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258 Cards in this Set

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Positive X Negative = ?
Negative
Negative X Negative = ?
Positive
Positive / Negative =
Negative
Negative / Negative =
Positive
Odd + Odd =
Even
Even + Even =
Even
Odd - Odd =
Even
Even - Even =
Even
Odd + Even =
Odd
Odd - Even =
Odd
Even x Odd =
Even
Even x Even =
Even
Odd x odd x odd x ... =
Odd
Odd / Even =
Not an Integer
Even / Odd =
Even (or a fraction)
Odd / Odd =
Odd (or a fraction)
Final Value [given X percent change) =
(1 + X%/100)Initial Value
% change [given Final and Initial values] =
(F-I)/I x 100
Simple Interest: R =
R = P X (1 + rt)
Compound Interest: R =
R = P X (1+ r/n)^nt
(^nt indicates nt is an exponent)
X^a * X^b =
X^(a+b)
x^a / x^b =
x^(a-b)
x^a * y^a =
(xy)^a
(x/y)^a =
x^a / y^a
(x^a)^b
x^(ab)
0! = ?
1
1! = ?
1
2! = ?
2
3! =
6
4! =
24
5! =
120
6! =
720
7! =
5040
x^-a
1 / x^a
x^0 =
1, unless x = 0
nPk =
Permutations (order matters) with n options for k slots
n! / (n-k)!
nCk =
Combinations (order does not matter) with n options for k slots
n! / (n-k)!k!
nPk =
Permutations (order matters) with identical objects k sub i
n is the total number of objects and ki is the number of objects of the ith kind
n! / k1!k2!...kn!
Arrangements in a circle of non-identical things =
(n-1)!
With two different types of things (men & women) it is
(m-1)!w! (only one "anchor" needed)
Probability is?
number of ways the particular something can happen divided by the number of ways that anything can happen
x^(a/b) =
b√(x^a)
[b root of x to the a power]
n√x =
[nth root of x]
x^(1/n)
[x to the 1/n power]
Quadratic Formula ?
x = (-b+/-√(b^2-4ac))/2a
Area of a triangle?
A = 1/2 bh
Sum of the angles of a triangle?
180 deg
The sum of the lengths of any two sides of a triangle is _____ than the length of the third?
longer
45-45-90 triangle has what relationship between its sides?
1-1-√2
30-60-90 triangle has what relationship among its sides?
1-√3-2
Right triangle: 3-4-___
5
Right triangle: ___ -8-10
6
Right triangle: 5-___-13
12
Right triangle: 10-24-____
26
Right triangle: ___-24-25
7
Right triangle: 8-__-17
15
Equation of a line:
y=mx+b
slope of a line equals?
m=(y2-y1)/(x2-x1)
x-intercept of a line =
-b/m
Area of a rhombus (all sides equal, opposite angles equal, perpendicular diagonals)?
A=1/2(d x d)
d = diagonal
Area of a trapezoid (one pair of sides parallel [sides a and c])
A=1/2(a+c)h
Area of a parallelogram (opposite sides equal and parallel, opposite angles equal)?
A=bh
Measure of all angles of a regular polygon?
(n-2)180
Measure of any interior angle of a regular polygon?
(n-2)/n ∗ 180
pi ≈ ? (fraction)
22/7
Area of a circle?
A=πr^2
Relationship between central angle and arc?
L/(2πr) = α /360 deg
Area of a sector of a circle?
A = (α/360) πr^2
Inscribed angle = ?
1/2 central angle
Definition of Central Angle?
An angle in a circle which uses the center of the circle as its vertex.
Definition of Inscribed Angle?
An angle formed by two chords within a circle. Its vertex is on the circle. The measure of an inscribed angle equals 1/2 the measure of its arc.
Diagonal of a cube =
√3 * length
Diagonal of a rectangular solid?
D = √(l^2 + w^2 + h^2)
Volume of a cylinder?
V = π(r^2)h
Surface area of a cylinder?
A = 2πrh +nπr^2, n= 0,1, or 2
Volume of a sphere?
V = 4/3 πr^3
Surface area of a sphere?
A = 4πr^2
Exponential growth formula?
F = Ia^n
Compound interest formula?
Earnings = Investment x (1+rate)^t
t= no. of periods
Average?
Add 'em all up and divide by the number of things added.
Standard Deviation formula?
σ = square root of the sum of the differences between each number and the mean, squared, divided by the number of numbers.
√((∑(xi-mean)^2)/n)
Permutation formula (order matters)?
nPk = n!/(n-k)!
Combination formula?
nCk = n! / (n-k)!k!
Possible circular arrangements of n items?
(n-1)!
P(A ∩B) =
Intersection of independent events (and)
P(A) * P(B)
P(A∩B) =
Intersection of dependent events
(and)
P(A)*Pa(B) or P(B)*Pb(A)
P(A∪B) =
Union of two overlapping events
(or)
P(A) + P(B) - P(A∩B)
P(A∪B∪C) =
Union of three overlapping events
(or)
P(A)+P(B)+P(C)-P(A∩B)-P(A∩C)-P(B∩C)+P(A∩B∩C)
12 x 6
72
12 x 7
84
12 x 8
96
12 x 9
108
12 x 12
144
12 x 11
132
13 x 4
52
13 x 5
65
13 x 6
78
13 x 7
91
13 x 8
104
13 x 9
117
13 x 11
143
13 x 12
156
13 x 13
169
14 x 3
42
14 x 4
56
14 x 5
70
14 x 6
84
14 x 7
98
14 x 8
112
14 x 9
126
14 x 11
154
14 x 12
168
14 x 13
182
14 x 14
196
15 x 5
75
15 x 6
90
15 x 7
105
15 x 8
120
15 x 9
135
15 x 11
165
15 x 12
180
15 x 13
195
15 x 14
210
15 x 15
225
1/6 =
0.166...
5/6 =
0.833...
1/8 =
0.125
3/8 =
0.375
5/8 =
0.625
7/8 =
0.875
1/9 =
0.111...
2/9 =
0.222...
17/20 =
0.85
1^2 =
1
1.4^2 ≈
2
1.7^2 ≈
3
2^2 =
4
3^2 =
9
4^2 =
16
5^2 =
25
6^2=
36
7^2 =
49
8^2 =
64
9^2=
81
11^2 =
121
12^2=
144
13^2 =
169
14^2=
196
15^2=
225
16^2=
256
17^2=
289
18^2=
324
19^2 =
361
21^2=
441
22^2=
484
23^2=
529
24^2=
576
25^2=
625
√1 =
1
√2 ≈
1.4
√3 ≈
1.7
√4 =
2
√9 =
3
√16 =
4
√25 =
5
√36
6
√49
7
√64 =
8
√81
9
√121
11
√144
12
√169
13
√196
14
√225
15
√256
16
√289
17
√324
18
√361
19
√441
21
√400
20
√441
21
√484
22
√529
23
√576
24
√625
25
2^(-3)
1/8
2^(-2)
1/4
2^(-1)
1/2
2^0
1
2^2
4
2^3
8
2^4
16
2^5
32
2^6
64
2^7
128
2^8
256
2^9
512
2^10
1024
3^(-3)
1/27
3^(-2)
1/9
3^(-1)
1/3
3^0
1
3^1
3
3^2
9
3^3
27
3^4
81
3^5
243
3^6
729
3^7
2187
3^8
6561
3^9
19,683
3^10
59,049
1^3
1
2^3
8
3^3
27
4^3
64
5^3
125
3√1
(cubed root of 1)
1
3√8
(cubed root of 8)
2
3√27
(cubed root of 27)
3
3√64
(cubed root of 64)
4
3√125
(cubed root of 125
5
0!
1
1!
1
2!
2
3!
6
4!
24
5!
120
6!
720
7!
5,040
Shortcut for the sum of consecutive integers?
1. Average the first and last term to find the middle point or term
2. Derive the total # of terms
3. The sum = middle point * # of terms
Positive x Negative =
Negative
Negative x Negative =
Positive
Positive ÷ Negative =
Negative
Negative ÷ Negative =
Positive
Odd + Odd =
Even
Even + Even =
Even
Odd - Odd =
Even
Even - Even =
Even
Odd + Even =
Odd
Odd - Even =
Odd
Even x Odd =
Even
Even x Even =
Even
Product of an even integer with any other integer is ?
Even
Product of ALL odd integers is?
Odd
Odd ÷ Even ≠
Integer
Even ÷ Odd =
Even (or Fraction)
Odd ÷ Odd =
Odd (or Fraction)
Divisibility test for 2:
last digit divisible by 2
Divisibility test for 3:
sum of digits
Divisibility test for 4:
last two digits
Divisibility test for 5:
Last digit 0 or 5
Divisibility test for 6:
test for 2 AND 3
Divisibility test for 8:
last three digits
(remember powers of 2 -> 64, 128, 256, 512, 1024, etc.)
Divisibility test for 9:
sum of digits
Divisibility test for 12:
test for 3 AND 4
Divisibility test for 14:
Test for 2 and 7
Divisibility test for 15:
Test for 3 and 5
Do Not Multiply Out Intermediate Calculations
Simplify later
X^2-Y^2 =
(X+Y)(X-Y)