Math Fundamentals on the GRE Flashcards
strategies
Plug In
plug in different values for n and look for consistent answers
question types
pattern and sequence questions
plug in simple values, in order, and identify the pattern. i.e. a question with an exponent to the 28th power might be solveable by looking for the pattern of plug in answers for even and odd powers, like squares and cubes instead of 28.
viz. “for every odd exponent value, the remainder is three and for every
p 311, 312, 319, 337
combinations of sets when order does not matter
313
combinatorics: C(n, r) = n! / (r! * (n - r)!)
i.e. s= {1, 2, 3, 4, 5, 7} and x and y are distinct numbers from S; how
because xy is a multiplation operation, order doesn’t matter
combinations of sets when order does matter
permutations: P(n, r) = n! / (n - r)!
In how many ways can 3 students be selected from a group of 12 students
P(12, 3) = 12! / (12 - 3)! = (12 * 11 * 10) / (3 * 2 * 1) = 220
Is 0 odd or even?
Even!
group formula
Total=Group A + Group B- Both + Neither
group problem can be answered by filling in information from the problem
power rule of exponents 1
“If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same”
(a^m)^n = a^mn
product rule of exponents
When multiplying exponential terms with the same base, add their exponents and keep the base the same
x^a * x^b = x^a+b
quotient rule of exponents
When dividing exponential terms with the same base, subtract their exponents and keep the base the same
x^a / x^b = x^a-b
negative exponent
a^-n= 1/a^n
a^-n= 1/a^n
zero exponent
a^0=1
power rule of exponents 2
(ab)^m = a^m * b^m
(a/b)^m = a^m/b^m
fractional exponents
a^1/2 = the square root of a
the cube root of a = a^1/3 and so on
consecutive integers
consecutive integers can be consecutive in an y manner so long as the distance between each consecvutive integers in the same
the distance between the least integer and each of the other integers di
is 1 prime?
no!
FOIL
strategy to factor quadratic equations.
First
Outside
Inside
Last
factors
ways numbers can be broken down into component parts. for example, prime factorization
factor pairs are two factors of x that, multiplied, equal x
Greatest Common Factor
- prime factorization
- compare the prime factor expressions
- identify prime factors shared between both numbers
- multiply them– this is your greatest common factor
Order of operations
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
(PEMDAS)
percent increase
find the difference between the original number and the new number. for percent increase, use the lesser number as the denominator
percent decrease
find the difference between the original and new number. then divide the difference by the greater number
can operators (like -) be distributed under the distributive law
yes
