All ACT Math Resources
Example Questions
Example Question #1 : Variables
Mike wants to sell candy bars for a profit. If he sells each bar for , how much did each bar cost him?
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 #2 : Monomials
Choose the answer that is the simplest form of the following expression of monomial quotients:
To divide monomial quotients, simply invert the divisor and multiply:
Then, reduce:
Example Question #3 : Variables
Choose the answer that is the simplest form of the following expression of monomial quotients:
To find your answer, you have to invert the divisor and multiply across:
Then, reduce:
Example Question #1 : How To Multiply A Monomial By A Polynomial
Multiply:
To solve you must multiply by both terms in
Example Question #2081 : Act Math
Multiply:
Multiply by both terms in
Example Question #5 : Monomials
Multiply
None of the other answers
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 #2 : Variables
Choose the answer that is the best solution to the following expression of monomial quotients:
To multiply monomial quotients, treat them as you would any other fraction. Combine like terms wherever possible:
Then, you need to reduce:
Example Question #3 : Variables
Choose the answer that is the simplest form of the following expression of monomial quotients:
To simplify, first multiply across:
Then, reduce:
Example Question #1 : Variables
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?
$301.75
$215.25
$135.00
$178.50
$281.25
$281.25
This is a direct variation problem of the form y = kx2 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, .
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: