### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #31 : Algebraic Concepts

Mulitply:

**Possible Answers:**

**Correct answer:**

The FOIL method works nicely here:

### Example Question #32 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

It is not possible to tell from the information given

is greater

and are equal

is greater

**Correct answer:**

is greater

is the greater amount.

### Example Question #33 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

is greater

It is not possible to tell from the information given

and are equal

is greater

**Correct answer:**

is greater

is the greater amount.

### Example Question #34 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

is greater

It is not possible to tell from the information given

and are equal

is greater

**Correct answer:**

and are equal

and are equal.

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

Which quantity is greater?

**Possible Answers:**

is greater

and are equal

is greater

It is not possible to tell from the information given

**Correct answer:**

is greater

Use the distributive property to expand.

To compare the expressions, we can remove common factors. and are common in both expressions, so they can be removed:

### Example Question #36 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

is greater

is greater

and are equal

It is not possible to tell from the information given

**Correct answer:**

is greater

Use the distributive property to evaluate and .

Since , we get:

is the greater quantity.

### Example Question #37 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

is greater

It is not possible to tell from the information given

and are equal

is greater

**Correct answer:**

is greater

Use the distributive property to evaluate each quantity.

and are common in both expressions, so we can write:

is the greater quantity

### Example Question #38 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

is greater

is greater

and are equal

It is not possible to tell from the information given

**Correct answer:**

and are equal

and are equal.

### Example Question #39 : Algebraic Concepts

Which quantity is greater?

**Possible Answers:**

It is not possible to tell from the information given

is greater

is greater

and are equal

**Correct answer:**

is greater

is the greater amount.

### Example Question #40 : Algebraic Concepts

Which of the following is equivalent to ?

**Possible Answers:**

All four of the expressions given in the other responses are correct.

**Correct answer:**

All four of the expressions given in the other responses are correct.

We demonstrate that all four of the expressions are equivalent to .

By the associative property of multiplication,

and

By combining like terms, and applying the distribution property: