All PSAT Math Resources
Example Questions
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 ?
varies directly as the fourth power of .
varies inversely as .
varies directly as the fourth root of .
varies inversely as the fourth power of .
varies inversely as the fourth root of .
varies inversely as the fourth power of .
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 #72 : 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 ?
varies directly as .
varies directly as the fourth power of .
varies inversely as the seventh power of .
varies inversely as the fourth power of .
varies inversely as .
varies directly as .
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 : Monomials
If you have a rectangle with a width of and a length of , what is the area of the rectangle?
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 : Monomials
Find the product:
Use the distributive property:
Simplify: don't forget to use the rules of multiplying exponents (add them)
Example Question #73 : Algebra
Find the product:
Find the product:
Use the distributive property:
When multiplying variables with exponents, add the exponents:
Example Question #3 : Monomials
Find the product:
Find the product:
Use the distributive property: