Babers - Formulas.xls

BABER'S - FORMULAS

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BABER'S - FORMULAS

ELLIPSOID

ANGLESARABIC TO ROMANAutoCADCALENDARCALENDAR ANNUALCALENDAR DESKTOPCIRCLECIRCUMSCRIBED RADIUS ICIRCUMSCRIBED RADIUS IICOMBINATIONSCONECONSTANTSCONVERSION FACTORSCOORDINATE AREACUBE & CUBIODCYLINDERCYLINDER (CSA)CYLINDER (SLANTED)DOS CHARACTERSELLIPSE OF SEMI-MAJOR AXIS a AND SEMI-MINOR AXIS b

EXCEL WORKSHEET FUNCTIONSFACTORIALFIG2NUMFILE TITLESFRUSTRUM OF CONEGIRDER I-SECTIONGRAPHSNATIONS OF THE WORLDPARABOLAPARABOLOIDPARALLELEPIPEDPARALLELOGRAMPERCENTAGE DIFFERENCEPERMUTATIONSPERPETUAL CALENDARPOCKET CALENDARPOLAR TO RECTANGULARPOLAR TO RECTANGULAR (2)PYRAMIDQUADRATIC EQUATIONRECTANGLE

RECTANGULAR PARALLELEPIPED OF LENGTH a, HEIGHT b, WIDTH cREGULAR POLYGONREGULAR POLYGON OF n SIDES CIRCUMSCRIBING A CIRCLE OF RADIUS rREGULAR POLYGON OF n SIDES INSCRIBED IN CIRCLE OF RADIUS rSLOPE m OF LINE JOINING TWO POINTS P1 (x1, y1) AND P2 (x2, y2)SPHERESQUARESTATISTICSTORUSTRACHTENBERG 3 DIGIT MULTIPLICATIONTRACHTENBERG PRACTICETRAPEZIUMTRIANGLETRIGONOMETRY ITRIGONOMETRY IITRIGONOMETRY IIITRIGONOMETRY IVUNITSWEDGEWINDOWS SHORTCUTS

ANGLES

60 ' = 1º 60 minutes = 1 degree

60" = 1' 60 seconds = 1 minute

1º =

1 radian = 57.3º

45º = radians 90º = radians



Acute angle Obtuse angle(less than 90º) (between 90º and 180º)

1 revolution = 360º = 2 π radians

π

180

π π4 2

π3

π

π3

2 π

2

3

Reflex angle(greater than 180º)

ARABIC TO ROMAN

This converts an Arabic Numeral into Roman Numeral

Arabic Numeral 1941

Roman Numeral MCMXLI

Notes1 The Roman Numeral do not have a zero2 Do not enter any decimals

AutoCAD Common Scales

Drawing Scales

1 : 10 100 XP Divide 1000 by the required scale to get the XP value1 : 20 50 XP1 : 25 40 XP1 : 50 20 XP

1 : 100 10 XP1 : 200 5 XP1 : 500 2 XP1 : 1000 1 XP1 : 1250 0.8 XP1 : 2500 0.4 XP

2002 CALENDAR

Jan Oct •Feb Mar Nov •Apr Jul •May •Jun •Aug •Sept Dec •

1 8 15 22 29 Sun Sat Fri Thurs Wed Tues Mon2 9 16 23 30 Mon Sun Sat Fri Thurs Wed Tues3 10 17 24 31 Tues Mon Sun Sat Fri Thurs Wed4 11 18 25 Wed Tues Mon Sun Sat Fri Thurs5 12 19 26 Thurs Wed Tues Mon Sun Sat Fri6 13 20 27 Fri Thurs Wed Tues Mon Sun Sat7 14 21 28 Sat Fri Thurs Wed Tues Mon Sun

2003 CALENDAR

Jan Oct •Feb Mar Nov •Apr Jul •May •Jun •Aug •Sept Dec •


Jan-2003 Jan-2003 Jan-2003Sun Mon Tues Wed Thurs Fri Sat Sun Mon Tues Wed Thurs Fri Sat Sun Mon Tues Wed Thurs Fri Sat

1 2 3 4 5 1 2 1 1 2 3 4 5 6 7

3 4 5 6 7 8 9 2 3 4 5 6 7 8 8 9 10 11 12 13 14

10 11 12 13 14 15 16 9 10 11 12 13 14 15 15 16 17 18 19 20 21

17 18 19 20 21 22 22 16 17 18 19 20 21 21 22 23 24 25 26 27 27

24 25 26 27 28 29 30 23 24 25 26 27 28 29 29 30 31

31 30 31


1 2 3 1 2 1

4 5 6 7 8 9 10 3 4 5 6 7 8 9 2 3 4 5 6 7 8

11 12 13 14 15 16 17 10 11 12 13 14 15 16 9 10 11 12 13 14 15

18 19 20 21 22 23 23 17 18 19 20 21 22 22 16 17 18 19 20 21 21

25 26 27 28 29 30 31 24 25 26 27 28 29 30 23 24 25 26 27 28 29

31 30 31


1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5

8 9 10 11 12 13 14 7 8 9 10 11 12 13 6 7 8 9 10 11 12

15 16 17 18 19 20 21 14 15 16 17 18 19 20 13 14 15 16 17 18 19

22 23 24 25 26 27 27 21 22 23 24 25 26 26 20 21 22 23 24 25 25

29 30 31 28 29 30 31 27 28 29 30 31


1 2 3 4 1 2 3 1 2

5 6 7 8 9 10 11 4 5 6 7 8 9 10 3 4 5 6 7 8 9

12 13 14 15 16 17 18 11 12 13 14 15 16 17 10 11 12 13 14 15 16

19 20 21 22 23 24 24 18 19 20 21 22 23 23 17 18 19 20 21 22 22

26 27 28 29 30 31 25 26 27 28 29 30 31 24 25 26 27 28 29 30

31


1 1 2 3 4 5 6 7 1 2 3 4 5 6

2 3 4 5 6 7 8 8 9 10 11 12 13 14 7 8 9 10 11 12 13

9 10 11 12 13 14 15 15 16 17 18 19 20 21 14 15 16 17 18 19 20

16 17 18 19 20 21 21 22 23 24 25 26 27 27 21 22 23 24 25 26 26

23 24 25 26 27 28 29 29 30 31 28 29 30 31

30 31


1 2 3 4 5 6 1 1 2 3 4 5 6 7 1 2 3 4 5 6

2 3 4 5 6 7 8 8 9 10 11 12 13 14 7 8 9 10 11 12 13

9 10 11 12 13 14 15 15 16 17 18 19 20 21 14 15 16 17 18 19 20

16 17 18 19 20 21 21 22 23 24 25 26 27 27 21 22 23 24 25 26 26

23 24 25 26 27 28 29 29 30 31 28 29 30 31

30 31

Jan-2023Sunday Monday Tuesday Wednesday Thursday Friday Saturday

1 2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 24

26 27 28 29 30 31

CIRCLE

1. AREA OF CIRCLE = π r²

PI 3.14159r radiusd diameter = 2 x rp perimeter

r 120Known Values Solution

AREA 45238.93 AREA 78.53982 Radius

2. AREA OF CIRCLE = (π d²) / 4

d 120Known Values Solution

AREA 11309.73 AREA 78.53982 Diameter

3. PERIMETER OF CIRCLE = 2 π r or π d

r 120 Perimeter 753.9822 Known Values

Perimeter 75.39822d 10 Perimeter 31.41593

d

r

4. SEGMENT OF CIRCLE Segment Area = ½ r² (Φ - sin Φ)

Note that Φ is in radians

Φ r

Angle Φ

Area

5. SECTOR OF CIRCLE

Area = π r² θ / 360

Sectorθ

r 10 Known ValuesArea 26.17994

Angle θ Degrees30

Area 26.17994

6. ARC OF CIRCLE

Note that θ is in degrees

θ

Length of Arc = 2πr θ/360

Arc of Circler

Angle θ

Length

Note that θ is in degrees

Solution

5

Solution

10

Solution

Radius 12Diameter 24

Area = ½ r² (Φ - sin Φ)Note that Φ is in radians

10

Degrees Radians30 0.5235988

1.179939

Solutionr 4.166667

Angle θ 8.333334

10

Degrees30

5.235988

RADIUS OF CIRCLE CIRCUMSCRIBING A TRIANGLE OF SIDES a, b, c

R = a b c4 √ s (s-a) (s-b) (s-c)

a 15b 20c 25s 30

Radius 12.5

Ra

b

c

RADIUS OF CIRCLE CIRCUMSCRIBING A TRIANGLE OF SIDES a, b, c

1. AREA = nr² TAN (π/n) = nr² TAN (180°/n)

n 5r 15

Area 817.3603

2. PERIMETER = 2 nr TAN (π/ n) = 2 nr TAN (180°/n)

n 5r 15

Perimeter 108.9814

REGULAR POLYGON OF n SIDES CIRCUMSCRIBING A CIRCLE OF RADIUS

r

SIDES CIRCUMSCRIBING A CIRCLE OF RADIUS r

COMBINATIONS

A selection in which order is not imporn = No. of Objectsr = No. taken at a time

i.e 5!=

5!=

120=

(5-3)! 2! 2

However, for each arrangement of three letters, 6 arrangements are the same group. For example, the arangementsusing the letters ABC are ABC, ACB, BAC, BCA, CAB, and CBA. The number of arrangements is 3! = 6. Note,however, that all six arrangements are the same group, we must therefore divide the 60 ways to arrange the lettersby 6 (3!) to find the number of groups.

C5 3 Number of combinationsn r

a) 5 at a time?

Solution:


b) 2 at a time?

Solution:

Also see Permutations

n C r

Example 1: How many groups of three letters are there if choosing from the letters A, B, C, D, E?

Solution: There are 5 P 3 ways to arrange 3 letters

Example 2: How many combinations of the letters A B C D E are there taken:


a) all are equally eligible?

Solution:Total number of teachers and students is 9Total number of committee members 6


b) the committee must include three teachers and three students?

Solution:We can chose 3 out of a possible 5 teachersand 3 out of a possible 4 students

C C5 3 x 4 3n r n r

CBLANK 0 0 Number of combinationsn r

Example 3: How many ways can a committee of 6 be chosen from 5 teachers and 4 students if:

C C0 0 x 0 0n r n r

n = No. of Objectsr = No. taken at a time

60

However, for each arrangement of three letters, 6 arrangements are the same group. For example, the arangementsusing the letters ABC are ABC, ACB, BAC, BCA, CAB, and CBA. The number of arrangements is 3! = 6. Note,however, that all six arrangements are the same group, we must therefore divide the 60 ways to arrange the lettersby 6 (3!) to find the number of groups.

Number of combinations 10


How many groups of three letters are there if choosing from the letters A, B, C, D, E?

ways to arrange 3 letters

How many combinations of the letters A B C D E are there taken:


Total number of teachers and students is 9Total number of committee members 6


b) the committee must include three teachers and three students?

We can chose 3 out of a possible 5 teachersand 3 out of a possible 4 students



How many ways can a committee of 6 be chosen from 5 teachers and 4 students if:

However, for each arrangement of three letters, 6 arrangements are the same group. For example, the arangements n 120 r

using the letters ABC are ABC, ACB, BAC, BCA, CAB, and CBA. The number of arrangements is 3! = 6. Note,however, that all six arrangements are the same group, we must therefore divide the 60 ways to arrange the letters

6 n-r 2 n/r 20

CONE

1. VOLUME OF CONE = 1/3 π r² h

lh

r

r 5 Known Valuesh 25 Volume

r 5h 25

Volume 654.4985

2. CURVED SURFACE AREA OF CONE = π r l

r 5 Known Valuesl 15.75 CSA 247.4004

r 5Curved Surface Area 247.4004 h

3. TOTAL SURFACE AREA OF CONE = π r l + π r ²

r 25 Known Valuesl 15.75 TSA 3200.498

rTotal Surface Area 3200.498 l 15.75

SolutionVolume 654.49847

rh

SolutionCSA

rh 15.749999

SolutionTSA

r 25l

π 3.14159 26535 89793 23846 2643 …

e 2.71828 18284 59045 23536 0287

1 radian 180° / π

1° π / 180 radians

√ 2 1.41421 35623 73095 0488 …

√ 3 1.73205 08075 68877 2935 …

√ 5 2.23606 79774 99789 6964 …

1.77245 38509 05516 02729 8167 …

23.14069 26327 79269 006 …

22.45915 77183 61045 47342 715 …

√ π

eπ

πe

57.59577 95130 8232 …°

0.01745 32925 19943 29576 92 … Radians

04/20/2023

Baber Beg of 154

C O N V E R S I O N F A C T O R STo Convert From Into

Square Millimetres Circular Mil

Square Millimetres Square Centimetres

Square Millimetres Square Feet

Square Millimetres Square Inches

Square Millimetres Square Yards

04/20/2023

Baber Beg of 154

Multiply by

1973.5544

0.01

1.0764E-05

0.00155

1.195985211595E-06

AREA BY COORDINATES

NOTES:1 The minimum number of points is 3 for a closed shape.2 The starting and end points are the same as you must close the shape.3 This should only be used for outlines with straight lines.

Insert No. of Points 4

Point No. x yStart Point 1 531434.9 189623.4197

2 531453.5 189641.2532 5957650.07 25.74033 564275.34 0

End Point 1 0

AREA 2978825.03

PERIMETER 564301.062

45 3

21

CUBE & CUBOID

A cube has the lengths of sides equal.

a 3

Volume of Cube 27

Surface area of cube 54

A cubiod is a rectangular solid

a 4b 6c 8

Volume of cuboid 192

Surface area of cuboid 240

a

cb

a

aa

CYLINDER

1. VOLUME OF CYLINDER = π r² h

h

r 5 Known Valuesh 15.75 Volume 2136

r 15.32Volume 1237.002 h

2. CURVED SURFACE AREA OF CYLINDER = 2 π r h

r 5 Known Valuesh 15.75 CSA

r 5Curved Surface Area 494.8008 h 15.75

3. TOTAL SURFACE AREA OF CYLINDER = 2 π r (r + h)

r 5 Known Valuesh 15.75 TSA

r 5Total Surface Area 651.8805 h 15.75

r

SolutionVolume

rh 2.896902

2 π r h

SolutionCSA 494.8008

rh

2 π r (r + h)

SolutionTSA 651.8805

rh

CYLINDER CSA A AND SLANT HEIGHT l

1. VOLUME =

A 15l 12.99607

Volume 194.9411

A 15h 12.36

θ ° 72

Volume 194.9411

2. LATERAL SURFACE AREA = pl = ph / SIN θ

p 17.89l 12.99607

Volume 232.4997

p 17.89h 12.36

θ ° 72

Volume 232.4997

Al = Ah / SIN θ

θ

l

A

h

CIRCULAR CYLINDER OF RADIUS r AND SLANT HEIGHT l

1. VOLUME = π r² h = π r² l SIN θ

r 5h 15 l

Volume 1178.097

θr 5l 15.81139

θ ° 71.56505

Volume 1178.097

2. CURVED SURFACE AREA = 2 π r l = 2 π r h =SIN θ

r 5l 15.81139

CSA 496.7294

r 5 r 5h 15 h 15

θ ° 71.56505 θ ° 71.56505

CSA 496.7294 CSA 496.7294

CIRCULAR CYLINDER OF RADIUS r AND SLANT HEIGHT l

r

h

2 π r h COSEC θ

By: Mr. B. A. Beg

DOS Characters

0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z0321 0322 0323 0324 0325 0326 0327 0328 0329 0330 0331 0332 0333 0334 0335 0336 0337 0338 0339 0340 0341 0342 0343 0344 0345 0346

0097 0098 0099 0100 0101 0102 0103 0104 0105 0106 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122

a b c d e f g h I j k l m n o p q r s t u v w x y z0353 0354 0355 0356 0357 0358 0359 0360 0361 0362 0363 0364 0365 0366 0367 0368 0369 0370 0371 0372 0373 0374 0375 0376 0377 0378

0192 0193 0194 0195 0196 0197 0198 0199 0200 0201 0202 0203 0205 0206 0207 0208 0209 0210 0211 0212 0213 0214 0216 0140 0138 0217

À Á Â Ã Ä Å Æ Ç È É Ê Ë Í Î Ï Ð Ñ Ò Ó Ô Õ Ö Ø Œ Š Ù0448 0449 0450 0451 0452 0453 0454 0455 0456 0457 0458 0459 0461 0462 0463 0464 0465 0466 0467 0468 0469 0470 0472 0396 0394 04730218 0219 0220 0221 0159

Ú Û Ü Ý Ÿ0474 0475 0476 0477 0415

0204 0222 0223 0224 0225 0226 0227 0228 0229 0230 0231 0162 0232 0233 0234 0235 0131 0236 0237 0238 0239 0161 0240 0156 0242 0243

Ì Þ ß à á â ã ä å æ ç ¢ è é ê ë ƒ ì í î ï ¡ ð œ ò ó0460 0478 0479 0480 0481 0482 0483 0484 0485 0486 0487 0418 0488 0489 0490 0491 0387 0492 0493 0494 0495 0417 0496 0412 0498 04990244 0245 0246 0248 0241 0154 0249 0250 0251 0252 0181 0253 0254 0255

ô õ ö ø ñ š ù ú û ü µ ý þ ÿ0500 0501 0502 0504 0497 0410 0505 0506 0507 0508 0437 0509 0510 0511

0048 0049 0050 0051 0052 0053 0054 0055 0056 0057 0046 0183 0247 0042 0215 0129 0150 0173 0177 0060 0062 0139 0155 0061

0 1 2 3 4 5 6 7 8 9 . · ÷ * × � – ± < > ‹ › =0304 0305 0306 0307 0308 0309 0310 0311 0312 0313 0302 0439 0503 0298 0471 0385 0406 0429 0433 0316 0318 0395 0411 0317

0188 0189 0190 0037 0137 0176 0035 0126 0040 0041 0091 0093 0123 0125 0171 0187 0036 0163 0165 0064 0169 0174

¼ ½ ¾ % ‰ ° # ~ ( ) [ ] { } « » $ £ ¥ @ © ®0444 0445 0446 0293 0393 0432 0291 0382 0296 0297 0347 0349 0379 0381 0427 0443 0292 0419 0421 0320 0425 0430

0038 0063 0191 0033 0182 0134 0135 0167 0153 0170 0186 0185 0178 0179

& ? ¿ ! ¶ † ‡ § ™ ª º ¹ ² ³0294 0319 0449 0289 0438 0390 0391 0423 0409 0426 0442 0441 0434 0435

0058 0059 0043 0044 0096 0130 0145 0146 0180 0184 0034 0132 0147 0148 0168

: ; + , ` ‚ ’ ’ ´ ¸ " „ “ ” ¨0314 0315 0299 0300 0352 0386 0401 0402 0436 0440 0290 0388 0403 0404 0424

0149 0133 0152 0094 0136 0092 0124 0095 0151 0175 0172 0166 0164

• … ˜ ^ ˆ \ | _ — ¯ ¬ ¦ ¤0405 0389 0408 0350 0392 0348 0380 0351 0407 0431 0428 0422 0420

ELLIPSE OF SEMI-MAJOR AXIS a AND SEMI-MINOR AXIS b

1. AREA = π a b

a 12b 5

Area 188.4956

2. PERIMETER =

= 2 π √ ½ (a² + b²) (Approximately)

a 12b 5

Perimeter 81.68141

4 a √ 1 - k² SIN² θ dθ

a

b

π/2

0

ELLIPSE OF SEMI-MAJOR AXIS a AND SEMI-MINOR AXIS b

ELLIPSOID OF SEMI-AXES a, b, c

1. VOLUME OF ELLIPSOID = 4/3 π a b c

a 7b 15.78c 13.45

Volume 6223.231

a

c

EXCEL WORKSHEET FUNCTIONS

1. RADIAN function

Angle ° Angle Radians

72 1.2566370614 i.e multiply angle in degrees by PI/180

2. DEGREE function

Angle Radians Angle ° i.e multiply angle in radians by 180/PI1.2566370614 72

3. SIN function

SIN (number) Number is the angle in radians for which you want the sine.

If your argument is in degrees, multiply it by PI()/180 or use the RADIANSfunction to convert it to radians.

Radians45 Sin 45° = 0.785398 0.707107 or 0.707107

Use ASIN (Number) to convert back to angle

Returns the arcsine, or inverse sine, of a number. The arcsine is the angle whosesine is number. The returned angle is given in radians in the range -pi/2 to pi/2.

45 degrees

4. COS function

COS (number) Number is the angle in radians for which you want the cosine.

If your argument is in degrees, multiply it by PI()/180 or use the RADIANSfunction to convert it to radians.

Sin θ

D25

RADIANS (Angle in Degrees)

E25

SIN (Angle) in Degrees

Radians30 Cos 30° = 0.523599 0.866025

Cos θ

D43

RADIANS (Angle in Degrees)

E43

COS (Angle) in Degrees

1.256637

72

If your argument is in degrees, multiply it by PI()/180 or use the RADIANS

Returns the arcsine, or inverse sine, of a number. The arcsine is the angle whosesine is number. The returned angle is given in radians in the range -pi/2 to pi/2.

If your argument is in degrees, multiply it by PI()/180 or use the RADIANS

FACTORIAL

The product of a number and all those below it.

Expressed as n!

5

<= 80 120

>= 81

Number 1,961

Text One Thousand Nine Hundred And Sixty One

NOTES1 Enter numbers between the range 1 to 99,999,999,9992 Do not enter any decimal points

FILE No.

TH

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2002

STREET SCENEHIGHWAYS

INFRASTRUCTURE

FRUSTRUM OF CONE

1. VOLUME OF FRUSTRUM OF CONE = 1/3 π h (R² + R r + r²)

r

h l

R

r 5 Known ValuesR 11.2 Volume 5512.678h 25.5 r

R 11.2Volume 5512.678 h 25.5

2. CURVED SURFACE AREA OF FRUSTRUM OF CONE =

r 5 Known ValuesR 11.2 CSAl 26.75 r 5

R 11.2Curved Surface Area 1361.409 l 26.75

3. TOTAL SURFACE AREA OF FRUSTRUM OF CONE =

r 5 Known ValuesR 11.2 TSA 1834.03

l 26.75 rR 11.2

Total Surface Area 1834.03 l 26.75

1/3 π h (R² + R r + r²)

Solution a 26.70354Volume b 299.0796

r 5 c -2162.987

Rh

2. CURVED SURFACE AREA OF FRUSTRUM OF CONE = π l (R + r)

SolutionCSA 1361.409

rRl

3. TOTAL SURFACE AREA OF FRUSTRUM OF CONE =

Solution a 3.141593TSA b 84.0376

π l (R + r) + π R² + π r²

r 5 c -498.7278Rl

Solution -b b² 4ac 2a5 -299.0796 89448.62 -231038 53.40708

-16.2b² - 4ac SQRT(b² - 4ac)320486.2 320486.2 566.115

Solution -b b² 4ac 2a5 -84.0376 7062.319 -6267.199 6.283185

x1

x2

x1

-31.75b² - 4ac SQRT(b² - 4ac)13329.52 13329.52 115.4535

x2

SQRT(b² - 4ac)

GIRDER I-SECTION

1. AREA OF GIRDER I-SECTION = (a1 h1) + 1/2 (a1 + a2) h2 + (a2 h3) + 1/2 ( a2 + a3 ) h4 + a3 h5

mma1 450 Height of Sectiona2 150a3 250 Length of I-Sectionh1 100h2 300 Volume of I-Sectionh3 1000h4 450h5 400

mm² 475000m² 0.475

a3

a1

a2

h1

h2

h3

h4

h5

(a1 h1) + 1/2 (a1 + a2) h2 + (a2 h3) + 1/2 ( a2 + a3 ) h4 + a3 h5

Height of Section 2250

Length of I-Section 25

Volume of I-Section 11.875 m³

GRAPHS

y

a

b

c

True Origin

m =

Non-linear relationships can sometimes be converted into linear relationships. The mostcommon of these are provided in table below:

EQUATION PLOT GRADIENT INTERCEPT

a b

a b

a b

The equation of a straight line can be written in the form "y = mx + c"gradient of the line and "c" is the intercept on the y-axis.

y = axn + b y v xn

y = a/xn + b y v 1/xn

y = a n√ x + b y v n√x

ab

a b

log y v log x n log a

log y v x log b log a

log y v x b log e log a

y = axn + bxn-1 y/xn-1 v x

y = axn

y = abx

y = aebx

x

Non-linear relationships can sometimes be converted into linear relationships. The most

INTERCEPT

b

b

b

The equation of a straight line can be written in the form "y = mx + c" where "m" is the

b

log a

log a

log a

RADIUS OF CIRCLE INSCRIBED IN TRIANGLE OF SIDES a, b, c

r = √ s (s-a) (s-b) (s-c)s

a c

b

a 26b 27c 14s 33.5

Radius 178.4543

r

RADIUS OF CIRCLE INSCRIBED IN TRIANGLE OF SIDES a, b, c

1. Area = ½ n r² SIN (2π/n) = ½ n r² SIN (360°/n)

n 5r 12

Area 342.3803

2. Perimeter = 2 πr SIN( π/n) = 2 πr SIN( 180°/n)

n 5r 12

Perimeter 71.70797

REGULAR POLYGON OF n SIDES INSCRIBED IN CIRCLE OF RADIUS

r

SIDES INSCRIBED IN CIRCLE OF RADIUS r

S # COUNTRY CAPITAL1 AFGHANISTAN KABUL2 ALBANIA TIRANA3 ALGERIA ALGIERS4 ARGENTINA BUENOS AIRES5 ARMENIA YEREVAN6 AUSTRALIA CANBERRA7 AUSTRIA VIENNA8 AZERBAIJAN BAKU9 BAHRAIN MANAMA

10 BANGLADESH DHAKKA11 BELGIUM BRUSSELS12 BHUTAN THIMPHU13 BRAZIL BRASILIA14 BRUNEI BANDAR SERI BEGAWAN15 BULGARIA SOFIA16 BURMA RANGOON17 CAMBODIA PHNOM PENH18 CAMEROON YAOUNDE19 CANADA OTTAWA20 CHAD N'DJAMENA21 CHILE SANTIAGO22 CHINA BEIJING23 COLOMBIA BOGOTA24 CYPRUS NICOSIA25 CZECHOSLOVAKIA PRAGUE26 DENMARK COPENHAGEN27 EGYPT CARIO28 ESTONIA TALLINN29 ETHIOPIA ADDIS ABABA30 FIJI SUVA31 FRANCE PARIS32 GEORGIA TBILISI33 GERMANY BERLIN34 GHANA ACCRA35 GREECE ATHENA36 HUNGARY BUDAPEST37 ICELAND REYKJAVIK38 INDIA NEW DEHLI39 INDONESIA JAKARTA40 IRAN TEHRAN41 IRAQ BAGHDAD42 IRELAND DUBLIN43 ISRAEL JERUSALEM

44 ITALY ROME45 JAPAN TOKYO46 JORDAN AMMAN47 KAZAKHSTAN ALMA ATA48 KENYA NAIROBI49 KOREA, SOUTH SEOUL50 KUWAIT KUWAIT CITY51 LATVIA RIGA52 LEBANON BEIRUT53 LITHUANIA VILNIUS54 LUXEMBOURG LUXEMBOURG55 MALAYSIA KUALA LUMPUR56 MALDIVES MALE57 MALTA VALLETTA58 MEXICO MEXICO CITY59 MONACO MONACOVILLE60 MONGOLIA ULAAN BATAAR61 MOROCCO RABAT62 MOZAMBIQUE MAPUTA63 NAMIBIA WINDHOCK64 NEPAL KATHMANDU65 NETHERLANDS (HOLLAND) AMSTERDAM66 NEW ZEALAND WELLINGTON67 NICARAGUA MANAGUA68 NIGERIA LAGOS69 NORWAY OLSO70 OMAN MUSCAT71 PAKISTAN ISLAMABAD72 PANAMA PANAMA73 PERU LIMA74 PHILLIPPINES MANILA75 POLAND WARSAW76 PORTUGAL LISBON77 QATAR DOHA78 ROMANIA BUCHAREST79 RUSSIA MOSCOW80 SAUDIA ARABIA RIYADH81 SENEGAL DAKAR82 SINGAPORE SINGAPORE83 SOUTH AFRICA CAPE TOWN84 SPAIN MADRID85 SRI LANKA COLOMBO86 SUDAN KHARTOUM87 SWEDEN STOCKHOLM

88 SWITZERLAND BERN89 SYRIA DAMASCUS90 TAIWAN TAIPEI91 TAJIKISTAN DUSHANBE92 TANZANIA DAR-ES-SALAAM93 THAILAND BANGKOK94 TURKEY ANKARA95 TURKMENISTAN ASHKHABAD96 UGANDA KAMPALA97 UKRAINE KIYEV98 UNITED KINGDOM LONDON99 UNITED STATES OF AMERIC WASHINGTON DC

100 UZBEKISTAN TASHKENT101 VIETNAM HANOI102 YUGLOSLAVIA BELGRADE103 ZAIRE KINSHAHA104 ZAMBIA LUSAKA105 ZIMBABWE HARARE

CURRENCY AREA: Km² PST 12 NOON DIFF PST GMT 12 NOONAFGHANI 647,497 11:30 -0.50 16:30LEK 28,748 8:00 -4.00 13:00ALGERIAN DINAR 2,381,741 8:00 -4.00 13:00PESO 2,766,889 4:00 -8.00 9:00RUBLE 29,800 10:00 -2.00 15:00AUSTRALIAN DOLLAR 7,686,848 17:00 5.00 22:00SCHILLING 83,849 8:00 -4.00 13:00RUBLE 86,800 10:00 -2.00 15:00DINAR 668 10:00 -2.00 15:00TAKKA 143,998 13:00 1.00 18:00BELGIAN FRANC 30,513 8:00 -4.00 13:00NGULTRUM 47,000 13:00 1.00 18:00CRUZADO 8,311,965 4:00 -8.00 9:00BRUNEI DOLLAR 5,800 15:00 3.00 20:00LEV 110,911 9:00 -3.00 14:00KYAT 676,577 13:30 1.50 18:30RIEL 181,035 14:00 2.00 19:00CFA FRANC 475,440 8:00 -4.00 13:00CANADIAN DOLLAR 997,613 2:00 -10.00 7:00FRANC 1,284,000 9:00 -3.00 14:00PESO 7,551,626 10:00 -2.00 15:00YUAN 9,560,951 15:00 3.00 20:00PESO 1,138,914 0:00 -12.00 5:00CYPRIAN POUND 9,251 10:00 -2.00 15:00KORUNA 127,905 8:00 -4.00 13:00KRONE 43,069 8:00 -4.00 13:00EGYPTIAN POUND 1,000,258 9:00 -3.00 14:00RUBLE 47,549 10:00 -2.00 15:00BIRR 1,128,221 10:00 -2.00 15:00FIJIAN DOLLAR 18,274 19:00 7.00 0:00FRENCH FRANC 547,026 8:00 -4.00 13:00RUBLE 69,700 10:00 -2.00 15:00DEUTSCHMARK 356,975 8:00 -4.00 13:00CEDI 238,537 7:00 -5.00 12:00DRACHMA 131,990 9:00 -3.00 14:00FORINT 93,030 9:00 -3.00 14:00KRONA 102,846 7:00 -5.00 12:00INDIAN RUPEE 3,287,590 12:30 0.50 17:30RUPIAH 2,027,087 14:30 2.50 19:30RIYAL 1,648,195 10:30 -1.50 15:30DINAR 434,924 10:00 -2.00 15:00POUND 70,283 8:00 -4.00 13:00SHEKEL 28,094 10:00 -2.00 15:00

LIRA 301,225 8:00 -4.00 13:00YEN 377,644 16:00 4.00 21:00DINAR 97,740 10:00 -2.00 15:00RUBLE 2,717,000 10:00 -2.00 15:00SHILLING 582,646 10:00 -2.00 15:00WON 98,484 16:00 4.00 21:00DINAR 17,819 10:00 -2.00 15:00RUBLE 65,786 10:00 -2.00 15:00POUND 10,400 10:00 -2.00 15:00RUBLE 64,445 9:00 -3.00 14:00FRANC 2,586 8:30 -3.50 13:30DOLLAR 329,749 15:30 3.50 20:30RULIYA 298 12:00 0.00 17:00LIRA 316 9:00 -3.00 14:00PESO 1,972,547 1:00 -11.00 6:00FRANC 149 9:00 -3.00 14:00TUGRIK 1,665,000 16:00 4.00 21:00DIRHAM 712,550 8:00 -4.00 13:00METICAL 303,769 9:00 -3.00 14:00RAND 824,292 9:00 -3.00 14:00RUPEE 140,797 12:45 0.75 17:45FLORIN 40,884 8:00 -4.00 13:00DOLLAR 269,056 20:00 8.00 1:00CORDOBA 130,000 1:00 -11.00 6:00NAIRA 923,768 8:00 -4.00 13:00KRONE 324,219 8:00 -4.00 13:00RIYAL 212,457 11:00 -1.00 16:00RUPEE 796,095 12:00 0.00 17:00BALBOA 77,083 0:00 -12.00 5:00INTI 1,285,216 0:00 -12.00 5:00PESO 300,000 15:00 3.00 20:00ZLOTY 312,670 8:00 -4.00 13:00ESCUDO 92,082 8:00 -4.00 13:00RIYAL 11,000 10:00 -2.00 15:00LEU 237,500 9:00 -3.00 14:00RUBLE 6,592,812 10:00 -2.00 15:00RIYAL 2,149,690 10:00 -2.00 15:00FRANC 196,192 7:00 -5.00 12:00DOLLAR 625.6 15:00 3.00 20:00RAND 1,272,037 9:00 -3.00 14:00PESETA 504,782 8:00 -4.00 13:00RUPEE 64,454 12:30 0.50 17:30POUND 2,505,813 9:00 -3.00 14:00KRONA 449,964 9:00 -3.00 14:00

SWISS FRANC 41,228 8:00 -4.00 13:00POUND 185,000 10:00 -2.00 15:00DOLLAR 35,981 15:00 3.00 20:00RUBLE 143,100 10:00 -2.00 15:00SHILLING 945,087 10:00 -2.00 15:00BAHT 514,000 14:30 2.50 19:30LIRA 814,578 9:00 -3.00 14:00RUBLE 488,100 10:00 -2.00 15:00SHILLING 236,036 10:00 -2.00 15:00RUBLE 603,677 10:00 -2.00 15:00POUND STERLING 244,046 7:00 -5.00 12:00US DOLLAR 3,618,770 2:00 -10.00 7:00RUBLE 447,400 10:00 -2.00 15:00DONG 329,556 14:00 2.00 19:00DINAR 255,804 8:00 -4.00 13:00ZAIRE 234,488 8:00 -4.00 13:00KWACHA 752,614 9:00 -3.00 14:00DOLLAR 390,580 9:00 -3.00 14:00

DIFF GMT4.50 1.00 1.00

-3.00 3.00

10.00 1.00 3.00 3.00 6.00 1.00 6.00

-3.00 8.00 2.00 6.50 7.00 1.00

-5.00 2.00 3.00 8.00

-7.00 3.00 1.00 1.00 2.00 3.00 3.00

-12.00 1.00 3.00 1.00 0.00 2.00 2.00 0.00 5.50 7.50 3.50 3.00 1.00 3.00

1.00 9.00 3.00 3.00 3.00 9.00 3.00 3.00 3.00 2.00 1.50 8.50 5.00 2.00

-6.00 2.00 9.00 1.00 2.00 2.00 5.75 1.00

-11.00 -6.00 1.00 1.00 4.00 5.00

-7.00 -7.00 8.00 1.00 1.00 3.00 2.00 3.00 3.00 0.00 8.00 2.00 1.00 5.50 2.00 2.00

1.00 3.00 8.00 3.00 3.00 7.50 2.00 3.00 3.00 3.00 0.00

-5.00 3.00 7.00 1.00 1.00 2.00 2.00

PARABOLA

1. AREA = 2/3 ab

Ba 4.5

a

b 7.75

Area 23.25

Ab

2. ARC LENGTH ABC = ½ √ b² +16a² + b² Ln 4a + √ b² +16a²

a 4.5b 7.75

ARC Length ABC 12.43357

8a b

Cb

4a + √ b² +16a²

PARABOLOID OF REVOLUTION

1. VOLUME OF PARABOLOID = ½ π b² a

a 15.75b 7.25

Volume 1300.398

PARALLELEPIPED OF CROSS-SECTIONAL AREA A AND HEIGHT h

1. VOLUME =

hθ

aA 256.326h 1.35

Volume 346.0401

a 15.75b 7.65c 4.5

θ ° 72.5

Volume 372.9495

A h = abc SIN θ

PARALLELEPIPED OF CROSS-SECTIONAL AREA A AND HEIGHT h

Ac

b

a

PARALLELOGRAM

1. AREA OF PARALLELOGRAM = bh

h

b

b 5 Known Valuesh 7 Area 35

bAREA 35 h 7

SolutionArea

b 5h

PERCENTAGE DIFFERENCE

a b4934.289 4983.681 1.0%

4934.289 4983.632 1%

PERMUTATIONS

An arrangement of objects in which order is important

For example the letters a, b, and c can be arranged in six different orders

abcacbbacbcacabcba

3 6

Also see Combinations

n P n = n!

An arrangement of objects in which order is important

For example the letters a, b, and c can be arranged in six different orders

6

PERPETUAL CALENDAR

Julian GregorianCentury

0 100 200 300 400 500 600 1500 1600 1700 1800 1900

Year700 800 900 1000 1100 1200 1300 2000 2100 2200 2300

1400 15000 DC ED FE GF AG BA CB … BA C E G1 29 57 85 B C D E F G A F G B D F2 30 58 86 A B C D E F G E F A C E3 31 59 87 G A B C D E F D E G B D4 32 60 88 FE GF AG BA CB DC ED CB DC FE AG CB5 33 61 89 D E F G A B C A B D F A6 34 62 90 C D E F G A B G A C E G7 35 63 91 B C D E F G A F G B D F8 36 64 92 AG BA CB DC ED FE GF ED FE AG CB ED9 37 65 93 F G A B C D E C D F A C10 38 66 94 E F G A B C D B C E G B11 39 67 95 D E F G A B C A B D F A12 40 68 96 CB DC ED FE GF AG BA GF AG CB ED GF13 41 69 97 A B C D E F G E F A C E14 42 70 98 G A B C D E F D E G B D15 43 71 99 F G A B C D E C D F A C16 44 72 ED FE GF AG BA CB DC … CB ED GF BA17 45 73 C D E F G A B … A C E G18 46 74 B C D E F G A … G B D F19 47 75 A B C D E F G … F A C E20 48 76 GF AG BA CB DC ED FE … ED GF BA DC21 49 77 E F G A B C D … C E F G22 50 78 D E F G A B C … B D F A23 51 79 C D E F G A B … A C E G24 52 80 BA CB DC ED FE GF AG … GF BA DC FE25 53 81 G A B C D E F … E G B D26 54 82 F G A B C D E C D F A C27 55 83 E F G A B C D B C E G B28 56 84 DC ED FE GF AG BA CB AG BA DC FE AG

Jan Oct A B C D E F GFeb Mar Nov D E F G A B CApr Jul G A B C D E FMay B C D E F G AJun E F G A B C DAug C D E F G A BSept Dec F G A B C D E

1 8 15 22 29 Sun Satur Fri Thurs Wednes Tues Mon2 9 16 23 30 Mon Sun Satur Fri Thurs Wednes Tues3 10 17 24 31 Tues Mon Sun Satur Fri Thurs Wednes4 11 18 25 Wednes Tues Mon Sun Satur Fri Thurs5 12 19 26 Thurs Wednes Tues Mon Sun Satur Fri6 13 20 27 Fri Thurs Wednes Tues Mon Sun Satur7 14 21 28 Satur Fri Thurs Wednes Tues Mon Sun

If the year is a leap year, use first letter for the months of January and February for theremainder of the months use the second letter.

On and before 1582, October 4 only. On and after 1582, October 15 only.

2003

JanFebMarAprMayJunJul

AugSeptOctNovDec


2004

JanFebMarAprMayJunJul

AugSeptOctNovDec


POLAR TO RECTANGULAR

Equation

P1 P2

2 3

2 4

d

d 2.236068

Known Values Solutiond 5.23645 d

-2.23645

4

3

4

d = Ö (x2 - x1)2 + (y2 - y1)2

x1 x2

y1 y2

x1 x1

y1 y1

x2 x2

y2 y2

x1, y1

x2, y2

POLAR TO RECTANGULAR

Equation

dP1

0P2

0

P30

P40

P50

P60

P70

P80

P90

P10

TOTAL DISTANCE 0

d = Ö (x2 - x1)2 + (y2 - y1)2

x1 y1

PYRAMID

1. VOLUME OF PYRAMID = 1/3 A h

hArea of Base = A

a 5 For area of base Known Valuesb 2.35 Volume 58.75h 15 a

b 2.35Volume 58.75 h 15

SolutionVolume

a 5bh

QUADRATIC EQUATION

If ax² + bx + c = 0

x = - b ± √ b² - 4ac2a

a 1b 10c 20

Solution

-2.763932

-7.236068

x1

x2

RECTANGLE

1. AREA OF RECTANGLE = B x H

B

H

Rectangle has both sides equal to one another and all angles are at 90°

B 10H 4

AREA 40

Known Values SolutionAREA AREA 40

B 10 BH 4 H

2. PERIMETER OF RECTANGLE = 2 x (B + H)

B 10H 4

Perimeter 28

Known Values SolutionPerimeter 28 Perimeter

B B 10H 4 H

RECTANGULAR PARALLELEPIPED OF LENGTH a, HEIGHT b, WIDTH c

1. VOLUME = a b c

a 4b 7.5c 15

Volume 450

2. SURFACE AREA = 2 (ab + ac + bc)

a 4b 7.5c 15

Surface Area 405

RECTANGULAR PARALLELEPIPED OF LENGTH a, HEIGHT b, WIDTH c

b

a

c

REGULAR POLYGON

b Perimeter = n b

b 4.563 1.256637 radiansn 5 72 degrees

Area 2373.211Perimeter 22.815

Regular Polygon of n sides, with sides each of length b

Area = 1/4 n b² cot (π / n)

2π / n

2π / n =

Area = 1/4 n b² cot (π / n)

Equationm = or m =

P1 P2

0

0

m 0.333333 q

Known Values Solution

m 0.1 m

1.2

524.26

39.32

528.072

SLOPE m OF LINE JOINING TWO POINTS P1 (x1, y1) AND P2 (x2, y2)

y2 - y1

tan qx2 - x1

x1 x2

y1 y2

x1 x1

y1 y1

x2 x2

y2 y2

P2

3

1

18.43495

V H Slope

1 in 2.78 0.360

1 in 2.78 0.36

(x1, y1) AND P2 (x2, y2)

SQUARE

1. AREA OF SQUARE = a²a

a

A square has both sides equal to one another, all four angles are 90°

a 5

AREA 25

2. PERIMETER OF SQUARE = 4 a

a 5

PERIMETER 20

STATISTICS

1234

1 Average or The sum of all the items divided by the number of itemsArithmetical Mean

n

1 322 253 334 265 256789

1011121314151617181920

Average 28.2

2 Mode The most frequently occurring, or repetetive, value in an array or range of data

1 322 25

AverageModeMedianStandard Deviation

∑ a1, a2, a3, a4 … an

3 334 265 256 327 278 259 31

10 2611 25121314151617181920

Mode 25

3 Median The median is the number in the middle of a set of numbers

1 252 253 254 255 266 267 278 319 32

10 3211 3312 34131415161718

1920

Median 26.5

4 Standard Deviation This is a statistic that measures the tendency of data to be spread out. Intuitively, it is amargin of error associated with a given expected value.

σ =N

1 26 45.25622 33 0.074383 25 59.710744 26 45.25625 45 150.61986 35 5.1652897 36 10.710748 37 18.25629 45 150.6198

10 25 59.7107411 27 32.80165121314151617181920

Average 32.72727

σ 52.56198

Σ ( x - x ) 2

The most frequently occurring, or repetetive, value in an array or range of data

This is a statistic that measures the tendency of data to be spread out. Intuitively, it is a

MESSAGE MESSAGE MESSAGE

To Time To Time To Time

Department Date Department Date Department Date

Call Received by Call Received by Call Received by

Caller Caller Caller

of (Company) of (Company) of (Company)

Telephone No. Tie line Extension Telephone No. Tie line Extension Telephone No. Tie line Extension

URGENT Telephoned URGENT Telephoned URGENT Telephoned

Wants to see you Returned your call Wants to see you Returned your call Wants to see you Returned your call

Called to see you Please ring back Called to see you Please ring back Called to see you Please ring back

Left the attached Will call again Left the attached Will call again Left the attached Will call again

Message Message Message

TORUS Inner radius a, Outer radius b

1. VOLUME = 1/4 π² (a + b)(b - a)²

a 10b 15.75

Volume 2100.645

2. SURFACE AREA = π² (b² - a²)

a 10b 15.75

Surface Area 1461.318

ab

TRACHTENBERG 3 DIGIT MULTIPLICATION

1 2 5 x 3 7 4

STEP 1 1 2 5 x 3 7 402

STEP 21 2 5 x 3 7 4

5 04 2

STEP 31 2 5 x 3 7 47 5 03 4 2

STEP 41 2 5 x 3 7 4

6 7 5 01 3 4 2

STEP 51 2 5 x 3 7 4

4 6 7 5 00 1 3 4 2

STEP 61 2 5 x 3 7 4

4 6 7 5 00 1 3 4 2

STEP 6


Multiply 4 x 5 20Write 0 under 5Carry 2

Multiply 4 x 2 8Multiply 7 x 5 35+ Carry 2 2

45

Write 5 under 2Carry 4

Multiply 4 x 1 4Multiply 7 x 2 14Multiply 3 x 5 15+ Carry 4 4

37

Write 7 under 1Carry 3


16

Write 6Carry 1


4

Write 4Carry 0

Multiply 4 x 0 0Multiply 7 x 0 0

Multiply 3 x 0 0+ Carry 0 0

0


0 0 0 4 2 1 x 2 5Answer 1 0 6 5 1 3

P P P P P P

Carry 2 2 1


3 = 106513

TRAPEZIUM

AREA OF TRAPEZIUM = 1/2 h (a + b)

a

h

a 9b 3 bh 6

Area 36Known Values SolutionArea Area

a 3 ab 7 b

h 2.53 h

Solution12.65

TRIANGLE

1. AREA OF TRIANGLE = 1/2 (b h)

H

B

B 3 Known ValuesH 4 Area 6

B 4AREA 6 H

2. AREA OF TRIANGLE (Sum of Sides)

where s = 1/2 (a + b + c)

a c

b

a 4b 3.45c 5.5s 6.475

AREA 6.874997

3. PERIMETER OF TRIANGLE (Sum of Sides)

A = Ö s(s - a) (s - b)(s - c)

a c

b

Perimeter = a + b + ca 3b 15c 5

Perimeter 23

SolutionArea

BH 3

where s = 1/2 (a + b + c)

s(s - a) (s - b)(s - c)

TRIGONOMETRY I

C

For a right angled triangleh = hypotenuse

o = opposite side

A a = adjacent side B

SIN A =opposite side

=o

hypotenuse h

COS A =adjacent side

=a

hypotenuse h

TAN A =opposite side

=o

adjacent side a

COSEC A =1

=hypotenuse

=SIN A opposite side

SEC A =1

=hypotenuse

=COS A adjacent side

TAN A =1

=adjacent side

=TAN A opposite side

SIN 60º =3 COS A =2

SIN A =

SIN 30º =1

√

SIN 30º =2

SIN 45º =22

COS 60º =12

COS 30º =32

COS 45º =22

TAN 60º = 3

TAN 30º =33

TAN 45º = 1

√

√

√

√

√

o = opposite side

ho

ha

ao

SIN (90º - A)

COS (90º - A)

TRIGONOMETRY II

C

3

5

o 3a 4h 5

4 B

SIN A =o

= 0.6 A = 36.8699 Degreesh

COS A =a

= 0.8 A = 36.8699 Degreesh

TAN A =o

= 0.75 A = 36.8699 Degreesa

Known Values Solutiono Angle 36.8699a 4 o 3h 5 a

h

TRIGONOMETRY III

Trigonmetrical Identities

SIN²A + COS²A = 1

SEC²A = 1 + TAN²A

COSEC²A = 1 + COT²A

TAN A =SIN ACOS A

The General Angle

Quadrant Angle

First 0 to 90°

Second 90° to 180°

Third 180° to 270°

Fourth 270° to 360°

SIN A COS A TAN A

SIN A COS A TAN A

SIN(180° - A) - COS(180° - A) - TAN(180° - A)

- SIN(A - 180°) - COS(A - 180°) TAN(A - 180°)

- SIN(360° - A) COS(360° - A) - TAN(360° - A)

TRIGONOMETRY IV

For any triangle

c b

a

SINE RULEa

=b

=c

SIN A SIN B SIN C

COSINE RULE

a² = b² + c² - 2bc COS A

b² = a² + c² - 2ac COS B

c² = a² + b² - 2ab COS C

TANGENT RULE TANB - C

=b - c

COT2 b + c

A

B C

SPHERE

1. VOLUME OF SPHERE = 4/3 π r³

r 5 d 10

Volume 523.5988

2. SURFACE AREA OF SPHERE = 4π r²

r 5


3. SPHERICAL TRIANGLE OF SIDES ABC ON SPHERE OF RADIUS r

AREA OF TRIANGLE ABC =( A + B + C - π) r²

r

B

r

4. SPHERICAL CAP OF RADIUS r AND HEIGHT h =

h 5r 15

Volume 1047.197551

5. SURFACE AREA OF SPHERICAL CAP = 2 π r h

h 5r 15


h

r

AC


Volume Volume 523.5988r 5 r


Surface Area 314.1593 Surface Arear r 5

3. SPHERICAL TRIANGLE OF SIDES ABC ON SPHERE OF RADIUS r

A 4B 6C 8r 15.75

Area 3685.814

1/3 π h² (3 r - h)

UNITS

Prefix Name Prefix Symbol Factor by which unit is multiplied Description

yotta Y 1E+24 ### One Million Million Million Million

zetta Z 1E+21 1,000,000,000,000,000,000,000 One Thousand Million Million Million

exa E 1E+18 1,000,000,000,000,000,000 One Million Million Million

peta P 1E+15 1,000,000,000,000,000 One Thousand Million Million

tera T 1E+12 1,000,000,000,000 One Million Million

giga G 1E+09 1,000,000,000 One Thousand Million

mega M 1E+06 1,000,000 One Million

myria my 1E+04 10,000 Ten Thousand

kilo k 1E+03 1,000 One Thousand

hecto h 1E+02 100 One Hundred

deca(aka deke) da 1E+01 10 Ten

unit 1E+00 1 Unit

deci d 1E-01 0.1 One Tenth

centi c 1E-02 0.01 One Hundredth

milli m 1E-03 0.001 One Thousandth

micro m 1E-06 0.000001 One Millionth

nano n 1E-09 0.000000001 One Thousand Millionth

pico p 1E-12 0.000000000001 One Million Millionth

femto f 1E-15 0.000000000000001 One Thousand Million Millionth

atto a 1E-18 0.000000000000000001 One Million Million Millionth

WEDGE

1. VOLUME OF WEDGE = 1/2 bhl

d h

lb

b 5 Known Valuesh 3 Volume 112.5l 15 b 5

h 3Volume 112.5 l

2. SURFACE AREA OF WEDGE = bh + l (d + b + h)

b 4 For rt. Angled wedgeh 3l 15d 5

Surface Area 192

d = Slant Length

sin angle = o / hcos angle = a / h

SolutionVolume

bhl 15

tan angle = o / a 0.75angle 36.8699sin(angle) in radians 0.643501sin(angle) in degrees 0.6hypotenuse 5

WINDOWS SHORTCUT KEYSCOMMON SHORTCUTS FOR OFFICE TOOLS COMMON SHORTCUTS FOR OFFICE TOOLS

SHORTCUT KEY DESCRIPTION APPLICATIONS SHORTCUT KEY DESCRIPTION APPLICATIONSF1 Get Online Help or Display the Office Assistant All F1 Get Online Help or Display the Office Assistant AllShift + F1 Activate Context-sensitive(What's This) Help All Shift + F1 Activate Context-sensitive(What's This) Help AllF10 Activate the Menu Bar Word F10 Activate the Menu Bar WordShift + F10 Display a Shortcut Menu at Current Insertion Point All Shift + F10 Display a Shortcut Menu at Current Insertion Point AllAlt + F8 Run a Macro Word, Excel, Powerpoint Alt + F8 Run a Macro Word, Excel, PowerpointAlt + F11 Display Visual Basic Editor All Alt + F11 Display Visual Basic Editor AllAlt + Spacebar Show the Program Icon Menu (on the Program Title Bar) All Alt + Spacebar Show the Program Icon Menu (on the Program Title Bar) AllCrtl + Alt + F1 Display Microsoft System Information All Crtl + Alt + F1 Display Microsoft System Information All

COMMON WINDOW / FILE SHORTCUTS COMMON DIALOG BOX SHORTCUTSSHORTCUT KEY DESCRIPTION APPLICATIONS SHORTCUT KEY DESCRIPTION APPLICATIONS

Ctrl + N Create a New File or Outlook Item using Default Options All Switch to Next Tab All

Display the Open Dialog Box All Switch to Previous Tab All

Ctrl + S Save the Current File All All

Ctrl + P Print a Document File using Default Settings All Arrow Keys Move between Options in List Box Option Group AllF12 Display the Save As Dialog Box All Spacebar All

Go to the Next / Previous Window All Alt + Letter Key All

Close Current Window All Alt + Down Arrow Open Selected Drop-down List Box All

Alt + F4 Quit the Current Program All Esc Close Selected Drop-down List Box All

COMMON FORMATTING SHORTCUTS COMMON DATA ENTRY / EDITING FORMATSSHORTCUT KEY DESCRIPTION APPLICATIONS SHORTCUT KEY DESCRIPTION APPLICATIONS

Ctrl + B Apply Bold Formatting All Ctrl + Backspace Delete One Word to the Left All except ExcelCtrl + I Apply Italic Formatting All Crtl + Delete Delete One Word to the Right All except ExcelCtrl + U Apply Underline Formatting All Ctrl + C Copy Selected Text or Object AllCtrl + D Font Menu Word, Powerpoint Ctrl + X Cut Selected Text or Object AllCtrl + M Tab Word, Powerpoint Ctrl + V Paste Text or Object AllCtrl + Shift + < Decrease Font Size Word, Powerpoint Ctrl + C, Ctrl + C Display the Clipboard Toolbar AllCtrl + Shift + > Increase Font Size Word, Powerpoint Ctrl + F Find All, except OutlookCtrl + Shift + L Bullets Word, Powerpoint Ctrl + G Goto All, except OutlookCtrl + Shift + F Change the Font Word, Excel, Powerpoint Ctrl + H Replace All, except OutlookCtrl + Shift + P Change the Font Size Word, Excel, Powerpoint Ctrl + K Insert Hyperlink All, except OutlookCtrl + Shift + C Copy Formats Word, Powerpoint F7 Check Spelling AllCtrl + Shift + V Paste Formats Word, Powerpoint Alt + F7 Find Next Misspelling or Grammatical Error Word, PowerpointCtrl + Shift + V Paste Formats Word, Powerpoint F4 Repeat Last Action All, except OutlookCtrl + Tab Insert a tab in a table cell Word Ctrl + Z Undo the Last Action AllShift + F3 Change the Case of Letters Word, Powerpoint Ctrl + Y Redo the Last Action All

Ctrl + Tab, Ctrl Page Down

Ctrl + O, Ctrl + F12

Ctrl + Shift + Tab, Ctrl + Shift + Page Up

Tab, Shift + Tab

Move to Next / Previous Option, Option Group, Button or Control

Perform the Action Assigned to the Selected Button;

Ctrl + F6, Ctrl + Shift + F6

Select Option or Toggle Check Box next to Underlined Letter

Ctrl + F4, Ctrl + W

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