ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #3 : How To Find Inverse Variation

When ,  .

When .

If  varies inversely with , what is the value of  when ?

Possible Answers:

Correct answer:

Explanation:

If  varies inversely with .

 

1. Using any of the two  combinations given, solve for :

Using :

 

2. Use your new equation  and solve when :

 

Example Question #33 : Algebraic Fractions

x

y

If  varies inversely with , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

An inverse variation is a function in the form:  or , where  is not equal to 0. 

Substitute each  in .

Therefore, the constant of variation, , must equal 24. If  varies inversely as must equal 24. Solve for .

Example Question #1 : How To Find Inverse Variation

Two numbers  and  vary inversely, and  when . If this is true, what is the value of  when ?

Possible Answers:

Correct answer:

Explanation:

If  when , and the variation is direct, then . Using this, we know that if .

Example Question #1 : How To Find Excluded Values

Which of the following provides the complete solution set for  ?

Possible Answers:

No solutions

Correct answer:

Explanation:

The absolute value will always be positive or 0, therefore all values of z will create a true statement as long as . Thus all values except for 2 will work.

Example Question #1 : How To Find Excluded Values

Find the excluded values in the following algebraic fraction.

Possible Answers:

Correct answer:

Explanation:

In order to find excluded values, find the values that make the denominator equal zero.

To do this, you must factor the denominator:

Now, set each part equal to zero and solve for .

Example Question #1 : How To Find Excluded Values

Find the excluded values for  for the following algebraic fraction.

Possible Answers:

Correct answer:

Explanation:

In order to find the excluded values for x, find the values that make the denominator zero. 

In order to find the zeroes, factor the denominator: 

Now, set each part equal to zero.

Example Question #1051 : Algebra

Find the excluded values for  for the following algebraic fraction.

Possible Answers:

Correct answer:

Explanation:

To find the excluded values, find the values that make the denominator zero. 

Example Question #1 : How To Find Excluded Values

Find the excluded values for  for the following algebraic fraction.

Possible Answers:

Correct answer:

Explanation:

To find the excluded values, find the values that make the denominator equal zero. 

To do that, set the denominator equal to zero and solve for

Begin by taking each multiple in the denominator and setting it equal to zero. 

Example Question #2 : How To Find Excluded Values

Find the excluded values for  in the following algebraic fraction.

Possible Answers:

Correct answer:

Explanation:

To find the excluded values, find the values that make the denominator equal zero. 

To do that, begin by factoring the denominator.

Now, set each part equal to zero.

Now, solve for .

Example Question #1 : How To Find Excluded Values

Find the excluded values for  in the following algebraic fraction.

Possible Answers:

Correct answer:

Explanation:

To find the excluded values, find the -values that make the denominator equal zero. 

To do this, set the denominator equal to zero:

Next, solve for x.

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