UTA Math 1301 Formula Sheet PDF

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Formula Sheet for Contemporary Math 1301...

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MATH 1301 Contemporary Mathematics Formula Pages The Number of Elements in A ∪ B

Square Root Property

n ( A ∪ B ) = n ( A) + n ( B ) − n ( A ∩ B )

If ฀฀ 2 = ฀฀, then ฀ ฀ = ±√฀฀

DeMorgan’s Laws for Sets

Quadratic Formula

(A ∩ B )/ = A/ ∪ B /

The solutions of the quadratic equation

(A ∪ B )

= A/ ∩ B /

/

Basic Truth Tables

ax 2 + bx + c = 0 , where a ≠ 0 , is

x=

− b ± b2 − 4ac 2a

Vertex of a Parabola The vertex of the parabola f( x) = ax2 + bx + c is the ordered pair

DeMorgan’s Laws and Other Equivalent Forms

(h, k ) =  −

~ ( p ∧ q ) ⇔ ~ p∨ ~ q

Temperature Conversion

~ ( p ∨ q ) ⇔ ~ p∧ ~ q

b b  , f  −   2  2a  a  

~ ( p → q ) ⇔ p∧ ~ q

9 F = C + 32 5 5 C = ( F − 32) 9

p ↔ q ⇔ [( p → q ) ∧ (q → p )]

Pythagorean Theorem

p → q ⇔~ p ∨ q

Exponent Rules ฀฀ ฀ ฀

� � ฀฀

฀฀ −฀฀

�฀฀ �

฀฀ ฀฀

=฀฀฀฀

฀฀ ฀฀

= ฀฀฀฀ 1

฀฀−฀฀ =฀฀฀฀ Slope Formula The slope m of a line through the points ( x1, y1 ) and

(x2 , y2 ) is m=

rise ∆ y y2 − y1 , where ∆x ≠ 0 . = = run ∆ x x2 − x1

Factoring Polynomials ฀฀2 − ฀฀2 = (฀ ฀ + ฀฀)(฀฀ − ฀฀) ฀฀2 + 2฀฀฀฀ + ฀฀ 2 = (฀ ฀ + ฀฀)2 ฀฀2 − 2฀฀฀฀ + ฀฀ 2 = (฀฀ − ฀฀)2

For a right triangle with legs of length ฀฀ and ฀฀ and hypotenuse of length ฀฀, ฀฀2 + ฀฀ 2 = ฀฀ 2 . Area Formulas Area of a square with side length ฀฀: ฀ ฀ = ฀฀ 2 Area of a rectangle with length ฀฀ and width ฀฀: ฀ ฀ = ฀฀฀฀ 1

Area of a triangle with base ฀฀ and height ℎ: ฀ ฀ =2 ฀฀ℎ

MATH 1301 Contemporary Mathematics Formula Pages Percent Change

Probability Facts

new − old × 100 old

The probability of an event that cannot occur is 0. The probability of an event that must occur is 1. Every probability must be a number between 0 and 1 inclusively; that is, 0 ≤ P (E ) ≤ 1 .

Simple Interest Formula

i = prt

The sum of the probabilities of all possible outcomes of

Compound Interest Formula nt

 r A = p1 +   n

/ an event is 1. P( A) + P ( A ) = 1

Standard 52-card Deck

Present Value Formula

p=

A nt r  1 +   n

Installment Payment Formula

r p  n  m= −nt r 1 − 1 +   n

Odds

Actuarial Method

u=

n ⋅ P ⋅V , where u is the unearned interest, n is 100 + V

the number of remaining payments (excluding the current payment), P is the monthly payment, and V is the value from the APR table that corresponds to the APR for the number of remaining payments (excluding the current payment). Ordinary Annuity Formula

  r nt  p   1 +  − 1   n  A=  r n Sinking Fund Payment Formula

r A   n (Round UP to the next cent) p= nt   r   1 +  − 1    n 

Standard Divisor and Standard Quota

MATH 1301 Contemporary Mathematics Formula Pages

Days in Each Month Day of Month

31

28

31

30

31

30

31

31

30

31

30

31

Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

Day 1

1

32

60

91

121

152

182

213

244

274

305

335

Day 2

2

33

61

92

122

153

183

214

245

275

306

336

Day 3

3

34

62

93

123

154

184

215

246

276

307

337

Day 4

4

35

63

94

124

155

185

216

247

277

308

338

Day 5

5

36

64

95

125

156

186

217

248

278

309

339

Day 6

6

37

65

96

126

157

187

218

249

279

310

340

Day 7

7

38

66

97

127

158

188

219

250

280

311

341

Day 8

8

39

67

98

128

159

189

220

251

281

312

342

Day 9

9

40

68

99

129

160

190

221

252

282

313

343

Day 10

10

41

69

100

130

161

191

222

253

283

314

344

Day 11

11

42

70

101

131

162

192

223

254

284

315

345

Day 12

12

43

71

102

132

163

193

224

255

285

316

346

Day 13

13

44

72

103

133

164

194

225

256

286

317

347

Day 14

14

45

73

104

134

165

195

226

257

287

318

348

Day 15

15

46

74

105

135

166

196

227

258

288

319

349

Day 16

16

47

75

106

136

167

197

228

259

289

320

350

Day 17

17

48

76

107

137

168

198

229

260

290

321

351

Day 18

18

49

77

108

138

169

199

230

261

291

322

352

Day 19

19

50

78

109

139

170

200

231

262

292

323

353

Day 20

20

51

79

110

140

171

201

232

263

293

324

354

Day 21

21

52

80

111

141

172

202

233

264

294

325

355

Day 22

22

53

81

112

142

173

203

234

265

295

326

356

Day 23

23

54

82

113

143

174

204

235

266

296

327

357

Day 24

24

55

83

114

144

175

205

236

267

297

328

358

Day 25

25

56

84

115

145

176

206

237

268

298

329

359

Day 26

26

57

85

116

146

177

207

238

269

299

330

360

Day 27

27

58

86

117

147

178

208

239

270

300

331

361

Day 28

28

59

87

118

148

179

209

240

271

301

332

362

Day 29

29

88

119

159

180

210

241

272

302

333

363

Day 30

30

89

120

150

181

211

242

273

303

334

364

Day 31

31

90

212

243

151

304

365

MATH 1301 Contemporary Mathematics Formula Pages

Monthly Principal and Interest Payment (per $1000 of mortgage) Rate %

Number of Years 20

10

15

25

30

4.0

$10.12451

$7.39688

$6.05980

$5.27837

$4.77415

4.5

10.36384

7.64993

6.32649

5.55832

5.06685

5.0

10.60655

7.90794

6.59956

5.84590

5.36822

5.5

10.85263

8.17083

6.87887

6.14087

5.67789

6.0

11.10205

8.43857

7.16431

6.44301

5.99551

6.5

11.35480

8.71107

7.45573

6.75207

6.32068

7.0

11.61085

8.98828

7.75299

7.06779

6.65302

7.5

11.87018

9.27012

8.05593

7.38991

6.99215

8.0

12.13276

9.55652

8.36440

7.71816

7.33765

8.5

12.39857

9.84740

8.67823

8.05227

7.68913

9.0

12.66758

10.14267

8.99726

8.39196

8.04623

9.5

12.93976

10.44225

9.32131

8.73697

8.40854

10.0

13.21507

10.74605

9.65022

9.08701

8.77572

10.5

13.49350

11.05399

9.98380

9.44182

9.14739

11.0

13.77500

11.36597

10.32188

9.80113

9.52323

11.5

14.05954

11.68190

10.66430

10.16469

9.90291

12.0

14.34709

12.00168

11.01086

10.53224

10.28613

Number of 4.0% payments

Annual Percentage Rate 4.5%

5.0%

5.5%

6.0%

6.5%

7.0%

7.5%

8.0%

8.5%

9.0%

9.5%

10.0%

(Finance charge per $100 of amount financed)

6

1.17

1.32

1.46

1.61

1.76

1.90

2.05

2.20

2.35

2.49

2.64

2.79

2.93

12

2.18

2.45

2.73

3.00

3.28

3.56

3.83

4.11

4.39

4.66

4.94

5.22

5.50

18

3.20

3.60

4.00

4.41

4.82

5.22

5.63

6.04

6.45

6.86

7.28

7.69

8.10

24

4.22

4.75

5.29

5.83

6.37

6.91

7.45

8.00

8.54

9.09

9.64

10.19

10.75

30

5.25

5.92

6.59

7.26

7.94

8.61

9.30

9.98

10.66

11.35

12.04

12.74

13.43

36

6.29

7.09

7.90

8.71

9.52

10.34

11.16

11.98

12.81

13.64

14.48

15.32

16.16

48

8.38

9.46

10.54

11.63

12.73

13.83

14.94

16.06

17.18

18.31

19.45

20.59

21.74

60

10.50

11.86

13.23

14.61

16.00

17.40

18.81

20.23

21.66

23.10

24.55

26.01

27.48

MATH 1301 Contemporary Mathematics Formula Pages

Customary to Metric Units Length 1 inch (in.) 1 foot (ft) 1 yard (yd) 1 mile (mi)

Customary Units = 2.54 centimeters (cm) = 30 centimeters (cm) = 0.9 meter (m) = 1.6 kilometers (km)

Area 1 square inch (in.2) 1 square foot (ft2) 1 square yard (yd2) 1 square mile (mi2) 1 acre

= 6.5 square centimeters (cm2) = 0.09 square meter (m2) = 0.8 square meter (m2) = 2.6 square kilometers (km2) = 0.4 hectare (ha)

Volume 1 teaspoon (tsp) 1 tablespoon (tbsp) 1 fluid ounce (fl oz) 1 cup (c) 1 pint (pt) 1 quart (qt) 1 gallon (gal) 1 cubic foot (ft3) 1 cubic yard (yd3)

= 5 milliliters (mℓ) = 15 milliliters (mℓ) = 30 milliliters (mℓ) = 0.24 liter (ℓ) = 0.47 liter (ℓ) = 0.95 liter (ℓ) = 3.8 liters (ℓ) = 0.03 cubic meter (m3) = 0.76 cubic meter (m3)

Weight (Mass) 1 ounce (oz) 1 pound (lb) 1 ton (T)

= 28 grams (g) = 0.45 kilogram (kg) = 0.9 tonne (t)

1 foot 1 yard 1 mile 1 pound 1 ton 1 cup (liquid) 1 pint 1 quart 1 gallon 1 minute 1 hour 1 day 1 year

= 12 inches = 3 feet = 5280 feet = 16 ounces = 2000 pounds = 8 fluid ounces = 2 cups = 2 pints = 4 quarts = 60 seconds = 60 minutes = 24 hours = 365 days

MATH 1301 Contemporary Mathematics Formula Pages Voting and Apportionment...