ISEE Lower Level Quantitative : Algebraic Concepts

Example Questions

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Example Question #1 : Algebraic Concepts

What is the value of x in the equation?

Explanation:

Next, divide .

So

Example Question #2 : Algebraic Concepts

Simplify.

Explanation:

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:

2) whole numbers:

The simplified expression is: .

Example Question #3 : Algebraic Concepts

Solve, when .

Explanation:

To solve, insert  for each :

Simplify:

*Common error: When solving this part of the equation  always remember the order of operations (PEMDAS) and square the number in the () BEFORE multiplying!

Solve for .

Explanation:

Example Question #5 : Algebraic Concepts

Use the equations to answer the question.

What is ?

Explanation:

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.

Example Question #6 : Algebraic Concepts

What story best fits the expression ?

Lisa had 9 pencils with two erasers each.

Jonah had 3 baseball cards, but after his friend gave him some, he had 12.

Nell bought 9 bags of candy with 3 pieces of candy in each bag.

Michelle had 3 stuffed animals and gave 1 away.

Nell bought 9 bags of candy with 3 pieces of candy in each bag.

Explanation:

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:

Explanation:

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?

Explanation:

From the question, we know that  plus a number equals  of . In order to find out what  of  is, multiply  by .

, 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:

Subtract  from both sides of the equation.

Example Question #9 : Algebraic Concepts

Solve for .

Explanation:

To solve for , we want to isolate , or get it by itself.

Add to both sides of the equation.

Now we need to divide both sides by the coefficient of , i.e. the number directly in front of the .

Solve for .