### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Add Variables

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Add Variables

Simplify:

**Possible Answers:**

**Correct answer:**

First, rewrite the problem so that like terms are next to each other.

Next, evaluate the terms in parentheses.

Rewrite the expression in simplest form.

### Example Question #2 : How To Add Variables

Simplify:

**Possible Answers:**

**Correct answer:**

First we rewrite the problem so that like terms are together.

Next we can place like terms in parentheses and evaluate the parentheses.

Now we rewrite the equation in simplest form.

### Example Question #2 : How To Add Variables

Which expression is equivalent to the expression ?

**Possible Answers:**

**Correct answer:**

The first step in simplifying this expression is to get the binomial out of the parentheses. It's important to note you cannot further simplify this binomial first, since there are no like terms in it.

Since you have a minus sign in front of the binomial, you need to flip the sign of both terms inside the parentheses to get rid of the parentheses (similar to distributing a negative one across the binomial):

Now you are able to combine like terms, making sure that exponents on the variables match exactly before you combine. The first and fourth terms are like terms, and the second and third terms are like terms.

To combine those terms, keep the variables and exponents the same and add up the coefficients. The first term has a coefficient of and the fourth term has a coefficient of , so they add up to a total of . The second term has a coefficient of and the third term has a coefficient of , so they add up to a total of .

This brings you to the final, simplified answer:

### Example Question #5 : How To Add Variables

Simplify:

**Possible Answers:**

**Correct answer:**

Combine like terms:

### Example Question #3 : How To Add Variables

Simplify the following:

**Possible Answers:**

**Correct answer:**

To simplify this expression, you need to combine like terms.

There are two terms with , one term with , and two terms without a variable.

This gives you the final answer:

Remember that when you subtract by a negative number, you are actually adding the inverse - thereby adding a positive number.

### Example Question #4 : How To Add Variables

Simplify the following:

**Possible Answers:**

**Correct answer:**

In this problem, you need to combine like terms. Be very careful when combining like terms, since a few terms differ only by a few exponents. You have two terms with , two terms with , and one term with .

This leads to the final answer:

### Example Question #8 : How To Add Variables

Multiply:

**Possible Answers:**

**Correct answer:**

### Example Question #9 : How To Add Variables

Simplify:

**Possible Answers:**

**Correct answer:**

Combine like terms:

### Example Question #10 : How To Add Variables

If two supplementary angles are equal to and , then what is the value of ?

**Possible Answers:**

**Correct answer:**

The sum of two supplementary angles is always 180 degrees; therefore:

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