All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #1 : How To Multiply Exponential Variables
Simplify:
Example Question #2 : How To Multiply Exponential Variables
Expand:
A binomial can be cubed using the pattern:
Set
Example Question #3 : How To Multiply Exponential Variables
Factor completely:
A trinomial whose leading term has a coefficent other than 1 can be factored using the -method. We split the middle term using two numbers whose product is and whose sum is . These numbers are , so:
Example Question #4 : How To Multiply Exponential Variables
Multiply:
This can be achieved by using the pattern of difference of squares:
Applying the binomial square pattern:
Example Question #5 : How To Multiply Exponential Variables
Simplify:
The cube of a sum pattern can be applied here:
Example Question #2 : How To Multiply Exponential Variables
Fill in the box to form a perfect square trinomial:
To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is , by 2, and square the quotient. The result is
Example Question #2 : How To Multiply Exponential Variables
Fill in the box to form a perfect square trinomial:
To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is , by 2, and square the quotient. The result is
Example Question #8 : How To Multiply Exponential Variables
Expand:
Which is the greater quantity?
(a) The coefficient of
(b) The coefficient of
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) 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)
(b)
(a) is the greater quantity.
Example Question #9 : How To Multiply Exponential Variables
Which is the greater quantity?
(a)
(b) 8
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
(a) is greater
(a) is greater
Since ,
, so
making (a) greater.
Example Question #1 : How To Multiply Exponential Variables
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal.
(b) is greater.
It is impossible to tell from the information given.
(a) is greater.
It is impossible to tell from the information given.
We show that either polynomial can be greater by giving two cases:
Case 1:
Case 2:
Certified Tutor
Certified Tutor