Reference Section

Common Powers
Greek Alphabet
SI Unit Prefixes
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
Properties of Complex Numbers
Properties of Rational Exponents and Radicals
Basic Trigonometric Functions & Values
Trigonometric Identities
Trigonometric Tables
Properties of Logarithmic Functions
Common Logarithmic Tables

Common Powers (and not so common)

Table of Powers
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 = 82 93 = 729 94 = 6561 95 = 59049 96 = 531441 97 = 4782969
102 = 100 103 = 1000 104 = 10000 105 = 100000 106 = 1000000 107 = 10000000
Less common Squares
112 = 121 122 = 144 132 = 160 142 = 198 152 = 225 202 = 400

Greek Alphabet

Uppercase Letter Lowercase Letter Greek Letter Name
A α Alpha
B β Beta
Γ γ Gamma
∆ δ Delta
E ε Epsilon
Z ζ Zeta
H η Eta
Θ θ Theta
I ι Iota
K κ  Kappa
Λ λ  Lambda
Μ μ  Mu
Ν ν  Nu
Ξ ξ  Xi
O ο  Omicron
∏ π  Pi
Ρ ρ  Rho
∑ σ  Sigma
Τ τ  Tau
Υ υ Upsilon
Φ φ Phi
Χ χ Chi
Ψ ψ Psi
Ω ω Omega

SI Unit Prefixes

Factor Name Symbol
10-18 atto a
10-15 femto f
10-12 pico p
10-9 nano n
10-6 micro µ
10-3 milli m
10-2 centi c
10-1 deci d
10  deca da
102  hecto h
103  kilo k
106  mega M
109  giga G
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 < -k

Metric to English (US) Conversions

Distance:

  • 12 in = 1 ft
  • 3 ft = 1 yd
  • 1760 yds = 1 mi
  • 5280 ft = 1 mi
  • 10 mm = 1 cm
  • 100 cm = 1 m
  • 1000m = 1 km
  • (English-Metric conversions: 1 inch = 2.54 cm; 1 mile = 1.61 km)

Area:

  • 144 in2 = 1 ft2
  • 43,560 ft2 = 1 acre
  • 640 acres = 1 mi2
  • 10,000 cm2 = 1 m2
  • 10,000 m2 = 1 hectare
  • 100 hectare = 1 km2
  • (English-Metric conversions: 1 in2 = 6.45 cm2; 1 mi2 = 2.59 km2)

Volume:

  • 57.75 in3 = 1 qt
  • 4 qt = 1 gal
  • 42 gal (petroleum) = 1 barrel
  • 1 cm3 = 1 ml
  • 1000 ml = 1 liter
  • 1000 liter = 1 m3
    (English-Metric conversions: 16.39 cm3 = 1 in3; 3.79 liters = 1 gal)

Mass:

  • 437.5 grains = 1 oz
  • 16 oz = 1 lb
  • 2000 lb = 1 short ton
  • 1000 mg = 1 g
  • 1000 g = 1 kg
  • 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

Shape Area Perimeter
Circle π r2 2 π r
Parallelogram Regular b h 2 h1 + 2 b
Polygon (1/2 s h) (number of sides) s (number of sides)
Square s2 4 s
Rectangle l w 2l + 2w
Rhombus b h 4 b
Trapezoid 1/2 (l1 + l2) h l1 + l2 + h1 + h2
Triangle 1/2 b h s1 + s2 + s3

Solid Geometry Formula

Shape Volume Surface Area
Cube s3 6 s2
Right Cylindrical Prism π r2 h 2 π r h + 2 π r2
Right Rectangular Prism l w h 2 l w + 2 h w + 2 l h
Right Triangular Prism (1/2 b h) l b h + 2 l s + l b
Sphere 4/3 π r3 4 π r2
Square Pyramid 1/3 (s2) h *

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)]
  • 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 + cx – 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)n (a – b)n
(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 + 10a2 b3 + 5ab4 + b5 (a – b)5 = a5 – 5a4b + 10a3b2 – 10a2 b3 + 5ab4 – b5
(a + b)6 = a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6 (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 Rational Exponents and Radicals

[latex]\text{Product Rule of Exponents: }x^m \times x^n = x^{m+n}[/latex]

[latex]\text{Power of a Power Rule of Exponents: }(x^m)^n = x^{mn}[/latex]

[latex]\text{Power of a Product Rule of Exponents: }(xy)^n = x^ny^n[/latex]

[latex]\text{Quotient Rule of Exponents: }\dfrac{x^m}{x^n}=x^{m-n}\hspace{0.25in} (x \ne 0)[/latex]

[latex]\text{Power of a Quotient Rule of Exponents: }\left(\dfrac{x}{y}\right)^n = \dfrac{x^n}{y^n}\hspace{0.25in} (y \ne 0)[/latex]

Basic Trigonometric Functions & Values

Basic Trigonometric Ratios

  • Sin = Opposite / Hypotenuse
  • Cos = Adjacent / Hypotenuse
  • Tan = Opposite / Adjacent
  • Sec = Hypotenuse / Opposite
  • Csc = Hypotenuse / Adjacent
  • Cot = 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

Trigonometric Tables

Angle Sin Cos Tan Csc
1 0.017 1.000 0.017 57.299
2 0.035 0.999 0.035 28.654
3 0.052 0.999 0.052 19.107
4 0.070 0.998 0.070 14.336
5 0.087 0.996 0.087 11.474
6 0.105 0.995 0.105 9.567
7 0.122 0.993 0.123 8.206
8 0.139 0.990 0.141 7.185
9 0.156 0.988 0.158 6.392
10 0.174 0.985 0.176 5.759
11 0.191 0.982 0.194 5.241
12 0.208 0.978 0.213 4.810
13 0.225 0.974 0.231 4.445
14 0.242 0.970 0.249 4.134
15 0.259 0.966 0.268 3.864
16 0.276 0.961 0.287 3.628
17 0.292 0.956 0.306 3.420
18 0.309 0.951 0.325 3.236
19 0.326 0.946 0.344 3.072
20 0.342 0.940 0.364 2.924
21 0.358 0.934 0.384 2.790
22 0.375 0.927 0.404 2.669
23 0.391 0.921 0.424 2.559
24 0.407 0.914 0.445 2.459
25 0.423 0.906 0.466 2.366
26 0.438 0.899 0.488 2.281
27 0.454 0.891 0.510 2.203
28 0.469 0.883 0.532 2.130
29 0.485 0.875 0.554 2.063
30 0.500 0.866 0.577 2.000
31 0.515 0.857 0.601 1.942
32 0.530 0.848 0.625 1.887
33 0.545 0.839 0.649 1.836
34 0.559 0.829 0.675 1.788
35 0.574 0.819 0.700 1.743
36 0.588 0.809 0.727 1.701
37 0.602 0.799 0.754 1.662
38 0.616 0.788 0.781 1.624
39 0.629 0.777 0.810 1.589
40 0.643 0.766 0.839 1.556
41 0.656 0.755 0.869 1.524
42 0.669 0.743 0.900 1.494
43 0.682 0.731 0.933 1.466
44 0.695 0.719 0.966 1.440
45 0.707 0.707 1.000 1.414
46 0.719 0.695 1.036 1.390
47 0.731 0.682 1.072 1.367
48 0.743 0.669 1.111 1.346
49 0.755 0.656 1.150 1.325
50 0.766 0.643 1.192 1.305
51 0.777 0.629 1.235 1.287
52 0.788 0.616 1.280 1.269
53 0.799 0.602 1.327 1.252
54 0.809 0.588 1.376 1.236
55 0.819 0.574 1.428 1.221
56 0.829 0.559 1.483 1.206
57 0.839 0.545 1.540 1.192
58 0.848 0.530 1.600 1.179
59 0.857 0.515 1.664 1.167
60 0.866 0.500 1.732 1.155
61 0.875 0.485 1.804 1.143
62 0.883 0.469 1.881 1.133
63 0.891 0.454 1.963 1.122
64 0.899 0.438 2.050 1.113
65 0.906 0.423 2.145 1.103
66 0.914 0.407 2.246 1.095
67 0.921 0.391 2.356 1.086
68 0.927 0.375 2.475 1.079
69 0.934 0.358 2.605 1.071
70 0.940 0.342 2.747 1.064
71 0.946 0.326 2.904 1.058
72 0.951 0.309 3.078 1.051
73 0.956 0.292 3.271 1.046
74 0.961 0.276 3.487 1.040
75 0.966 0.259 3.732 1.035
76 0.970 0.242 4.011 1.031
77 0.974 0.225 4.331 1.026
78 0.978 0.208 4.705 1.022
79 0.982 0.191 5.145 1.019
80 0.985 0.174 5.671 1.015
81 0.988 0.156 6.314 1.012
82 0.990 0.139 7.115 1.010
83 0.993 0.122 8.144 1.008
84 0.995 0.105 9.514 1.006
85 0.996 0.087 11.430 1.004
86 0.998 0.070 14.301 1.002
87 0.999 0.052 19.081 1.001
88 0.999 0.035 28.636 1.001
89 1.000 0.017 57.290 1.000
90 1.000 0.000 Undefined 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
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 0.7067x
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
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
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

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Intermediate Algebra Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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