
Lisa had 9 pencils with two erasers each.
Nell bought 9 bags of candy with 3 pieces of candy in each bag.Â
Nell's story fits best because if she bought 9 bags with 3 pieces each, that would be 27 total. This fits best with the equation.
Example Question #7 : Algebraic Concepts
What is equal to in this equation:Â
Find the number that makes the equation true. 2 works because when plugged in, the left side of the equation becomes 13, making the whole equation true.
Example Question #8 : Algebraic Concepts
Five more than a number is equal to  of twenty-five . What is the number?
From the question, we know that  plus a number equals  of . In order to find out what  of  is, multiply  by . Â
Â
, or .
The number we are looking for needs to be five less than , or .
You can also solve this algebraically by setting up this equation and solving:
Â
Subtract  from both sides of the equation.    Â
Â
Example Question #9 : Algebraic Concepts
Solve for .
To solve for , we want to isolate , or get it by itself.Â
Add to both sides of the equation.
      Â
Now we need to divide both sides by the coefficient of , i.e. the number directly in front of the .
  Â
Example Question #10 : Algebraic Concepts
Solve for .
First, subtract the three from both sides:
Then, divide by three on both sides:
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