### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Divide Monomial Quotients

Mike wants to sell candy bars for a profit. If he sells each bar for , how much did each bar cost him?

**Possible Answers:**

**Correct answer:**

In order to solve this problem, set up the following equation:

Cross multiply:

Divide:

The original cost of the of each candy bar is

### Example Question #1 : How To Divide Monomial Quotients

Choose the answer that is the simplest form of the following expression of monomial quotients:

**Possible Answers:**

**Correct answer:**

To divide monomial quotients, simply invert the divisor and multiply:

Then, reduce:

### Example Question #1 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

**Possible Answers:**

**Correct answer:**

To find your answer, you have to invert the divisor and multiply across:

Then, reduce:

### Example Question #1 : Variables

Multiply:

**Possible Answers:**

**Correct answer:**

To solve you must multiply by both terms in

### Example Question #5 : Variables

Multiply:

**Possible Answers:**

**Correct answer:**

Multiply by both terms in

### Example Question #1 : Monomials

Multiply

**Possible Answers:**

None of the other answers

**Correct answer:**

When multiplying a polynomial by a monomial, each term in the polynomial gets multiplied by the monomial. Calculate each term one at a time, then add the results to get the final answer. In this case, we start by multiplying . and , thus we get . For the second term of the polynomial, we multiply and , resulting in . Finally, we multiply and , resulting in . Adding the three terms that we just found, we come to the answer of .

### Example Question #1 : Variables

Choose the answer that is the best solution to the following expression of monomial quotients:

**Possible Answers:**

**Correct answer:**

To multiply monomial quotients, treat them as you would any other fraction. Combine like terms wherever possible:

Then, you need to reduce:

### Example Question #2 : Variables

Choose the answer that is the simplest form of the following expression of monomial quotients:

**Possible Answers:**

**Correct answer:**

To simplify, first multiply across:

Then, reduce:

### Example Question #1 : Direct And Inverse Variation

The price of silver varies directly as the square of the mass. If 3.6 g of silver is worth $64.80, what is the value of 7.5 g of silver?

**Possible Answers:**

$301.75

$135.00

$178.50

$281.25

$215.25

**Correct answer:**

$281.25

This is a direct variation problem of the form y = kx^{2} The first set of data 3.6 g and $64.80 is used to calculate the proportionality constant, k. So 64.80 = k(3.6)^{2} and solving the equation gives k = 5.

Now we move to the new data, 7.5 g and we get y = 5(7.5)^{2} to yield an answer of $218.25.

$135.00 is the answer obtained if using proportions. This is an error because it does not take into consideration the squared elements of the problem.

### Example Question #1 : Direct And Inverse Variation

The diameter of a specific brand of candy wrapper is longer than half the volume of the candy itself. Find the expression for the diameter, , in terms of the volume, .

**Possible Answers:**

**Correct answer:**

The question asks for an equation that can relate and to each other, based on the information given. We are told that half the volume + determines the total diameter.

This gives us:

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