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ACT Math : Algebra

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Example Questions

Example Question #23 : Algebraic Fractions

$\begin{matrix} & \x\ & \y\ & \\ & \\ & \end{matrix}$ When x=2 , y=18 .

When x=9 , y=4 .

If varies inversely with , what is the value of when x=12 ?

Possible Answers:

y=1.5

y=1

y=3

y=x

y=6

Correct answer:

y=3

Explanation:

If varies inversely with , $y=\frac{K}{x}$ .

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

Using (2,18) :

$18=\frac{K}{2}$

K=36

2. Use your new equation $y=\frac{36}{x}$ and solve when x=12 :

$y=\frac{36}{12}=3$

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Example Question #3 : How To Find Inverse Variation

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: xy = k or $y = \frac{k}{x}$ , where is not equal to 0.

Substitute each $\left ( x,y \right )$ in xy = k .

5(4.8) = 24

6.4(3.75) = 24

20(1.2) = 24

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

3n = 24

n = 8

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Example Question #1 : How To Find Inverse Variation

Two numbers and vary inversely, and x=3 when y=8 . If this is true, what is the value of when y =6 ?

Possible Answers:

Correct answer:

Explanation:

If x=3 when y=8 , and the variation is direct, then xy = 24 . Using this, we know that if y=6 , $x= \frac{24}{6} = 4$ .

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Example Question #1 : How To Find Excluded Values

Which of the following provides the complete solution set for |2-z|>0 ?

Possible Answers:

z<2

z=2

z>2

$\dpi{100} z|z\neq 2$

No solutions

Correct answer:

$\dpi{100} z|z\neq 2$

Explanation:

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

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Example Question #1 : How To Find Excluded Values

Find the excluded values in the following algebraic fraction.

$\frac{2x^{2}+3x-12}{2x^{2}+9x-5}$

Possible Answers:

$-\frac{1}{3}, 4$

$\frac{1}{3}, -4$

$\frac{1}{2}, -5$

$-\frac{1}{2}, 5$

Correct answer:

$\frac{1}{2}, -5$

Explanation:

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

To do this, you must factor the denominator:

(2x-1)(x+5)

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

2x-1=0

$x=\frac{1}{2}$

x+5=0

x=-5

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Example Question #1 : How To Find Excluded Values

Find the excluded values for for the following algebraic fraction.

$\frac{x^{2}+4x-12}{x^{2}+5x+6}$

Possible Answers:

3, 2

3, -2

-3, 2

-3, -2

Correct answer:

-3, -2

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:

(x+3)(x+2)

Now, set each part equal to zero.

(x+3)=0

(x+2)=0

x=-3

x=-2

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Example Question #1 : How To Find Excluded Values

Find the excluded values for for the following algebraic fraction.

$\frac{x+3}{4-x^{2}}$

Possible Answers:

2, -2, 0

2, -2

Correct answer:

2, -2

Explanation:

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

$4-x^{2}=0$

$4=x^{2}$

x=2, -2

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Example Question #1 : How To Find Excluded Values

Find the excluded values for for the following algebraic fraction.

$\frac{x-4}{x(x^{2}-9)}$

Possible Answers:

3, 0

-3, 0

3, -3

3, -3, 0

Correct answer:

3, -3, 0

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.

x=0

$x^{2}-9=0$

$x^{2}=9$

x=3, -3

x=3, -3, 0

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Example Question #2 : How To Find Excluded Values

Find the excluded values for in the following algebraic fraction.

$\frac{x^{3}+8x-9}{x^{2}+7x+12}$

Possible Answers:

4, -3

-4, -3

4, 3

-4, 3

Correct answer:

-4, -3

Explanation:

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

To do that, begin by factoring the denominator.

(x+4)(x+3)

Now, set each part equal to zero.

x+4=0

x+3=0

Now, solve for .

x=-4

x=-3

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Example Question #2 : How To Find Excluded Values

Find the excluded values for in the following algebraic fraction.

$\frac{x^{2}+9}{x^{2}-16}$

Possible Answers:

4, -4, 0

4, -4

Correct answer:

4, -4

Explanation:

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

To do this, set the denominator equal to zero:

$x^{2}-16=0$

Next, solve for x.

$x^{2}=16$

x=4, -4

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #23 : Algebraic Fractions

Example Question #3 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Find Excluded Values

Example Question #1 : How To Find Excluded Values

Example Question #1 : How To Find Excluded Values

Example Question #1 : How To Find Excluded Values

Example Question #1 : How To Find Excluded Values

Example Question #2 : How To Find Excluded Values

Example Question #2 : How To Find Excluded Values

All ACT Math Resources

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