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PSAT Math : Algebra

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Example Questions

Example Question #1 : How To Find Inverse Variation

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

Possible Answers:

y=4x-3

y=3x+4

y=3x-4

y=9x+12

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:

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

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

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

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

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:

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

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

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

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 #2 : 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=1.5

y=6

y=1

y=x

y=3

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 #611 : Algebra

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:

5.00

5.28

4.33

-1.94

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 #613 : Algebra

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

Possible Answers:

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{16}$

$\frac{1}{64}$

$\frac{1}{32}$

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 #614 : Algebra

Solve

Possible Answers:

infinitely many solutions

–1

no solution

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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Example Question #615 : Algebra

Evaluate when x=11. Round to the nearest tenth.

Possible Answers:

1.8

0.2

0.3

1.9

Correct answer:

1.8

Explanation:

Wherever there is an x, plug in 11 and perform the given operations. The numerator will be equal to 83 and the denominator will be equal to 46. 83 divided by 46 is equal to 1.804… and since the second decimal place is not greater than or equal to 5, the first decimal place stays the same when rounding so the final answer is 1.8.

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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #2 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #611 : Algebra

Example Question #1 : How To Evaluate A Fraction

Example Question #613 : Algebra

Example Question #614 : Algebra

Example Question #615 : Algebra

All PSAT Math Resources

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