Quantitative Flashcards
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.
Order of Operations
PEMDAS: parentheses, exponents, multiplication/division, addition/subtraction
Prime Numbers
Number that is divisible only by itself and 1. Examples are 2, 3, 5, 7, 11. 1 is not a prime, 2 is the smallest prime and only even prime.
Prime Factorization
The prime factorization of a number is dividing it into its constituent primes. So for 21, this is 3 x 7; for 60, 2 x 2 x 3 x 5. 7644 = 2 x 2 x 3 x 7 x 7 x 13.
Greatest Common Factor (aka greatest common divisor)
The biggest factor shared by the two given numbers. The GCF of 12 and 30 is 6 – it is the biggest divisor they both share. If two numbers share no primes, the GCF is 1.
Least Common Multiple
The smallest positive integer between two numbers as a factor. The LCM of 4 and 6 is 12 – it is the smallest number that has both 4 and 6 in its divisors.
Absolute Values
The absolute value of a number is its distance from a number line (no negatives).
|x| = x, |-x| = x
Percentages
Percent is per 100. To find what percent some part of a whole use:
part / whole = percent / 100
Percent Change
Percent change: % change = change/original value
If the price of something goes from $40 to $52, the percent change is:
(52-40)/40 = 12/40 = 3/10 = 30/100 = 30%
Roots: Perfect Squares
Numbers with integers as their square roots: 4, 9, 16, 25, etc.
Roots: Cube roots
3√x is a number that, when cubed, equals x.
Example 3√-8 = -2.
Roots: Adding roots
2√7 + 9√7 = 11√7.
Roots can be added like variables.
Statistics: Mean, Median, Mode
Mean = average, total sum / n Median = middlemost value when numbers are arranged in ascending order; for an even amount of numbers, take the average of the middle two Mode = the number that occurs most frequently
Statistics: Standard Deviation and Variance
The standard deviation represents the average distance the data values are away from the mean. Variance = SD^2
Counting: Combinations
nCr = n! / r!(n - r)!
Example: 5c3 = 5! / 3!(2!) = 10
When the order does not matter – for example, picking any 3 friends from a group of 5.
Counting: Permutations
nPr = n! / (n - r)!
When the order does matter – for example, how many ways you could order 3 letters from the word PARTY?
Probability: Formula
Probability that event A will happen:
P(A) = number of outcomes where A occurs / total number of outcomes
Formulas: Area of Square
A = s x s (s = side)
Formulas: Perimeter of Square
P = s + s + s + s
Formulas: Area of Rectangle
A = L x w
length times width
Formulas: Perimeter of Rectangle
P = 2L + 2W
Formulas: Area of Triangle
A = 1/2bh
half base times height
Formulas: Perimeter of Triangle
P = a + b + c
add all sides
Formulas: Area of Trapezoid
A = ((b1+b2)/2)*h
base 1 plus base 2
Formulas: Perimeter of Trapezoid
P = s1 + s2 + b1 + b2
add all the sides
Formulas: Area of Circle
A = πr^2
Formulas: Circumference of Circle
C = 2πr
Formulas: Area of Semicircle
A = (πr^2)/2
Formulas: Perimeter of Semicircle
P = 1/2πd + d
Special Triangles: 45-45-90
An isosceles right triangle, side lengths create a ratio of 1:1:√2. Sides opposite of the 45 angles are x and side opposite of the 90 angle is x√2.
Special Triangles: 30-60-90
Angles are 30, 60, 90. Side lengths create a ratio of 1:√3:2. Hypotenuse is twice the length of the side opposite of the 30, the other side is √3 times the side opposite of the 30.
x^-2 = _____
1/x^2
Law of negative exponents. N^-a = 1/N^a
x^1/3 = _____
3sqrt(x)
Law of fractional exponents. n^1/a = asqrt(n)
1^0, 5^0, 10^0, x^0 = _____
1.
Zero exponents.
x^-1 = _____
1/x
Negative 1 exponents. n^-1 = 1/n
3^4 x 3^6 = _____
3^10
Product of exponents. N^a x N^b = N^(a+b)
2^5 x 4 ^5 = _____
(2 x 4)^5
Product of exponents. N^a x M^a = (N x M)^a
Formulas: Rates (speed, distance, time)
Distance = s x t Time = d / s Speed = d / t
Formulas: Average Speed
Average speed = total distance / total time
Formulas: Work
Work = xy / x + y
Where x is the time it takes the first worker to complete the job.
Where y is the time it takes the second worker to complete the job.
Coordinate Geometry: Slope
M = rise/run = (y2-y1) / (x2-x1)
Coordinate Geometry: Slope intercept form
y = mx + b
Odd + Odd = _____
Even
-Number Properties
Even + Even = _____
Even
-Number Properties
Odd + Even = _____
Odd
-Number Properties
Odd x Odd = _____
Odd
-Number Properties
Even x Even = _____
Even
-Number Properties
Odd x Even = _____
Even
-Number Properties
