PSAT Math : Variables

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #71 : Algebra

 varies inversely as both the square of  and the square root of . Assuming that  does not depend on any other variable, which statement is true of  concerning its relationship to ?

Possible Answers:

 varies inversely as the fourth power of .

 varies directly as the fourth power of .

 varies inversely as .

 varies directly as the fourth root of .

 varies inversely as the fourth root of .

Correct answer:

 varies inversely as the fourth power of .

Explanation:

 varies inversely as both the square of  and the square root of , meaning that for some constant of variation ,

.

Square both sides, and the expression becomes

  takes the role of the new constant of variation here, and we now have

,

meaning that  varies inversely as the fourth power of .

Example Question #71 : Algebra

 varies directly as the square of  and inversely as  and . Assuming that  does not depend on any other variables, which of the following gives the variation relationship of  to  ?

Possible Answers:

 varies inversely as .

 varies directly as the fourth power of .

 varies inversely as the seventh power of .

 varies inversely as the fourth power of .

 varies directly as .

Correct answer:

 varies directly as .

Explanation:

 varies directly as the square of  and inversely as ; therefore, for some constant of variation ,

Setting  and , the formula becomes 

Setting  as the new constant of variation, we have a new variation equation

,

meaning that  varies directly as .

 

Example Question #1 : How To Multiply A Monomial By A Polynomial

If you have a rectangle with a width of  and a length of , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

To find the area of a rectangle, multiply the length times the width.  Therefore, you must multiply  times .  To do that, you must multiply the monomial times each part of the trinomial, like so:

 

Example Question #2 : How To Multiply A Monomial By A Polynomial

Find the product:

Possible Answers:

Correct answer:

Explanation:

Use the distributive property:

Simplify: don't forget to use the rules of multiplying exponents (add them)

Example Question #3 : How To Multiply A Monomial By A Polynomial

Find the product:

Possible Answers:

Correct answer:

Explanation:

Find the product:

Use the distributive property:

When multiplying variables with exponents, add the exponents:

Example Question #1 : How To Multiply A Monomial By A Polynomial

Find the product:

Possible Answers:

Correct answer:

Explanation:

Find the product:

Use the distributive property:

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