Properties of Numbers Flashcards
.167
1/6
.143
1/7
.125
1/8
.111
1/9
.083
1/12
.0909
1/11
.286
2/7
.429
3/7
.571
4/7
.714
5/7
.857
6/7
.875
7/8
.375
3/8
.222
2/9
2n= odd or even?
even
odd - even
odd
even + odd
odd
even - odd
odd
odd + odd
even
even + even
even
odd-odd
even
Product of even and any integer
Even
Product of two odd numbers
Odd
Even divided by even
Even or odd
Even divided by odd
Even
Odd divided by odd
Odd
sqrt(2)
1.4
sqrt(3)
1.7
sqrt(5)
2.2
sqrt(6)
2.4
sqrt(7)
2.6
sqrt(8)
2.9
2^6
64
13^2
169
16^2
256
14^2
196
15^2
225
18^2
324
17^2
289
3^5
243
6^3
216
ax^2+bx+c=0 has 2 solutions. What is the sum of the solutions
-b/a
ax^2+bx+c=0 has 2 solutions. What is the product of the solutions?
c/a
divisibility of 4
If last 2 digits are divisible by 4; can be 00 too ex: 100, 244
divisibility of 6
divisible by 3 and 2
divisibility by 8
If # is even, last 3 digits must be divisible by 8; can be 1000, 160, etc
divisibility by 9
If sum of all digits is divisible by 9
divisibility by 12
if divisible by 3 and 4
divisibility by 11
If the sum of the odd numbered digits minus the sum of even numbered digits is divisble by 11; ex: 2915 because (9+5)-(2+1)=11
Equation to find Sum of the first n terms of an arithmetic sequence
Sn = n/2 ( a1 + an)
Arithmetic Sequence Equation
an = a1 + (n-1) * d
Geometric Sequence
an = a1 * r^(n-1)
Reflection over x-axis
(x, y) -> (x, -y)
Reflection over y-axis
(x, y) -> (-x, y)
Reflection over origin
(x, y) -> (-x, -y)
Reflection over y = x
(x, y) -> (y, x)
Reflection over y = - x
(x, y) -> (-y, -x)
Reflection over y = b
(x, y) -> (x, 2b-y)
Reflection over x = a
(x, y) -> (2a-x, y)
Absolute value of the sum of two numbers will ALWAYS be (less than or equal to/greater than or equal to) the sum of the absolute values of the 2 numbers
Absolute value of the sum of two numbers will ALWAYS be LESS THAN OR EQUAL TO the sum of the absolute values of the 2 numbers
What can we say when |a + b| = |a| + |b|
Either
1. One or both quantities are zero
2. Both quantities are of the same sign
(If question says a and b are non-zero then that implies both quantities have same sign)
What can we say when |a| = |b|
Either
1. The expressions within the absolute values are equal
2. The expressions within the absolute values are opposite
Absolute value of the subtraction of two numbers will ALWAYS be (less than or equal to/greater than or equal to) the subtraction of the absolute values of the 2 numbers
Absolute value of the subtraction of two numbers will ALWAYS be GREATER THAN OR EQUAL TO the subtraction of the absolute values of the 2 numbers
What can we say when |a - b| = |a| - |b|
Either
1. One or both quantities are zero
2. Both quantities are of same sign
Minimum value of a quadratic function
If a>0 then minimum occurs at x = -b/2a
Maximum value of a quadratic function
If a<0, then maximum occurs at x=-b/2a
b^2-4ac < 0
Zero roots
b^2-4ac = 0
One Root
b^2-4ac > 0
Two Roots
If a quadratic equation has exactly 2 solutions then:
The sum of the two solutions = ( - b) / a
The product of the two solutions = (c) / a
How many solutions does a system of linear equations have if the equations are identical
Infinitely many; you can cancel them and say 0=0
How many solutions does a system of linear equations have if system is equivalent to equation 0 = k where k is nonzero
Zero solutions.
How many solutions does a system of linear equations have if we can solve the system
Exactly one solution
3^3
27
3^4
81
3^5
243
2^7
128
4^3
64
4^4
256
5^3
125
5^4
625
6^3
216
6^4
1296
7^3
343
7^4
2401
8^3
512
8^4
4096
9^3
729
Surface area of a box
2(l * w) + 2(l * h) + 2(w * h)
Surface area of a cube
6 * (edge)^2
1 meter = x cm
1 m = 100 cm
Volume of a box
l * w * h
Prime Numbers to 100
2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
If T distinct people are arranged such that g are next to each other, what is the total possible arrangements?
Total Possible Arrangements = (T - g + 1)! * g!
X is what % less than y?
( x - y ) / y * 100%
Distance between 2 points
sqrt[ delta(x)^2 + delta(y)^2 ]
(x+y)^3
x^3 + y^3 +3x^2y + 3xy^2
(x-y)^3
x^3 - y^3 - 3x^2y + 3xy^2
|x-a|<b
a is the center of the segment, b is half of the length of the segment
Adding the same positive constant to the numerator and denominator of a proper fraction (increases/decreases) the number?
Adding the same positive constant to the numerator and denominator of a proper fraction INCREASES the number
Subtracting the same positive constant to the numerator and denominator of a proper fraction (increases/decreases) the number?
Subtracting the same positive constant to the numerator and denominator of a proper fraction DECREASES the number?
Adding the same positive constant to the numerator and denominator of an improper fraction (increases/decreases) the number?
Adding the same positive constant to the numerator and denominator of an improper fraction DECREASES the number
Subtracting the same positive constant to the numerator and denominator of an improper fraction (increases/decreases) the number?
Subtracting the same positive constant to the numerator and denominator of an improper fraction INCREASES the number as new numerator and denominator are still positive.
If the product of two integers is 1
Then the two integers are -1, -1 OR 1, 1
|px-a| = b
Divide everything by p –> |x - a/p | = b/p . Remember a = midpoint b = distance
Assuming equal distances (in a rate/time/distance problem), if we have 1 leg (e.g. a->b) avg speed of 10 miles/hr then the average speed for the entire trip cannot be 20 miles/hr or greater.
