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PSAT Math : Algebraic Fractions

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Example Questions

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Example Question #1 : How To Find Inverse Variation

Find the inverse of y=2x+1 .

Possible Answers:

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

y=x+2

y=2x-1

y=x-1

Correct answer:

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

Explanation:

To find the inverse of a function we need to first switch the and . Therefore, y=2x+1 becomes

x=2y+1

We now solve for y by subtracting 1 from each side

x-1=2y

From here we divide both sides by 2 which results in

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

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Example Question #7 : How To Find Inverse Variation

Find the inverse of 9y=3x+12 .

Possible Answers:

y=3x+4

y=9x+12

y=3x-4

y=4x-3

Correct answer:

y=3x-4

Explanation:

To find the inverse we first switch the variables then solve for y.

9x=3y+12

Then we subtract from each side

9x-12=3y

Now we divide by to get our final answer. When we divide by we are left with . When we divide by we are left with . Thus resulting in:

y=3x-4

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Example Question #1 : How To Find Inverse Variation

Find the inverse equation of:

3y-2x=20

Possible Answers:

$\frac{2x+20}{3}=y$

$\frac{1}{2}x+10=y$

$\frac{3x-20}{2}=y$

$\frac{2x-20}{3}=y$

Correct answer:

$\frac{3x-20}{2}=y$

Explanation:

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

$\frac{3x-20}{2}=y$

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Example Question #1 : How To Find Inverse Variation

Find the inverse equation of 5x-4y=18 .

Possible Answers:

$x=\frac{4y+18}{5}$

$y=\frac{4x+18}{5}$

$y=\frac{4x+5}{18}$

x=y

$y=\frac{x+18}{4}$

Correct answer:

$y=\frac{4x+18}{5}$

Explanation:

5x-4y=18

1. Switch the and variables in the above equation.

5y-4x=18

2. Solve for :

5y-4x=18

5y-4x+4x=18+4x

5y=4x+18

$\frac{5y}{5}=\frac{4x+18}{5}$

$y=\frac{4x+18}{5}$

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Example Question #3 : How To Find Inverse Variation

$\begin{matrix} & \x\ & \y\ & \\ & \\ & \end{matrix}$ 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

y=3

y=6

y=1.5

y=x

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 #1 : 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 Evaluate A Fraction

Evaluate the following equation when x=5 and round your answer to the nearest hundredth.

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

Possible Answers:

-1.94

4.33

5.28

5.00

2.32

Correct answer:

2.32

Explanation:

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

1. Plug in wherever there is an in the above equation.

$\frac{5^{3}-(2)(5^{2})-(3)(5)+5}{(5)(5)+3}$

2. Perform the above operations.

$\frac{5^{3}-(2)(25)-(3)(5)+5}{(5)(5)+3}$

$\frac{125-50-15+5}{25+3}$

$\frac{65}{28}=2.32$

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Example Question #1 : How To Evaluate A Fraction

Mary walked to school at an average speed of 2 miles per hour and jogged back along the same route at an average speed of 6 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?

Possible Answers:

Correct answer:

Explanation:

Since Mary traveled 3 times as quickly coming from school as she did going to school (6 miles per hour compared to 2 miles per hour), we know that Mary spent only a third of the time coming from school as she did going. If x represents the number of hours it took to get to school, then x/3 represents the number of hours it took her to return.

Knowing that the total trip took 1 hour, we have:

x + x/3 = 1

3x/3 + 1x/3 = 1

4x/3 = 1

x = 3/4

So we know it took Mary 3/4 of an hour to travel to school (and the remaining 1/4 of an hour to get back).

Remembering that distance = rate * time, the distance Mary traveled on her way to school was (2 miles per hour) * (3/4 of an hour) = 3/2 miles. Furthermore, since she took the same route coming back, she must have traveled 3/2 of a mile to return as well.

Therefore, the the total number of miles in Mary's round trip is 3/2 miles + 3/2 miles = 6/2 miles = 3 miles.

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Example Question #2 : How To Evaluate A Fraction

If $w=\frac{1}{8}$ then which of the following is equal to $w^\frac{2}{3}$ ?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{64}$

$\frac{1}{16}$

$\frac{1}{32}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{4}$

Explanation:

To raise $\frac{1}{8}$ to the exponent $\frac{2}{3}$ , square $\frac{1}{8}$ and then take the cube root.

$w^\frac{2}{3}=\sqrt[3]{w^2}$

$(\frac{1}{8})^\frac{2}{3}=\sqrt[3]{(\frac{1}{8})^2}=\sqrt[3]{\frac{1}{64}}$

$\sqrt[3]{\frac{1}{64}}=\frac{1}{4}$

$(\frac{1}{8})^{\frac{2}{3}}=\frac{1}{4}$

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Example Question #1 : How To Evaluate A Fraction

Solve

Possible Answers:

no solution

–1

infinitely many solutions

Correct answer:

infinitely many solutions

Explanation:

The common denominator of the left side is x(x–1). Multiplying the top and bottom of 1/x by (x–1) yields

Since this statement is true, there are infinitely many solutions.

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PSAT Math : Algebraic Fractions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find Inverse Variation

Example Question #7 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #3 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Evaluate A Fraction

Example Question #1 : How To Evaluate A Fraction

Example Question #2 : How To Evaluate A Fraction

Example Question #1 : How To Evaluate A Fraction

All PSAT Math Resources

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