### All Algebra II Resources

## Example Questions

### Example Question #1 : Factorials

What is the value of .

**Possible Answers:**

None of the other answers.

**Correct answer:**

When evaluating a factorial, you multiply the original number by each integer less than it, stopping at 1.

For this problem, this means that

.

Then adding 3, we get the answer 123

### Example Question #2 : Factorials

Which of the following best represents the approximate value of ?

**Possible Answers:**

**Correct answer:**

The value of is defined as .

To find , simply cube the decimal number.

The closest value of this number is:

### Example Question #4 : Multiplying And Dividing Factorials

Stewie has marbles in a bag. How many marbles does Stewie have?

**Possible Answers:**

**Correct answer:**

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

**Alternative Solution**

### Example Question #5 : Multiplying And Dividing Factorials

Which of the following is NOT the same as ?

**Possible Answers:**

**Correct answer:**

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

### Example Question #3 : Factorials

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

Recall that .

Likewise, .

Thus, the expression can be simplified in two parts:

and

The product of these two expressions is the final answer:

### Example Question #4 : Factorials

**Possible Answers:**

**Correct answer:**

To simplify this, just write out each factorial:

### Example Question #5 : Factorials

Find the value of:

**Possible Answers:**

**Correct answer:**

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it. So, can also be written as:

To make this easier for ourselves, we can cancel out the numbers that appear on both the top and bottom:

### Example Question #7 : Multiplying And Dividing Factorials

Which of the following is equivalent to ?

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

This is a factorial question. The formula for factorials is .

### Example Question #6 : Factorials

Divide by

**Possible Answers:**

**Correct answer:**

A factorial is a number which is the product of itself and all integers before it. For example

In our case we are asked to divide by . To do this we will set up the following:

We know that can be rewritten as the product of itself and all integers before it or:

Substituting this equivalency in and simplifying the term, we get:

### Example Question #7 : Factorials

If is a postive integer, which of the following answer choices is a possible value for the expression.

**Possible Answers:**

**Correct answer:**

This expression of factorials reduces to (n+1)(n+2). Therefore, the solution must be a number that multiplies to 2 consecutive integers. Only 30 is a product of 2 consecutive integers.

So n would have to be 4 in this problem.

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