### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : Variables And Exponents

Simplify:

**Possible Answers:**

The expression cannot be simplified further

**Correct answer:**

Group and combine like terms :

### Example Question #1 : Variables And Exponents

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(b) is greater.

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

**Correct answer:**

(b) is greater.

Since and have different signs,

, and, subsequently,

Therefore,

This makes (b) the greater quantity.

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

Assume that and are not both zero. Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

**Correct answer:**

It is impossible to tell from the information given.

Simplify the expression in (a):

Therefore, whether (a) or (b) is greater depends on the values of and , neither of which are known.

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

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

**Correct answer:**

It is impossible to tell from the information given

We give at least one positive value of for which (a) is greater and at least one positive value of for which (b) is greater.

Case 1:

(a)

(b)

Case 2:

(a)

(b)

Therefore, either (a) or (b) can be greater.

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

Assume all variables to be nonzero.

Simplify:

**Possible Answers:**

None of the answer choices are correct.

**Correct answer:**

None of the answer choices are correct.

Any nonzero expression raised to the power of 0 is equal to 1. Therefore,

.

None of the given expressions are correct.