ISEE Upper Level Quantitative : How to add variables
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Example Questions
Example Question #1 : How To Add Variables
Simplify:
Group and collect like terms:
Example Question #1 : How To Add Variables
Simplify the expression:
The expression cannot be simplified further.
The expression cannot be simplified further.
There are no like terms among these three; one has only 
Example Question #1 : How To Add Variables
Which is the greater quantity?
(a) The sum of the integers from 1 to 1,000
(b) The sum of the integers from 1,001 to 1,500
(a) and (b) are equal
(b) is greater
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) The sum of the integers from 1 to 1,000 is
(b) The sum of the integers from 1,001 to 1,500 is
(b) is greater
Example Question #4 : How To Add Variables
Which is the greater quantity?
(A)
(B)
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
Which quantity is the greater depends on the value of 
Case 1:
Then
and
Subsequently, (A) is greater
Case 2:
Then
and
Subsequently, (B) is greater
Example Question #1 : How To Add Variables
Evaluate for 
Substitute and evaluate, remembering that in order of operations, squaring comes before adding:
Example Question #3 : How To Add Variables
Which of the following is the greater quantity?
(A)
(B)
(B) is greater
It is impossible to determine which is greater from the information given
(A) is greater
(A) and (B) are equal
(B) is greater
(A) Substitute and evaluate, remembering that by order of operations, squaring precedes addition:
(B) Substitute and evaluate
(B) is greater
Example Question #4 : How To Add Variables
(A)
(B)
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
(A) is greater
(B) is greater
Since 
Also, 
making (B) greater.
Example Question #8 : How To Add Variables
(A)
(B)
(A) and (B) are equal
(A) is greater
It is impossible to determine which is greater from the information given
(B) is greater
It is impossible to determine which is greater from the information given
The values of both terms depend on the value of 
Case 1:
Case 2:
Therefore, the information given is insufficient.
Example Question #5 : How To Add Variables
When evaluating the expression
assuming you know the values of all five variables, what is the third operation that must be performed?
Multiplication
Subtraction
Division
Addition
Squaring
Multiplication
The operation that must be performed first is the operation in parentheses, which is the division.
After this, the order of operations is:
Exponents
Multiplication and division (left to right)
Addition and subtraction (left to right)
The second thing that must be done is the exponentiation - the squaring. Of the three remaining operations, the multiplication takes precedence. The correct response is multiplication.
Example Question #10 : How To Add Variables
The Fibonacci sequence is defined as follows:
For integers 
Which is the greater quantity?
(a) The sum of 
(b)
(b) is greater
It is impossible to determine which is greater from the information given
(a) is greater
(a) and (b) are equal
(a) and (b) are equal
Using the definition of the sequence for all terms beginning with the third, substitute 778 for 
The two quantities are equal.
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