All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #1 :How To Add Exponential Variables
Simplify:
The expression cannot be simplified further
Group and combine like terms:
Example Question #2 :Variables And Exponents
Which is the greater quantity?
(a)
(b)
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
(a) and (b) are equal.
(b) is greater.
Sinceandhave different signs,
, and, subsequently,
Therefore,
This makes (b) the greater quantity.
Example Question #3 :Variables And Exponents
Assume thatandare not both zero. Which is the greater quantity?
(a)
(b)
(b) is greater.
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
It is impossible to tell from the information given.
Simplify the expression in (a):
Therefore, whether (a) or (b) is greater depends on the values ofand, neither of which are known.
Example Question #4 :Variables And Exponents
Which is the greater quantity?
(a)
(b)
It is impossible to tell from the information given
(b) is greater
(a) is greater
(a) and (b) are equal
It is impossible to tell from the information given
We give at least one positive value offor which (a) is greater and at least one positive value offor which (b) is greater.
Case 1:
(a)
(b)
Case 2:
(a)
(b)
Therefore, either (a) or (b) can be greater.
Example Question #5 :Variables And Exponents
Assume all variables to be nonzero.
Simplify:
None of the answer choices are correct.
None of the answer choices are correct.
Any nonzero expression raised to the power of 0 is equal to 1. Therefore,
.
None of the given expressions are correct.
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