Escuela

Alt Codes for typing Spanish characters:

Capitals Á ALT + 0193 É ALT + 0201 Í ALT + 0205 Ó ALT + 0211 Ú ALT + 0218 Ñ ALT + 0209 Ü ALT + 0220

Lowercase á ALT + 0225 é ALT + 0233 í ALT + 0237 ó ALT + 0243 ú ALT + 0250 ñ ALT + 0241 ü ALT + 0252

Punctuation ¿ ALT + 0191 ¡ ALT + 0161 « ALT + 0171 (Left Angle Quote) » ALT + 0187 (Right Angle Quote) € ALT + 0128

Los Verbos Regulars

-ar ayudar to help bailar to dance besar to kiss buscar to look for caminar to walk comprar to buy conversar to converse enseñar to teach escuchar to listen estudiar to study hablar to speak llegar to arrive mirar to look at nadar to swim necesitar to need preparar to prepare regresar to return tomar to take; to drink trabajar to work viajar to travel

-er aprender to learn beber to drink comer to eat creer to believe leer to read vender to sell comprender to understand

-ir abrir to open asistir to attend decidir to decide escribir to write recibir to receive vivir to live

Las Conjugacións

-ar Singular yo -o tú -as él/ella/usted -a Plural nosotros -amos ellos/ellas/ustedes -an

-er Singular yo -o tú -es él/ella/usted -e Plural nosotros -emos ellos/ellas/ustedes -en

-ir Singular yo -o tú -es él/ella/usted -e Plural nosotros -imos ellos/ellas/ustedes -en

Mathematical Symbols

Fractions ¼ ALT + 0188 ½ ALT + 0189 ¾ ALT + 0190	Exponents ± ALT + 241 √ ALT + 251 ⁿ ALT + 252 ¹ ALT + 0185 ² ALT + 0178 ³ ALT + 0179	Inequality ≈ ALT + 247 < ALT + 60 > ALT + 62 ≥ ALT + 242 ≤ ALT + 243	Greek Symbols π ALT + 227 Σ ALT + 228 µ ALT + 230 δ ALT + 235 ⌂ ALT + 127
Sundry ∞ ALT + 236 ∩ ALT + 239 ° ALT + 248

Formulas:

Lines General Form ax + by = c Point Slope y – y1 = m (x – x1) Slope Intercept y = mx + b

Circles Standard Form (x – h)2 + (y – k)2 = r2 General Form x2 + y2 + ax + by + c = 0

More Formulas:

Stuff d (P1, P2) d = √((x2 – x2)2 + (y1 – y2)2) Midpoint (Mx = (X1 + X2) / 2 , My = (Y1 + Y2) / 2) Slope or Average Rate of Change (A.R.M.) m = ⌂y / ⌂x OR m = rise / run OR m = (y2 – y1) / (x2 – x1) Difference Quotient: Slope in function notation m = ⌂y / ⌂x OR m = (f(x + h) – f(x))/h OR m = (y2 – y1) / (x2 – x1)

Completing the square:

Stuff Given x2 + bx + c = 0 Move Constant to RHS: x2 + bx = -c Find (b/2)2 and add to both sides: x2 + bx + (b/2)2 = -c + (b/2)2 This is now a perfect Square Trinomial: Factor it. (x +b/2)2 = -c + (b/2)2 Example: x2 + y2 – 6x + 2y + 9 = 0 Move Constant to RHS: x2 – 6x + ___ + y2 + 2y + ___= -9 + ___ + ___ Find (b/2)2… x –> (b/2)2 = (-6/2)2 = (-3)2 = 9 y –> (b/2)2 = (2/2)2 = (1)2 = 1 …and add to both sides: x2 – 6x + 9 + y2 + 2y + 1 = -9 + 9 + 1 This is now two perfect Square Trinomials: Factor them. (x – 3)2 + (y + 1)2 = 1