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PSAT Math : Algebra

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Example Questions

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

No solutions

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

z=2

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

If the average (arithmetic mean) of , , and is , what is the average of x+2 , y-6 , and ?

Possible Answers:

There is not enough information to determine the answer.

Correct answer:

Explanation:

If we can find the sum of $\dpi{100} \small x+2$ , $\dpi{100} \small y-6$ , and 10, we can determine their average. There is not enough information to solve for $\dpi{100} \small x$ or $\dpi{100} \small y$ individually, but we can find their sum, $\dpi{100} \small x+y$ .

Write out the average formula for the original three quantities. Remember, adding together and dividing by the number of quantities gives the average: $\frac{x + y + 9}{3} = 12$

Isolate $\dpi{100} \small x+y$ :

$x + y + 9 = 36$

$x + y = 27$

Write out the average formula for the new three quantities:

$\frac{x + 2 + y - 6 + 10}{3} = ?$

Combine the integers in the numerator:

$\frac{x + y + 6}{3} = ?$

Replace $\dpi{100} \small x+y$ with 27:

$\frac{27+ 6}{3} = \frac{33}{3} = 11$

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Example Question #2 : How To Find Excluded Values

Find the excluded values of the following algebraic fraction

$\frac{2x^2-5x-12}{x^2-11x+28}$

Possible Answers:

$x\neq4,7$

$x\neq-11$

The numerator cancels all the binomials in the denomniator so ther are no excluded values.

$x\neq4$

$x\neq7$

Correct answer:

$x\neq4,7$

Explanation:

To find the excluded values of a algebraic fraction you need to find when the denominator is zero. To find when the denominator is zero you need to factor it. This denominator factors into

(x-7)(x-4)

so this is zero when x=4,7 so our answer is

$x\neq4,7$

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Example Question #1 : How To Find Inverse Variation

A school's tornado shelter has enough food to last 20 children for 6 days. If 24 children ended up taking shelter together, for how many fewer days will the food last?

Possible Answers:

Correct answer:

Explanation:

Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:

20*6=24*x

120=24x

x=120/24

x=5

In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.

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Example Question #1 : How To Find Inverse Variation

varies inversely as the cube of .

If A = 8 when B = 66 , then evaluate when B = 100 . (Nearest tenth)

Possible Answers:

27.8

5.3

7.0

2.3

9.2

Correct answer:

2.3

Explanation:

If varies inversely as the cube of , then, if A ,B are the initial values of the variables and A' ,B' are the final values,

$A'B' ^{3} = AB^{3}$

Substitute A = 8, B = 66, B'= 100 and find :

$A' \cdot 100 ^{3} = 8 \cdot 66^{3}$

$A' =\frac{ 8 \cdot 66^{3}}{100^{3}} = \frac{ 8 \cdot 287,496}{1,000,000} =2.299968$

This rounds to 2.3.

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Example Question #604 : Algebra

varies inversely as the cube root of .

If A = 8 when B = 66 , then evaluate when B = 100 . (Nearest tenth)

Possible Answers:

9.2

7.0

2.3

5.3

27.8

Correct answer:

7.0

Explanation:

If varies inversely as the cube root of , then, if A ,B are the initial values of the variables and A' ,B' are the final values,

$A'\sqrt[3]{B'} = A\sqrt[3]{B}$

Substitute A = 8, B = 66, B'= 100 and find :

$A'\sqrt[3]{100} = 8\sqrt[3]{66}$

$A'=\frac{ 8\sqrt[3]{66}}{\sqrt[3]{100} } \approx \frac{ 8 \cdot 4.0412}{4.6416} \approx 7.0$

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Example Question #3 : How To Find Inverse Variation

Find the inverse of

$y=\frac{1}{2}x-4$

Possible Answers:

y=x-4

y=2x+8

y=2x+4

y=2x-8

Correct answer:

y=2x+8

Explanation:

To find the inverse we first switch the x and y variables

$x=\frac{1}{2}y-4$

Now we add 4 to each side

$x+4=\frac{1}{2}y$

From here to isolate y we need to multiply each side by 2

2(x+4)=y

By distributing the 2 we get our final solution:

y=2x+8

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Example Question #1 : How To Find Inverse Variation

varies inversely as the square of .

If A = 8 when B = 66 , then evaluate when B = 100 . (Nearest tenth)

Possible Answers:

9.8

5.3

18.4

6.5

3.5

Correct answer:

3.5

Explanation:

If varies inversely as the square of , then, if A ,B are the initial values of the variables and A' ,B' are the final values,

$A'B' ^{2} = AB^{2}$ .

Substitute A = 8, B = 66, B'= 100 and find :

$A' \cdot 100 ^{2} = 8 \cdot 66^{2}$

$A' =\frac{ 8 \cdot 66^{2}}{100^{2}} =\frac{ 8 \cdot 66^{2}}{100^{2}} = \frac{ 8 \cdot 4,356}{10,000} =3.4848$

This rounds to 3.5.

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Example Question #4 : How To Find Inverse Variation

varies inversely with the square root of .

If A = 8 when B = 66 , then evaluate when B = 100 . (Nearest tenth)

Possible Answers:

3.5

6.5

5.3

9.8

18.4

Correct answer:

6.5

Explanation:

If varies inversely with the square root of , then, if A ,B are the initial values of the variables and A' ,B' are the final values,

$A'\sqrt{B'} = A\sqrt{B}$ .

Substitute A = 8, B = 66, B'= 100 and find :

$A'\sqrt{100} = 8\sqrt{66}$

$A'=\frac{ 8\sqrt{66}}{\sqrt{100} } \approx \frac{ 8 \cdot 8.1240}{10} \approx 6.5$

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Example Question #5 : How To Find Inverse Variation

Find the inverse of y=2x+1 .

Possible Answers:

y=2x-1

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

y=x-1

y=x+2

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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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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 #1 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #604 : Algebra

Example Question #3 : How To Find Inverse Variation

Example Question #1 : How To Find Inverse Variation

Example Question #4 : How To Find Inverse Variation

Example Question #5 : How To Find Inverse Variation

All PSAT Math Resources

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