### All ISEE Upper Level Math Resources

## Example Questions

### Example Question #11 : Operations

**Possible Answers:**

**Correct answer:**

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify. The negative in the fraction can be applied to either the numerator or the denominator, but not both; we will apply it to the numerator.

The fraction cannot be simplified further.

### Example Question #11 : Operations

Solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #12 : Operations

If the product of three consecutive numbers is 990, what is the smallest number?

**Possible Answers:**

**Correct answer:**

If the product of three consecutive numbers is 990, then the smallest number can be found by plugging in each answer choice into the scenario to see whether it is correct.

If we plug in 9 as the smallest number, then the two consecutive numbers would be 10 and 11.

Given that 9 times 10 times 11 equals 990, that is the correct answer.

### Example Question #13 : Operations

What is the simplified version of the expression below?

**Possible Answers:**

**Correct answer:**

The first step is to simplify the values in the parentheses:

### Example Question #14 : Operations

**Possible Answers:**

**Correct answer:**

Reorder the expression to group like-terms together.

### Example Question #15 : Operations

If is a positive number, what is a possible value of ?

**Possible Answers:**

**Correct answer:**

If x is equal to , then the equation could be written as follows:

Given that is a positive number, is a possible value of .

### Example Question #16 : Operations

Megan teaches a cooking class. Every time a student takes a class, the student receives a 10% discount off of the price he paid for the previous class. The first class that Jose took cost $50. What will be the first class in which Jose pays less than $38?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, the price of $50 must be discounted by 10% until we get to a price of $38 or less.

The first class is 50.

The second class, being 10 percent less than the previous one, is

The third class, being 10 percent less than the previous one, is

The fourth class, being 10 percent less than the previous one, is

Therefore, the answer is 4.

### Example Question #17 : Operations

Simplify the following expression

**Possible Answers:**

**Correct answer:**

Simplify the following expression

Let's begin by multiplying our coefficients:

Next, we need to realize that we can combine our x's by adding the exponents.

Put it all together to get:

### Example Question #18 : Operations

Simplify the following:

**Possible Answers:**

**Correct answer:**

Simplify the following:

To begin, our coefficient will not change. We have just one integer (the 9) and nothing to multiply it by.

To combine our exponents, we will add them. This is because we are multiplying them

Put it together to get:

### Example Question #19 : Operations

and are both positive.

Evaluate .

**Possible Answers:**

**Correct answer:**

Multiply the binomials using the FOIL method - first, outer, inner, last - then combine like terms:

and ; also, by the Power of a Product Principle:

.

and are both positive, so, substituting:

.

Again, using substitution:

Certified Tutor

Certified Tutor