Reference Section
Symbols & Abbreviations
Common Powers
SI Unit Prefixes
Greek Alphabet
Linear Inequalities
Properties of Absolute Values
Metric to English (US) Conversions
Plane Geometry Formula
Solid Geometry Formula
Pythagorean Theorem (Variations)
Linear Equations
Conic Sections
Polynomials, Pascals Triangle
Properties of Complex Numbers
Exponents & Radicals
Trigonometric Functions & Values
Trigonometric Identities
Basic Trigonometric Ratios Graphs
Trigonometric Tables
Properties of Logarithmic Functions
Common Logarithmic Tables
Common Powers
(and not so common)
Squares Cubes 4th Power 5th Power 6th Power 7th Power
22 = 4 23 = 8 24 = 16 25 = 32 26 = 64 27 = 128
32 = 9 33 = 27 34 = 81 35 = 243 36 = 729 37 = 2187
42 = 16 43 = 64 44 = 256 45 = 1024 46 = 4096 47 = 16384
52 = 25 53 = 125 54 = 625 55 = 3125 56 = 15625 57 = 78125
62 = 36 63 = 216 64 = 1296 65 = 7776 66 = 46656 67 = 279936
72 = 49 73 = 343 74 = 2401 75 = 16807 76 = 117649 77 = 823543
82 = 64 83 = 512 84 = 4096 85 = 32768 86 = 262144 87 = 2097152
92 = 81 93 = 729 94 = 6561 95 = 59049 96 = 531441 97 = 4782969
102 = 100 103 = 1000 104 = 10000 105 = 100000 106 = 1000000 107 = 10000000
112 = 121 122 = 144 132 = 169 142 = 196 152 = 225 202 = 400
Greek Alphabet
A α Alpha N v Nu
B β Beta Ξ ξ Xi
Γ γ Gamma O o Omicron
∆ δ Delta ∏ π Pi
E ε Epsilon P ρ Rho
Z ζ Zeta ∑ σ Sigma
H η Eta T τ Tau
Θ θ Theta Υ v Upsilon
I i Iota Φ φ Phi
K k Kappa Χ χ Chi
Λ λ Lambda Ψ ψ Psi
M µ Mu Ω ω Omega
SI Unit Prefixes
Factor Name Symbol Factor Name Symbol
10-18 atto a 10-1 deci d
10-15 femto f 10 deca da
10-12 pico p 102 hecto h
10-9 nano n 103 kilo k
10-6 micro µ 106 mega M
10-3 milli m 109 giga G
10-2 centi c 1012 tera T
Linear Inequalities
Interval Notation Set Builder Notation Graph of the Inequality
(a, + ∞) {x | x > a}
[a, + ∞) {x | x ≥ a}
(- ∞, a) {x | x < a}
(- ∞, a] {x | x ≤ a}
[a, b] {x | a ≤ x ≤ b}
(a, b) {x | a < x < b}
[a, b) {x | a ≤ x < b}
(a, b] {x | a < x ≤ b}
(- ∞, + ∞) {x | x ∈ R}
(- ∞, b) or (a, + ∞) {x | x < a or x > b}
(- ∞, a] or [a, + ∞) {x | x < a or x > b}
(- ∞, a] or [a, + ∞) {x | x < a or x > b}
(- ∞, a] or [a, + ∞) {x | x < a or x > b}
Properties of Absolute Values
If | X | = k, then X = k or X = -k
If | X | < k, then -k < X < k
If | X | > k, then X > k or X < -kMetric to English (US) Conversions
Distance:
12 in = 1 ft
3 ft = 1 yd 10 mm = 1 cm
1760 yds = 1 mi 100 cm = 1 m
5280 ft = 1 mi 1000m = 1 km
(English-Metric conversions: 1 inch = 2.54 cm; 1 mile = 1.61 km)
Area:
144 in2 = 1 ft2 10,000 cm2 = 1 m2
43,560 ft2 = 1 acre 10,000 m2 = 1 hectare
640 acres = 1 mi2 100 hectare = 1 km2
(English-Metric conversions: 1 in2 = 6.45 cm2; 1 mi2 = 2.59 km2)
Volume:
57.75 in3 = 1 qt 1 cm3 = 1 ml
4 qt = 1 gal 1000 ml = 1 liter
42 gal (petroleum) = 1 barrel 1000 liter = 1 m3
(English-Metric conversions: 16.39 cm3 = 1 in3; 3.79 liters = 1 gal)
Mass:
437.5 grains = 1 oz 1000 mg = 1 g
16 oz = 1 lb 1000 g = 1 kg
2000 lb = 1 short ton 1000 kg = 1 metric ton
(English-Metric conversions: 453 g = 1 lb; 2.2 lb = 1 kg)
Temperature:
(Fahrenheit – Celsius Conversions: °C = 5/9 (°F – 32) and °F = 9/5 °C + 32)
Plane Geometry Formula
Circle Square Rectangle
Area = π r2 Area = s2 Area = l w
Perimeter = 2 π r Perimeter = 4 s Perimeter = 2l + 2w
Triangle Rhombus Trapezoid
Area = 1/2 b h Area = b h Area = 1/2 (l1 + l2) h
Perimeter = s1 + s2 + s3 Perimeter = 4 b Perimeter = l1 + l2 + h1 + h2
Parallelogram Regular Polygon (n-gon)
Area = b h Area = (1/2 s h) (number of sides)
Perimeter = 2 h1 + 2 b Perimeter = s (number of sides)
Solid Geometry Formula
Cube Right Rectangular Prism Right Cylindrical Prism
Volume = s3 Volume = l w h Volume = π r2 h
S. A. = 6 s2 S. A. = 2 l w + 2 h w + 2 l h S. A. = 2 π r h + 2 π r2
Sphere Torus Right Triangular Prism
Volume = 4/3 π r3 Volume = 2 π2 r2 R Volume = (1/2 b h) l
S. A. = 4 π r2 S. A. = 4 π2 r R S. A. = b h + 2 l s + l b
Right Circular Cone General Cone/Pyramid Square Pyramid
Volume = 1/3 (π r2) h Volume = 1/3 (base area) h Volume = 1/3 (s2) h
S. A. = π r (r2 + h2)1/2 + π r2 S.A. = s [s + (s2 + 4h2)
Pythagorean Theorem (Variations)
For any right triangle a, b and c:
a2 + b2 = c2
For any non-right triangle a, b and c:
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
c2 = a2 + b2 – 2ab cos C
For any rectangular prism a, b and c, the diagonal (d) length is:
d2 = a2 + b2 + c2
Linear Equations
An Ordered Pair: (x, y)
Distance between Two Ordered Pairs: d2 = ∆ x2 + ∆ y2 or d2 = (x2 – x1)2 + (y2 – y1)2
Midpoint between Two Ordered Pairs: [(x1 + x2) , (y1 + y2)]
2 2
Slope: m = ∆ y or m = (y2 – y1) … where ∆y = y2 – y1, ∆ x = x2 – x1 and ∆ x ≠ 0
∆ x (x2 – x1)
The slope for Two Parallel Lines: m1 = m2
The slope for Two Perpendicular Lines: m1 . m2 = -1 or m1 = -1/m2
To find the Linear Equation Using Two Ordered Pairs: (x2 – x1) m = (y2 – y1)
General Form of a Linear Equation: Ax + By + C = 0 (A, B, C are integers, A is positive)
Slope Intercept Form of a Linear Equation: y = mx + b
Conic Sections
Conic Equations (Standard Form):
Circle: (x – h)2 + (y – k)2 = r2 (h, k) is the center point, r is the radius from the
center to the circles (x, y) coordinates
Parabolas: y – k = a(x – h)2 Parabolas, commonly written as y = ax2 + bx + c
x – h = a(y – k)2
Ellipse: (x – h)2 + (y – k)2 = 1 (h, k) is the center point, rx is the radius length in rx2 ry2 the ± x direction, ry is the radius length in the ± y direction
Hyperbola: (x – h)2 – (y – k)2 = 1 (h, k) is the center point, rx is the distance from the
rx2 ry2 center to the hyperbola’s ± x asymptote. ry is the distance from the center to the hyperbola’s ± x asymptote.Polynomials
Quadratic Solutions:
The solution for x from a quadratic equation ax2 + bx + c = 0, (where a ≠ 0), can be found from:
Factoring:
a2 – b2 = (a + b)(a – b) a2 + b2 … cannot be factored
a3 – b3 = (a – b)(a2 + ab + b2) a3 + b3 = (a + b)(a2 – ab + b2)
Binomial Expansions:
(a + b)0 = 1 (a – b)0 = 1
(a + b)1 = a + b (a – b)1 = a – b
(a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3 (a – b)3 = a3 – 3a2b + 3ab2 – b3
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
(a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5
(a – b)5 = a5 – 5a4b + 10a3b2 – 10a2b3 + 5ab4 – b5
(a + b)6 = a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b5
(a – b)6 = a6 – 6a5b + 15a4b2 – 20a3b3 + 15a2b4 – 6ab5 + b5
Properties of Complex Numbers
( a + bi) + (c + di) = a + c + (b + d)i ( a + bi) – (c + di) = a – c + (b – d)i
( a + bi) (c + di) = ac – bd + (ab + bd)i ( a + bi) (a – bi) = a2 + b2
(-a)1/2 = i(a)1/2, a ≥ 0
Properties of Exponents
Properties of Rational Exponents and Radicals
Basic Trigonometric Functions & Values
Basic Trigonometric Ratios
Sin = Opposite Cos = Adjacent Tan = Opposite
Hypotenuse Hypotenuse Adjacent
Sec = Hypotenuse Csc = Hypotenuse Cot = Adjacent
Opposite Adjacent Opposite
Trigonometric Identities
Reciprocal Identities:
sin θ = 1/csc θ tan θ = 1/cot θ cos θ = 1/sec θ
csc θ = 1/sin θ cot θ = 1/tan θ sec θ = 1/cos θ
Tangent and Cotangent Identities:
tan θ = sin θ / cos θ cot θ = cos θ / sin θ
Pythagorean Identities:
sin2 θ + cos2 θ =1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ
Double Angle Formulas:
sin 2θ = 2 sin θ cos θ
cos 2θ = cos2 θ − sin2 θ cos 2θ = 2 cos2 θ − 1 cos 2θ = 1− 2sin2 θ
tan 2θ = 2 tan θ / 1− tan2 θ
Sum and Difference Formulas:
sin (α + β ) = sin α cos β + cos α sin β sin (α − β ) = sin α cos β − cos α sin β
cos (α + β ) = cos α cos β − sin α sin β cos (α − β ) = cos α cos β + sin α sin β
tan(α + β) = tan α + tan β / 1 − tan α tan β tan(α − β) = tan α − tan β / 1 + tan α tan β
Graphs of Basic Trigonometric Ratios
Trigonometric Tables
Angle Sin Cos Tan Csc Angle Sin Cos Tan Csc
1 0.017 1.000 0.017 57.299 46 0.719 0.695 1.036 1.390
2 0.035 0.999 0.035 28.654 47 0.731 0.682 1.072 1.36
3 0.052 0.999 0.052 19.107 48 0.743 0.669 1.111 1.346
4 0.070 0.998 0.070 14.336 49 0.755 0.656 1.150 1.325
5 0.087 0.996 0.087 11.474 50 0.766 0.643 1.192 1.305
6 0.105 0.995 0.105 9.567 51 0.777 0.629 1.235 1.287
7 0.122 0.993 0.123 8.206 52 0.788 0.616 1.280 1.269
8 0.139 0.990 0.141 7.185 53 0.799 0.602 1.327 1.252
9 0.156 0.988 0.158 6.392 54 0.809 0.588 1.376 1.236
10 0.174 0.985 0.176 5.759 55 0.819 0.574 1.428 1.221
11 0.191 0.982 0.194 5.241 56 0.829 0.559 1.483 1.206
12 0.208 0.978 0.213 4.810 57 0.839 0.545 1.540 1.192
13 0.225 0.974 0.231 4.445 58 0.848 0.530 1.600 1.179
14 0.242 0.970 0.249 4.134 59 0.857 0.515 1.664 1.167
15 0.259 0.966 0.268 3.864 60 0.866 0.500 1.732 1.155
16 0.276 0.961 0.287 3.628 61 0.875 0.485 1.804 1.143
17 0.292 0.956 0.306 3.420 62 0.883 0.469 1.881 1.133
18 0.309 0.951 0.325 3.236 63 0.891 0.454 1.963 1.122
19 0.326 0.946 0.344 3.072 64 0.899 0.438 2.050 1.113
20 0.342 0.940 0.364 2.924 65 0.906 0.423 2.145 1.103
21 0.358 0.934 0.384 2.790 66 0.914 0.407 2.246 1.095
22 0.375 0.927 0.404 2.669 67 0.921 0.391 2.356 1.086
23 0.391 0.921 0.424 2.559 68 0.927 0.375 2.475 1.079
24 0.407 0.914 0.445 2.459 69 0.934 0.358 2.605 1.071
25 0.423 0.906 0.466 2.366 70 0.940 0.342 2.747 1.064
26 0.438 0.899 0.488 2.281 71 0.946 0.326 2.904 1.058
27 0.454 0.891 0.510 2.203 72 0.951 0.309 3.078 1.051
28 0.469 0.883 0.532 2.130 73 0.956 0.292 3.271 1.046
29 0.485 0.875 0.554 2.063 74 0.961 0.276 3.487 1.040
30 0.500 0.866 0.577 2.000 75 0.966 0.259 3.732 1.035
31 0.515 0.857 0.601 1.942 76 0.970 0.242 4.011 1.031
32 0.530 0.848 0.625 1.887 77 0.974 0.225 4.331 1.026
33 0.545 0.839 0.649 1.836 78 0.978 0.208 4.705 1.022
34 0.559 0.829 0.675 1.788 79 0.982 0.191 5.145 1.019
35 0.574 0.819 0.700 1.743 80 0.985 0.174 5.671 1.015
36 0.588 0.809 0.727 1.701 81 0.988 0.156 6.314 1.012
37 0.602 0.799 0.754 1.662 82 0.990 0.139 7.115 1.010
38 0.616 0.788 0.781 1.624 83 0.993 0.122 8.144 1.008
39 0.629 0.777 0.810 1.589 84 0.995 0.105 9.514 1.006
40 0.643 0.766 0.839 1.556 85 0.996 0.087 11.430 1.004
41 0.656 0.755 0.869 1.524 86 0.998 0.070 14.301 1.002
42 0.669 0.743 0.900 1.494 87 0.999 0.052 19.081 1.001
43 0.682 0.731 0.933 1.466 88 0.999 0.035 28.636 1.001
44 0.695 0.719 0.966 1.440 89 1.000 0.017 57.290 1.000
45 0.707 0.707 1.000 1.414 90 1.000 0.000 1.000 Properties of Logarithmic Functions
x = ay is equivalent to y = loga x ex = y is equivalent to ln y = x
loga (xy) = loga x + loga y loga (x/y) = loga x – loga y loga (1/x) = – loga x
ln (xy) = ln x – ln y ln (x/y) = ln x – ln y ln (1/x) = – ln x
loga x = log x/ log a loga a = 1 loga 1 = 0 loga xy = y loga x
loga x = ln x/ ln a ln e = 1 ln 1 = 0 ln xy = y ln x
Common Logarithm Table
N 0 1 2 3 4 5 6 7 8 9
1.0 0.0000 0.0043 0.0086 0.0128 0.0170 0.0212 0.0253 0.0294 0.0334 0.0374
1.1 0.0414 0.0453 0.0492 0.0531 0.0569 0.0607 0.0645 0.0682 0.0719 0.0755
1.2 0.0792 0.0828 0.0864 0.0899 0.0934 0.0969 0.1004 0.1038 0.1072 0.1106
1.3 0.1139 0.1173 0.1206 0.1239 0.1271 0.1303 0.1335 0.1367 0.1399 0.1430
1.4 0.1461 0.1492 0.1523 0.1553 0.1584 0.1614 0.1644 0.1673 0.1703 0.1732
1.5 0.1761 0.1790 0.1818 0.1847 0.1875 0.1903 0.1931 0.1959 0.1987 0.2014
1.6 0.2041 0.2068 0.2095 0.2122 0.2148 0.2175 0.2201 0.2227 0.2253 0.2279
1.7 0.2304 0.2330 0.2355 0.2380 0.2405 0.2430 0.2455 0.2480 0.2504 0.2529
1.8 0.2553 0.2577 0.2601 0.2625 0.2648 0.2672 0.2695 0.2718 0.2742 0.2765
1.9 0.2788 0.2810 0.2833 0.2856 0.2878 0.2900 0.2923 0.2945 0.2967 0.2989
2.0 0.3010 0.3032 0.3054 0.3075 0.3096 0.3118 0.3139 0.3160 0.3181 0.3201
2.1 0.3222 0.3243 0.3263 0.3284 0.3304 0.3324 0.3345 0.3365 0.3385 0.3404
2.2 0.3424 0.3444 0.3464 0.3483 0.3502 0.3522 0.3541 0.3560 0.3579 0.3598
2.3 0.3617 0.3636 0.3655 0.3674 0.3692 0.3711 0.3729 0.3747 0.3766 0.3784
2.4 0.3802 0.3820 0.3838 0.3856 0.3874 0.3892 0.3909 0.3927 0.3945 0.3962
2.5 0.3979 0.3997 0.4014 0.4031 0.4048 0.4065 0.4082 0.4099 0.4116 0.4133
2.6 0.4150 0.4166 0.4183 0.4200 0.4216 0.4232 0.4249 0.4265 0.4281 0.4298
2.7 0.4314 0.4330 0.4346 0.4362 0.4378 0.4393 0.4409 0.4425 0.4440 0.4456
2.8 0.4472 0.4487 0.4502 0.4518 0.4533 0.4548 0.4564 0.4579 0.4594 0.4609
2.9 0.4624 0.4639 0.4654 0.4669 0.4683 0.4698 0.4713 0.4728 0.4742 0.4757
3.0 0.4771 0.4786 0.4800 0.4814 0.4829 0.4843 0.4857 0.4871 0.4886 0.4900
N 0 1 2 3 4 5 6 7 8 9
3.1 0.4914 0.4928 0.4942 0.4955 0.4969 0.4983 0.4997 0.5011 0.5024 0.5038
3.2 0.5051 0.5065 0.5079 0.5092 0.5105 0.5119 0.5132 0.5145 0.5159 0.5172
3.3 0.5185 0.5198 0.5211 0.5224 0.5237 0.5250 0.5263 0.5276 0.5289 0.5302
3.4 0.5315 0.5328 0.5340 0.5353 0.5366 0.5378 0.5391 0.5403 0.5416 0.5428
3.5 0.5441 0.5453 0.5465 0.5478 0.5490 0.5502 0.5514 0.5527 0.5539 0.5551
3.6 0.5563 0.5575 0.5587 0.5599 0.5611 0.5623 0.5635 0.5647 0.5658 0.5670
3.7 0.5682 0.5694 0.5705 0.5717 0.5729 0.5740 0.5752 0.5763 0.5775 0.5786
3.8 0.5798 0.5809 0.5821 0.5832 0.5843 0.5855 0.5866 0.5877 0.5888 0.5899
3.9 0.5911 0.5922 0.5933 0.5944 0.5955 0.5966 0.5977 0.5988 0.5999 0.6010
4.0 0.6021 0.6031 0.6042 0.6053 0.6064 0.6075 0.6085 0.6096 0.6107 0.6117
4.1 0.6128 0.6138 0.6149 0.6160 0.6170 0.6180 0.6191 0.6201 0.6212 0.6222
4.2 0.6232 0.6243 0.6253 0.6263 0.6274 0.6284 0.6294 0.6304 0.6314 0.6325
4.3 0.6335 0.6345 0.6355 0.6365 0.6375 0.6385 0.6395 0.6405 0.6415 0.6425
4.4 0.6435 0.6444 0.6454 0.6464 0.6474 0.6484 0.6493 0.6503 0.6513 0.6522
4.5 0.6532 0.6542 0.6551 0.6561 0.6571 0.6580 0.6590 0.6599 0.6609 0.6618
4.6 0.6628 0.6637 0.6646 0.6656 0.6665 0.6675 0.6684 0.6693 0.6702 0.6712
4.7 0.6721 0.6730 0.6739 0.6749 0.6758 0.6767 0.6776 0.6785 0.6794 0.6803
4.8 0.6812 0.6821 0.6830 0.6839 0.6848 0.6857 0.6866 0.6875 0.6884 0.6893
4.9 0.6902 0.6911 0.6920 0.6928 0.6937 0.6946 0.6955 0.6964 0.6972 0.6981
5.0 0.6990 0.6998 0.7007 0.7016 0.7024 0.7033 0.7042 0.7050 0.7059 0.7067
5.1 0.7076 0.7084 0.7093 0.7101 0.7110 0.7118 0.7126 0.7135 0.7143 0.7152
5.2 0.7160 0.7168 0.7177 0.7185 0.7193 0.7202 0.7210 0.7218 0.7226 0.7235
5.3 0.7243 0.7251 0.7259 0.7267 0.7275 0.7284 0.7292 0.7300 0.7308 0.7316
N 0 1 2 3 4 5 6 7 8 9
5.4 0.7324 0.7332 0.7340 0.7348 0.7356 0.7364 0.7372 0.7380 0.7388 0.7396
5.5 0.7404 0.7412 0.7419 0.7427 0.7435 0.7443 0.7451 0.7459 0.7466 0.7474
5.6 0.7482 0.7490 0.7497 0.7505 0.7513 0.7520 0.7528 0.7536 0.7543 0.7551
5.7 0.7559 0.7566 0.7574 0.7582 0.7589 0.7597 0.7604 0.7612 0.7619 0.7627
5.8 0.7634 0.7642 0.7649 0.7657 0.7664 0.7672 0.7679 0.7686 0.7694 0.7701
5.9 0.7709 0.7716 0.7723 0.7731 0.7738 0.7745 0.7752 0.7760 0.7767 0.7774
6.0 0.7782 0.7789 0.7796 0.7803 0.7810 0.7818 0.7825 0.7832 0.7839 0.7846
6.1 0.7853 0.7860 0.7868 0.7875 0.7882 0.7889 0.7896 0.7903 0.7910 0.7917
6.2 0.7924 0.7931 0.7938 0.7945 0.7952 0.7959 0.7966 0.7973 0.7980 0.7987
6.3 0.7993 0.8000 0.8007 0.8014 0.8021 0.8028 0.8035 0.8041 0.8048 0.8055
6.4 0.8062 0.8069 0.8075 0.8082 0.8089 0.8096 0.8102 0.8109 0.8116 0.8122
6.5 0.8129 0.8136 0.8142 0.8149 0.8156 0.8162 0.8169 0.8176 0.8182 0.8189
6.6 0.8195 0.8202 0.8209 0.8215 0.8222 0.8228 0.8235 0.8241 0.8248 0.8254
6.7 0.8261 0.8267 0.8274 0.8280 0.8287 0.8293 0.8299 0.8306 0.8312 0.8319
6.8 0.8325 0.8331 0.8338 0.8344 0.8351 0.8357 0.8363 0.8370 0.8376 0.8382
6.9 0.8388 0.8395 0.8401 0.8407 0.8414 0.8420 0.8426 0.8432 0.8439 0.8445
7.0 0.8451 0.8457 0.8463 0.8470 0.8476 0.8482 0.8488 0.8494 0.8500 0.8506
7.1 0.8513 0.8519 0.8525 0.8531 0.8537 0.8543 0.8549 0.8555 0.8561 0.8567
7.2 0.8573 0.8579 0.8585 0.8591 0.8597 0.8603 0.8609 0.8615 0.8621 0.8627
7.3 0.8633 0.8639 0.8645 0.8651 0.8657 0.8663 0.8669 0.8675 0.8681 0.8686
7.4 0.8692 0.8698 0.8704 0.8710 0.8716 0.8722 0.8727 0.8733 0.8739 0.8745
7.5 0.8751 0.8756 0.8762 0.8768 0.8774 0.8779 0.8785 0.8791 0.8797 0.8802
7.6 0.8808 0.8814 0.8820 0.8825 0.8831 0.8837 0.8842 0.8848 0.8854 0.8859
N 0 1 2 3 4 5 6 7 8 9
7.7 0.8865 0.8871 0.8876 0.8882 0.8887 0.8893 0.8899 0.8904 0.8910 0.8915
7.8 0.8921 0.8927 0.8932 0.8938 0.8943 0.8949 0.8954 0.8960 0.8965 0.8971
7.9 0.8976 0.8982 0.8987 0.8993 0.8998 0.9004 0.9009 0.9015 0.9020 0.9025
8.0 0.9031 0.9036 0.9042 0.9047 0.9053 0.9058 0.9063 0.9069 0.9074 0.9079
8.1 0.9085 0.9090 0.9096 0.9101 0.9106 0.9112 0.9117 0.9122 0.9128 0.9133
8.2 0.9138 0.9143 0.9149 0.9154 0.9159 0.9165 0.9170 0.9175 0.9180 0.9186
8.3 0.9191 0.9196 0.9201 0.9206 0.9212 0.9217 0.9222 0.9227 0.9232 0.9238
8.4 0.9243 0.9248 0.9253 0.9258 0.9263 0.9269 0.9274 0.9279 0.9284 0.9289
8.5 0.9294 0.9299 0.9304 0.9309 0.9315 0.9320 0.9325 0.9330 0.9335 0.9340
8.6 0.9345 0.9350 0.9355 0.9360 0.9365 0.9370 0.9375 0.9380 0.9385 0.9390
8.7 0.9395 0.9400 0.9405 0.9410 0.9415 0.9420 0.9425 0.9430 0.9435 0.9440
8.8 0.9445 0.9450 0.9455 0.9460 0.9465 0.9469 0.9474 0.9479 0.9484 0.9489
8.9 0.9494 0.9499 0.9504 0.9509 0.9513 0.9518 0.9523 0.9528 0.9533 0.9538
9.0 0.9542 0.9547 0.9552 0.9557 0.9562 0.9566 0.9571 0.9576 0.9581 0.9586
9.1 0.9590 0.9595 0.9600 0.9605 0.9609 0.9614 0.9619 0.9624 0.9628 0.9633
9.2 0.9638 0.9643 0.9647 0.9652 0.9657 0.9661 0.9666 0.9671 0.9675 0.9680
9.3 0.9685 0.9689 0.9694 0.9699 0.9703 0.9708 0.9713 0.9717 0.9722 0.9727
9.4 0.9731 0.9736 0.9741 0.9745 0.9750 0.9754 0.9759 0.9763 0.9768 0.9773
9.5 0.9777 0.9782 0.9786 0.9791 0.9795 0.9800 0.9805 0.9809 0.9814 0.9818
9.6 0.9823 0.9827 0.9832 0.9836 0.9841 0.9845 0.9850 0.9854 0.9859 0.9863
9.7 0.9868 0.9872 0.9877 0.9881 0.9886 0.9890 0.9894 0.9899 0.9903 0.9908
9.8 0.9912 0.9917 0.9921 0.9926 0.9930 0.9934 0.9939 0.9943 0.9948 0.9952
9.9 0.9956 0.9961 0.9965 0.9969 0.9974 0.9978 0.9983 0.9987 0.9991 0.9996
