GRE Math Formulas Flashcards
Pythagorean theorem
a^2 + b^2 = c^2
Define Integer, Positive number, negative number, real numbers,
Integers:
Any counting number including negative numbers (e.g. -3, -1, 2, 7…but not 2.5)
Real Numbers:
Numbers that appear on the number line (i.e., one that is not imaginary) including pi, the square
root of 2, etc.
A positive number is greater than 0, a negative number is less than 0.
Cummulative Property
a + b = b + a (and same for multiplication)
Associative Property
(a + b) + c = (c + a) + b
Distributive Property
a * (b + c) = ab + ac
What is a prime number?
A prime number is one that is divisible only by itself and 1. In other words, a positive integer with exactly 2
positive divisors. This includes 2, 3, 5, 7, and 11, but not 9, because 9 = 3 x 3.
Name all the prime numbers between 1-100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97
What is factorization?
If X can be multiplied by Y to get Z, assuming all of these are positive integers, then X and Y are
considered factors of Z.
What is the prime factorization of 7644?
7644 = 2 x 2 x 3 x 7 x 7 x 13.
Define the greatest common factor. What is the easiest way to find it? What is the greatest common factor of 56 and 70?
The greatest common factor (aka greatest common divisor) of two numbers is the biggest factor shared by
ttwo numbers.
The easiest way to find
the GCF is to take the prime factorization and multiply all of the primes that appear in both numbers.
GCF of 56 and 70 is 14
Define the Least Common Multiple. What is the easiest way to find it? What is the least common multiple of LCM of 4 and 6?
The least common multiple of two numbers is the smallest positive integer with both numbers as a
factor
To find the LCM of any
two numbers, take the prime factorization of each number, find what prime factors appear in both, and
multiply one of each of the shared primes and then by all the unshared primes.
The LCM of 4 and 6 is 12 – it is the smallest number that has both 4 and 6 in its divisors.
x^A * x^B
x^(A+B)
x^A / x^B
x^(A - B)
(x^A)^B
x^(A*B)
x^(1/2)
√x
x^(2/3)
3√x^2
x^-1
1 / x
x^-2
1 / x^2
Simplifying roots –> √20
√252 = 2√5
Simplifying roots –> √54
√336 = 3√6
Simplifying roots –> √72
√98 = √3322*2= 6√2
2√7 + 9√7
11√7
6x^2+12x-144 / (2x^2 - 32)
3(x + 6) / (x+4)
How do you solve equations containing inequalities?
They can be treated like regular equations, with the following exception: multiplying or
dividing an inequality by a negative number reverses the sign of the inequality.
How do you calculate the total degrees of a polygon?
Polygon is any shape with more than 3 sides
180(n-2)
Average degree per side or degree measure per side of a congruent polygon
180(n-2) / n
Area of triangle
1/2bh
What is an isosceles triangle?
Right triangle - 45:45-90 degrees - sides ratio x : x : x√2
Equilateral triangle
equal on all sides and equal angles 60-60-60
Name the Pythagorean triples
3-4-5, 5-12-13, 8-15-17, 7-24-25
Name general facts about triangles
The length of the longest side can never be greater than the sum of the two other sides.
The length of the shortest side can never be less than the positive difference of the other two sides.
Area of Circle
π r^2
Circumference of Circle
2π r
Arc length
(x / 360) 2π r
Area of sector
(x / 360) π r^2
Area and Perimeter of a square
Perimeter = 4s (s=side length) Area = s^2
Area and Perimeter of a rectangle
Perimeter = 2l + 2w Area=l*w
Area and Perimeter of a trapezoid
Area = ((Base1 + Base2) / 2) * height
