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Algebra
11th
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82 Terms
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1
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quadratic formula
\[-b ± √(b² - 4ac)] / (2a)
2
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slope formula
(y₂- y₁) / (x₂- x₁)
3
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integers
..., -3, -2, -1, 0, 1, 2, 3, ...
4
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rationals
fractions (anything expessable as a ratio of integers)
5
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reals
integers, rationals, plus special \#s (like √2 or pi)
6
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order of opperations
PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)
7
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Arithmetic Sequences
t₁, t₁+ d, t₁+2d, ...
8
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Geometric Sequences
t₁, t₁· r, t₁· r², ...
9
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percentages
part \= (percent / 100) x whole
10
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average
average \= sum of terms / number of terms
11
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average speed
average speed \= total distance / total time
12
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sum
sum \= average x (number of terms)
13
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mode
mode \= value in the list that appears most often
14
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median
median \= middle value in the list
15
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probability
probability \= number of desired outcomes / number of total outcomes
16
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adding exponents
x^a · x^b \= x^(a+b)
17
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subtracting exponents
x^a / x^b \= x^(a-b)
18
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negative exponents
1 / x^b \= x^(-b)
19
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multiplying exponents
(x^a)^b \= x^(a·b)
20
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x^0
1
21
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roots
√(xy) \= √x · √y
22
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FOIL
(x+a)(x+b) \= x^2 + (b+a)x + ab
23
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difference of squares
a^2 -b^2 \= (a+b)(a-b)
24
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a^2 + 2ab + b^2
(a+b)^2
25
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a^2 - 2ab + b^2
(a-b)(a-b)
26
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distance formula
√[(x₂- x₁)^2 + (y₂- y₁)^2)]
27
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mid-point formula
\[(x₁+ x₂)/2 , (y₁+ y₂)/2]
28
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intersecting lines
opposite angles are equal (each pair of angles along the same line add to 180 degrees)
29
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area of triangle
area \= (1/2)bh
30
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angles of triangle
add up to 180 degrees
31
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length of triangle sides
length of 1 side is always less than the sum of the other 2
32
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equilateral
three equal sides, all angles \= 60 degrees
33
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isosceles
2 equal sides, 2 equal angles
34
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similar
same shape, corresponding angles are equal, corresponding sides are in proportion
35
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circle area
pi · r^2
36
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circle circumference
2 · pi · r
37
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full circle
\= 360 degrees
38
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length of arc
(n degrees / 360 degrees) · 2 · pi · r
39
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area of sector
(n degree / 360 degrees) · pi · r^2 (fraction of circle’s area)
40
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rectangle area
area \= lw
41
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parallelogram area
area \= lh
42
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rectangular solid volume
volume \= lwh
43
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right cylinder volume
volume \= pi · r^2 · h
44
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prime factors
2, 3, 5, 7, 11, ...
45
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Greatest Common Factor
ex. GCF of 200 and 60 is 20
46
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Least Common Multiple
ex. LCM of 200 and 60 is 600
47
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trapezoid area
area \= [(base1 + base2) / 2] · h
48
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Slope intercept form
y\=mx+b
49
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Point-Slope form
y - y₁\= m(x - x₁)
50
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standard form
Ax + By\=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
51
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Dividing by a negative number in an inequality
You must flip the sign
52
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Graphing < or \> on a coordinate plane
dotted line
53
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Graphing ≥ or ≤ on a coordinate plane
solid line
54
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Graphing ≥ or \> on a coordinate plane
shade upwards or to the right
55
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Graphing ≤ or < on a coordinate plane
shade downwards or to the left
56
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circle perimeter
2 pi r
57
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Chord
The distance from one point on the circle to another point on the circle.
58
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Sector
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
59
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arc
Part of a circle connecting two points on the circle.
60
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Central Angle
An angle whose vertex is the center of the circle
61
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Percent Change
old(1 +/- %) = new
62
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<
1. less than
2. fewer than
63
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>
1. greater than
2. exceeds
3. more than
64
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≤
1. at most
2. less than or equal to
3. no more than
65
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≥
1. greater than or equal to
2. no less than
3. at least
66
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Exponential growth
y = a(1 +/- r)^t
a = initial value
r = growth rate
t = time
67
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Vertex Form
y = a(x-h)^2 + k
(h,k) = A vertex
68
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Distance =
rt
69
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Sine and Cosine
sin(x) = cos(90-x)
70
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Sum of solutions
\-b/a
71
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The discriminant
b^2 - 4ac
\-3 < 0 = NO SOL
0 = 0 = 1 REAL SOL
7 > 0 = 2 REAL SOL
72
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Area of equilateral triangle
s^2√3/4
73
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Sum of angles in polygon
(n-2)180
74
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Circle Equation
(x-h)^2 + (y-k)^2 = r^2
75
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Weighted average
sum of terms/number of terms
76
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Part
Percent x whole
77
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Odd num + even num =
Odd num
78
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Percent Increase
100 + (asked percent increase)/100 x whole number
79
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Interior Angles
180 (n - 2)
80
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30-60-90 Triangle
Short Leg: x
Second Leg: x√3
Hypotenuse: 2x
81
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45-45-90 Triangle
Short Leg: x
Second Leg: x
Hypotenuse: x√5
82
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3-4-5 Triangle
Short Leg: 3x
Second Leg: 4x
Hypotenuse: 5x
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