ACT Math : Variables
Study concepts, example questions & explanations for ACT Math
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Example Questions
Example Question #1 : How To Use The Direct Variation Formula
An instrument reads two values, 
An instrument reads two values, 
Direct variation means that any pairing of the related values will always have the same ratio, thus we know that for any other values 
Thus, for our information, we know:
This means that the new values of 
Example Question #2 : Direct And Inverse Variation
In an experimental setting, the pressure and the temperature of gas in a container are directly proportional. In the first experiment, the pressure of the gas was 
It cannot be determined.
For direct variation of related variables, we know that the following equation holds:
For our data, this would be:
To start simplifying and solving this, first factor the top of the left fraction:
Cancel the 
Next, multiply by 
Since 
Simplify:
Example Question #3 : How To Use The Direct Variation Formula
In a given solution, the proportion of water to apple juice is directly proportional. If the first batch of the solution contained 
This problem is easily solved by setting up a ratio. For directly proportional amounts, we know:
For our data, this would be:
This is first simplified as being:
Next, multiply by 
Finally:
Example Question #2 : How To Use The Direct Variation Formula
The length, in inches, of a box is 
Since the question asks for the length in terms of width, I like to start by setting the problem up as 
Example Question #2 : Direct And Inverse Variation
1. Use the given values of 
2. Solve for 
Example Question #2 : How To Use The Inverse Variation Formula
If 
To solve this algebraic equation, subtract 
We end up with the equation 
Example Question #1 : How To Use The Inverse Variation Formula
In a given set of experiments, the values of two variables are always inversely proportional. If in the first experiment the first variable was 
Recall that inverse variation means that when one variable increases, the other decreases. This gives you the following equation:
Now, for our data, we know:
You merely have to solve for 
Divide by 
Example Question #14 : Variables
Throughout a party, the number of joyful non-philosophers in a room is always inversely proportional to the number of philosophers in the room. The room begins with 
Recall that inverse variation means that when one variable increases, the other decreases. This gives you the following equation:
For our data, this means:
You merely need to solve for 
Example Question #1 : Polynomials
What type of equation is the following?
(y + 2)(y + 4)(y + 1) = z
constant
quartic
linear
cubic
quadratic
cubic
The degree of a polynomial is the highest exponent of the terms.
Degree 0 – constant
Degree 1 – linear
Degree 2 – quadratic
Degree 3 – cubic
Degree 4 – quartic
Multiply out the equation:
(y + 2)(y + 4)(y + 1) = z
(y2 + 2y + 4y + 8)(y + 1) = z
y3 + 2y2 + 4y2 + 8y + y2 + 2y + 4y + 8 = z
The highest exponent is y3;therefore the equation is a degree 3 cubic.
Example Question #1 : Polynomial Operations
Find the degree of the polynomial:
The degree of a polynomial is determined by the term with the highest degree. In this case that is 
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