GRE MATH- FUNCTIONS, FORMULAS
AND SEQUENCES
When dealing with a nested function, what should you do first? - You should solve the
innermost function and then plug it into the outer function.
The GRE can use made-up symbols in the place of f(x) to represent a function. What
does it mean when a symbol is used twice, as in 2 boxes around a number? - It is
asking you to plug the number into the function once and then plug the result into the
function again.
What is the square root of any value greater than or equal to 0 equal to? - The non-
negative square root of the value. Ex. the square root of 4 is just 2, not -2.
What does the term "undefined" refer to when it comes to solving functions? What two
circumstances does the GRE consider that result in an undefined answer? - It refers to
the circumstance when the solution to the function is not a real number. Ex. dividing by
0. The GRE considers two main circumstances for an undefined answer:
1. The division by 0. To test what values would make a function that is in the form of a
fraction undefined, set expressions in the denominator equal to 0.
2. The square root of a negative number. Check to see if a possible value, when
plugged into a function with square roots, would result in taking the square root of a
negative number.
When solving equations with multiple variables, what two ways can you approach
solving for variables? - 1. isolate variables and substitute, then solve
2. line up the equations and add or subtract to eliminate variables and solve for others
What is meant by the term "arithmetic sequence"? - It means a sequence in which the
same number is being added to or subtracted from each new term.
How would you write the mathematical formula for an arithmetic sequence whose first 3
terms are 30, 33 and 36? - Each new term is the previous term plus 3. To get from 30 to
33, 3 is being added once. To get from 30 to 36, 3 is being added twice. The formula
would be:
30 + 3(n-1), where n=number of term.
How do you find the sum of any evenly spaced set of integers? - Multiply the average
(arithmetic mean) by the number of elements in the set.
To find the average, add the first and last terms and divide by two.
To find the total number of elements in a set, subtract the first term from the last term
and divide by 2. Then "add one before you're done".
