Facts Flashcards
11²
121
12²
144
13²
169
14²
196
15²
225
16²
256
17²
289
18²
324
19²
361
20²
400
2³
8
3³
27
4³
64
5³
125
6³
216
7³
343
8³
512
9³
729
2⁶
64
2⁷
128
2⁸
256
2⁹
512
4⁴
256
3⁴
81
5⁴
625
9²
81
Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 97
1%
1⁄100 (0.01)
5%
1⁄20 (0.05)
10%
1⁄10 (0.1)
20%
1⁄5 (0.2)
25%
1⁄4 (0.25)
40%
2⁄5 (0.4)
50%
1⁄2 (0.5)
60%
3⁄5 (0.6)
75%
3⁄4 (0.75)
80%
4⁄5 (0.8)
11 1⁄9 %
1⁄9 (0.111…)
22 2⁄9 %
2⁄9 (0.222…)
33 3⁄9 %
3⁄9 = 1⁄3 (0.333…)
44 4⁄9 %
4⁄9 (0.444…)
55 5⁄9 %
5⁄9 (0.555…)
66 6⁄9 % / 66.66%
6⁄9=2/3 (0.666…)
77 7⁄9 %
7⁄9 (0.777…)
88 8⁄9 %
8⁄9 (0.888…)
12 1⁄2 %
1⁄8 (0.125)
37 1⁄2 %
3⁄8 (0.375)
62 1⁄2 %
5⁄8 (0.625)
87 1⁄2 %
7⁄8 (0.875)
16 2⁄3 %
1⁄6 (0.1666…)
83 1⁄3 %
5⁄6 (0.833…)
1⁄7
0.14
Normal Distribution - both sides from mean (Bell shaped, symmetric about mean)
68% - 95% - 99.7%
Normal Distribution - one side from mean (Bell shaped, symmetric about mean)
34% - 13.5% - 2.35% - 0.15%
Roots of a Quadratic Equation (ax²+bx+c=0)
(-b ± √ (b² – 4ac) )/2a
Determinant of a Quadratic Equation (ax²+bx+c=0)
b² – 4ac (=0, equal roots; >0, 2 real roots; <0, imaginary roots
Sum of the Roots of a Quadratic Equation (ax²+bx+c=0)
-b/a
Product of the Roots of a Quadratic Equation (ax²+bx+c=0)
c/a
0/x
0
x/0
undefined
|x| < a
-a < x < a
|x| > a
a < x < -a
Horizontal Line
y=b; slope = 0
Million
10⁶
Billion
10⁹
Decimal places (right of decimal point)
Tenths, Hundredths, Thousandths, Ten Thousandths, Hundred Thousandths, Millionths)
x = √(k+ √(k + √(k+ …
x = √(k+x)
Line y=x divides quadrant into
x<y & x>y
√2
1.4
√3
1.7
√5
2.2
Every ODD integer can be expressed as
a difference of 2 consecutive squares of integers
Evenly spaced nos
Mean=Median
Consecutive integers
Mean=Median
Consecutive multiples of same no
Mean=Median
Symmetrical list
Mean=Median
Overlapping Sets (3)
A=a+d+g+e; B=b+d+g+f; C=c+e+g+f; T=n+[a+b+c+d+e+f+g]
Overlapping Sets (3) [sum of 2-group overlaps]
T=A+B+C-(sum of 2-group overlaps)+(all 3)+n
Overlapping Sets (3) [sum of exactly 2-group overlaps]
T=A+B+C-(sum of exactly 2-group overlaps)-2*(all 3)+n
Positive Integers
1,2,3… (Does NOT include 0)
Overlapping Sets (2)
T=A+C-(both A&C)+n / T=a+b+c+n
Vertical Line
x=a; slope=undefined
Parabola Eq (vertex form)
y=(x-h)² + k; vertex: (h,k)
Point position w.r.t line/curve
Curve y=ax²+bx+c; Point (p,q) lies above if q>ap²+bp+c below if q<
Pascal’s triangle for combinations
2, 3, 4-6, 5-10, 6-15-20, 7-21-35
(even)² - (even)²
Divisible by 4
(odd)² - (odd)²
Divisible by 4
|x - c|
Distance b/w x & c
0^(¹⁄ₙ)
0
1^(¹⁄ₙ)
1
|x| = -x
x is negative
|x| = x
x is positive
A number is divisible by 11 if
the sum of the
odd-numbered place digits minus the sum
of the even-numbered place digits is
divisible by 11.
The units digits of positive powers of 2 will
follow the four-number pattern
2-4-8-6
The units digits of positive powers of 3 will
follow the four-number pattern
3-9-7-1
The units digits of positive powers of 4 will
follow a two-number pattern
4-6
All positive powers of 5 & 6 end in
5 & 6
The units digits of positive powers of 7 will
follow the four-number pattern
7-9-3-1
The units digits of positive powers of 8 will
follow the four-number pattern
8-4-2-6
The units digits of positive powers of 9 will
follow a two digit pattern
9-1
The smallest five non-negative integers which are both perfect squares and perfect cubes
0, 1, 64, 729, 4096
Any integer of the form a^6 (where a is an integer) is both a perfect square and a perfect cube.
The number of trailing zeros of a number is
the number of (5x2) pairs in the prime factorization of that number.
If X (not a perfect power of 10) is an integer with k digits, then 1/x will have ___ leading zeros.
k – 1
If X (a perfect power of 10) is an integer with k digits, then 1/x will have ___ leading zeros.
k - 2
GCF of two consecutive integers
1
2¹⁰
1024
