All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #3 : How To Find The Exponent Of Variables
Expand:
Which is the greater quantity?
(a) The coefficient of
(b) The coefficient of
It is impossible to tell from the information given.
The two quantities are equal.
(a) is greater.
(b) is greater.
The two quantities are equal.
By the Binomial Theorem, if is expanded, the coefficient of is
.
(a) Substitute : The coerfficient of is
.
(b) Substitute : The coerfficient of is
.
The two are equal.
Example Question #223 : Algebraic Concepts
Which is greater?
(a)
(b)
(a) is greater.
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(b) is greater.
A negative number to an odd power is negative, so the expression in (a) is negative. The expression in (b) is positive since the base is positive. (b) is greater.
Example Question #5 : How To Find The Exponent Of Variables
Which is the greater quantity?
(a)
(b)
It is impossble to tell from the information given.
(a) and (b) are equal.
(b) is greater.
(a) is greater.
(a) is greater.
Simplify the expression in (a):
Since ,
,
making (a) greater.
Example Question #11 : Variables And Exponents
Expand:
Which is the greater quantity?
(a) The coefficient of
(b) The coefficient of
The two quantities are equal.
It is impossible to tell from the information given.
(a) is greater.
(b) is greater.
(b) is greater.
Using the Binomial Theorem, if is expanded, the term is
.
This makes the coefficient of .
We compare the values of this expression at for both and .
(a) If and , the coefficient is
.
This is the coefficient of .
(b) If and , the coefficient is
.
This is the coefficient of .
(b) is the greater quantity.
Example Question #2 : How To Find The Exponent Of Variables
Consider the expression
Which is the greater quantity?
(a) The expression evaluated at
(b) The expression evaluated at
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(b) is greater
(b) is greater
Use the properties of powers to simplify the expression:
(a) If , then
(b) If , then
(b) is greater.
Example Question #6 : How To Find The Exponent Of Variables
Which of the following expressions is equivalent to
?
None of the other answers is correct.
None of the other answers is correct.
Use the square of a binomial pattern as follows:
This expression is not equivalent to any of the choices.
Example Question #14 : Variables And Exponents
Express in terms of .
, so
, so
Example Question #901 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
. Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(a) is the greater quantity
By the Power of a Power Principle,
Therefore,
It follows that
Example Question #62 : Variables
is a real number such that . Which is the greater quantity?
(a)
(b) 11
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
It is impossible to determine which is greater from the information given
By the Power of a Power Principle,
Therefore, is a square root of 121, of which there are two - 11 and . Since it is possible for a third (odd-numbered) power of a real number to be positive or negative, we cannot eliminate either possibility, so either
or
.
Therefore, we cannot determine whether is less than 11 or equal to 11.
Example Question #912 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
By the Power of a Product Principle,
Also, by the Power of a Power Principle
Therefore,
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