MATEMÁTICAS SECUNDARIA

N Ú M E R O S : Nº * * ROM. * LETRA ==== . ===== . ========== 9 * * * [blank_start]IX[blank_end] * * * [blank_start]nueve[blank_end] 15 * * [blank_start]XV[blank_end] * * * [blank_start]quince[blank_end] 23 * * [blank_start]XXIII[blank_end] * * [blank_start]veintitrés[blank_end] 46 * * [blank_start]XLVI[blank_end] * * [blank_start]cuarenta y seis[blank_end] 94 * * [blank_start]XCIV[blank_end] * * [blank_start]noventa y cuatro[blank_end] 160 * [blank_start]CLX[blank_end] * * * [blank_start]ciento sesenta[blank_end] 450 * [blank_start]CDL[blank_end] * * * [blank_start]cuatrocientos cincuenta[blank_end] 509 * [blank_start]DIX[blank_end] * * * [blank_start]quinientos nueve[blank_end] 904 * [blank_start]CMIV[blank_end] * * [blank_start]novecientos cuatro[blank_end]

SUMA o [blank_start]ADICIÓN[blank_end]: . . . . . . . . . . . . . . MULTIPLICACIÓN: . . . . . . . . . . POTENCIA: Operandos: [blank_start]SUMANDOS[blank_end] . . . . . . . . Operandos: [blank_start]FACTORES[blank_end] . . . . . .Operando: [blank_start]BASE[blank_end] Resultado: SUMA o [blank_start]TOTAL[blank_end] . . . . . . Resultado: [blank_start]PRODUCTO[blank_end] . . . . . . Repetición: [blank_start]EXPONENTE[blank_end] RESTA o [blank_start]SUSTRACCIÓN[blank_end]: . . . . . . . . DIVISIÓN: . . . . . . . . . . . . . . . . . . RAÍZ [blank_start]CUADRADA[blank_end]: Operando 1º: [blank_start]MINUENDO[blank_end] . . . . . . Operando 1º: [blank_start]DIVIDENDO[blank_end] . . . . Símbolo: [blank_start]RADICAL[blank_end] Operando 2º: [blank_start]SUSTRAENDO[blank_end] . . . . Operando 2º: [blank_start]DIVISOR[blank_end] . . . . . . . Operando: [blank_start]RADICANDO[blank_end] Resultado: [blank_start]DIFERENCIA[blank_end] . . . . . . . . Resultado: [blank_start]COCIENTE[blank_end] . . . . . . . . Resultado: [blank_start]RAÍZ[blank_end] . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sobrante: [blank_start]RESTO[blank_end]

DIVISIÓN con sus TÉRMINOS... . =[blank_start]Dividendo[blank_end] 1. 3 5 9 . . . . . . |_5______=[blank_start]Divisor[blank_end] . .[blank_start]3[blank_end].[blank_start]5[blank_end] . . . . . . . [blank_start]2[blank_end].[blank_start]7[blank_end].[blank_start]1[blank_end] . =[blank_start]Cociente[blank_end] . . . [blank_start]0[blank_end].[blank_start]9[blank_end] . . . . . [blank_start]4[blank_end] . . =[blank_start]Resto[blank_end]

CÁLCULOS con [ 3, 5 y 7] ... ========================= 1 = 5 + [blank_start]3[blank_end] – [blank_start]7[blank_end] . . . . 1 = [blank_start]3[blank_end] – ([blank_start]7[blank_end] – 5) 1 = 5 – ([blank_start]7[blank_end] – [blank_start]3[blank_end]) . . . 2 = ([blank_start]7[blank_end] + 3) / [blank_start]5[blank_end] 4 = ([blank_start]7[blank_end] + 5) / [blank_start]3[blank_end] . . . 5 = 7 – ([blank_start]5[blank_end] – [blank_start]3[blank_end]) 5 = 3 + [blank_start]7[blank_end] – [blank_start]5[blank_end] . . . . 6 = [blank_start]3[blank_end] x ([blank_start]7[blank_end] – 5) 8 = 3 x [blank_start]5[blank_end] – [blank_start]7[blank_end] . . . . 9 = [blank_start]5[blank_end] + 7 – [blank_start]3[blank_end] 14 = ([blank_start]5[blank_end] – 3) x [blank_start]7[blank_end] . . 15 = 3 + [blank_start]5[blank_end] + 7 20 = ([blank_start]7[blank_end] – 3) x [blank_start]5[blank_end] . . 22 = 3 x [blank_start]5[blank_end] + [blank_start]7[blank_end] 26 = 3 x [blank_start]7[blank_end] + [blank_start]5[blank_end] . . . 32 = [blank_start]7[blank_end] x 5 – [blank_start]3[blank_end] 36 = (5 + [blank_start]7[blank_end]) x [blank_start]3[blank_end] . . 38 = [blank_start]7[blank_end] x 5 + [blank_start]3[blank_end] 50 = ([blank_start]3[blank_end] + 7) x [blank_start]5[blank_end] . . 56 = (5 + [blank_start]3[blank_end]) x [blank_start]7[blank_end] 56 = [blank_start]7[blank_end] x ([blank_start]5[blank_end] + 3) . . 105 = 3 x 5 x [blank_start]7[blank_end]

CÁLCULOS con [1, 3, 5 y 7] ====================== [blank_start](7+3)/5-1[blank_end]= 1 * * * [blank_start](5x3-1)/7[blank_end]= 2 [blank_start](7+5)/3-1[blank_end]= 3 * * * [blank_start](7x3-1)/5[blank_end]= 4 [blank_start](7-5)x3-1[blank_end]= 5 * * * [blank_start](7+5)/(3-1)[blank_end]= 6 [blank_start](7-5)x3+1[blank_end]= 7 * * * [blank_start]7+5-1-3[blank_end]= 8 [blank_start](7+1-5)x3[blank_end]= 9 * * *[blank_start]7+5-3+1[blank_end]= 10 [blank_start](5+1)x3-7[blank_end]= 11 * * [blank_start](7x5+1)/3[blank_end]= 12 [blank_start]5x(3+1)-7[blank_end]= 13 * * [blank_start](5+1)/3x7[blank_end]= 14 [blank_start]3x7-1-5[blank_end]= 15 * * * [blank_start]3+7+1+5[blank_end]= 16

EXPRESIONES ARITMÉTICAS... ======================== Doble de la diferencia de 7 y 3 => 2x([blank_start]7-3[blank_end]) = [blank_start]8[blank_end] Mitad de la suma de 3 y 5 => ([blank_start]3+5[blank_end])/2 = [blank_start]4[blank_end] Doble de 7, menos 5 => [blank_start]2x7[blank_end]-5 = [blank_start]9[blank_end] Mitad de 8 por 3 => [blank_start]8/2x3[blank_end] = [blank_start]12[blank_end] Suma de 7 y el doble de 4 => [blank_start]7+2x4[blank_end] = [blank_start]15[blank_end] Diferencia del doble de 3 y 1 => [blank_start]2x3-1[blank_end] = [blank_start]5[blank_end] Doble de la suma de 3 y 5 => [blank_start]2x(3+5)[blank_end] = [blank_start]16[blank_end] Mitad de la diferencia de 7 y 3 => [blank_start](7-3)/2[blank_end] = [blank_start]2[blank_end] Triple de la mitad de 6 => [blank_start]3x6/2[blank_end] =[blank_start]9[blank_end]

POTENCIAS ...

POTENCIAS: ========== 2³·3²·5² / (6·9·10) = = 2³·3²·5² / (2·[blank_start]3[blank_end]·3·[blank_start]3[blank_end]·2·[blank_start]5[blank_end]) = = 2³·3²·5² / ([blank_start]2[blank_end]²·[blank_start]3[blank_end]³·[blank_start]5[blank_end]) = = [blank_start]2[blank_end]·[blank_start]5[blank_end]/[blank_start]3[blank_end] = [blank_start]10[blank_end]/[blank_start]3[blank_end] = [blank_start]3[blank_end],3...

RAÍZ CUADRADA...

CÁLCULO MENTAL de 1 a 10 ... =========================== 1 = [blank_start]2³–(3+4)[blank_end] * * * * 2 = [blank_start](5+3)/4[blank_end] 3 = [blank_start]√[5+4][blank_end] * * * * * 4 = [blank_start](10/5)²[blank_end] 5 = [blank_start]3²–4[blank_end] * * * * * * 6 = [blank_start](2²–1)x2[blank_end] 7 = [blank_start](3²+5)/2[blank_end] * * * * 8 = [blank_start]5x3–7[blank_end] 9 = [blank_start]3+√[9x4][blank_end] * 10 = [blank_start]4+2x√[2+7][blank_end]

NÚMEROS DECIMALES...

FRACCIONES: Parte COLOREADA de cada DIBUJO ...

. . . . . . . . . FRACCIONES . . . . . . . . . . . 2/3 de 21 = [blank_start]14[blank_end] . . . 2/5 de 30 = [blank_start]12[blank_end] 1/2 de 32 = [blank_start]16[blank_end] . . . 5/6 de 24 = [blank_start]20[blank_end] 3/5 de 45 = [blank_start]27[blank_end] . . . 3/7 de 49 = [blank_start]21[blank_end] 1/6 de 42 = [blank_start]7[blank_end] . . . . 1/4 de 60 = [blank_start]15[blank_end] 5/7 de 42 = [blank_start]30[blank_end] . . . 4/5 de 40 = [blank_start]32[blank_end] 3/4 de 100=[blank_start]75[blank_end] . . . 1/3 de 18 = [blank_start]6[blank_end] 1/3 de 27 = [blank_start]9[blank_end] . . . . 2/7 de 28 = [blank_start]8[blank_end]

MAYOR (>) o MENOR (<) 1/2 [blank_start]>[blank_end] 2/5 . . . 1/4 [blank_start]<[blank_end] 2/7 2/3 [blank_start]<[blank_end] 3/4 . . . 2/3 [blank_start]>[blank_end] 4/7 3/5 [blank_start]>[blank_end] 4/7 . . . 1/3 [blank_start]<[blank_end] 2/5 2/3 [blank_start]<[blank_end] 5/7 . . . 2/5 [blank_start]<[blank_end] 3/7 1/2 [blank_start]<[blank_end] 4/7 . . . 3/4 [blank_start]>[blank_end] 5/7 2/3 [blank_start]>[blank_end] 3/5 . . . 3/4 [blank_start]<[blank_end] 4/5 1/2 [blank_start]<[blank_end] 3/5 . . . 4/5 [blank_start]>[blank_end] 5/7

FRACCIÓN a DECIMAL ... ===================== 3/4 = [blank_start]0,75[blank_end] . . . 3/2 = [blank_start]1,5[blank_end] 1/2 = [blank_start]0,5[blank_end] . . . . 5/2 = [blank_start]2,5[blank_end] 1/4 = [blank_start]0,25[blank_end] . . . 5/4 = [blank_start]1,25[blank_end] 1/5 = [blank_start]0,2[blank_end] . . . . 7/2 = [blank_start]3,5[blank_end] 1/8 = [blank_start]0,125[blank_end] . . 7/4 = [blank_start]1.75[blank_end] 2/5 = [blank_start]0,4[blank_end] . . . . 7/5 = [blank_start]1,4[blank_end] 3/5 = [blank_start]0,6[blank_end] . . . . 8/5 = [blank_start]1,6[blank_end] 3/8 = [blank_start]0,375[blank_end] . . 9/2 = [blank_start]4,5[blank_end] 4/5 = [blank_start]0,8[blank_end] . . . . 9/4 = [blank_start]2,25[blank_end] 5/8 = [blank_start]0,625[blank_end] . . 9/5 = [blank_start]1,8[blank_end] 7/8 = [blank_start]0,875[blank_end] . . 9/8 = [blank_start]1,125[blank_end]

SUMA y RESTA: ============= \(\frac{2}{3} + \frac{3}{5}\ – \frac{3}{4}\) = = (2x[blank_start]5x4[blank_end] + 3x[blank_start]3x4[blank_end] – 3x[blank_start]3x5[blank_end]) / (3x[blank_start]5x4[blank_end]) = = (40+[blank_start]36[blank_end]–[blank_start]45[blank_end]) / [blank_start]60[blank_end] = [blank_start]31/60[blank_end] MULTIPLICACIÓN y DIVISIÓN: ======================== \(\frac{2}{3}\)x\(\frac{1}{5}\) = 2x1 / [blank_start]3x5[blank_end] = [blank_start]2/15[blank_end] \(\frac{1}{3}:\frac{3}{5}\) = 1/3 x [blank_start]5/3[blank_end] = 1x5 / [blank_start]3x3[blank_end] = [blank_start]5/9[blank_end]

a * * b * * * a+b * * * a–b * * * a·b * * * a:b == * === * ===== * ====== * ===== * ====== -2 * +5 * * [blank_start]+3[blank_end] * * * * [blank_start]-7[blank_end] * * * [blank_start]-10[blank_end] * * * [blank_start]-0,4[blank_end] +3 * -2 * * [blank_start]+1[blank_end] * * * [blank_start]+5[blank_end] * * * * [blank_start]-6[blank_end] * * * [blank_start]-1,5[blank_end] +5 * +4 * * [blank_start]+9[blank_end] * * * [blank_start]+1[blank_end] * * * [blank_start]+20[blank_end] * * [blank_start]+1,25[blank_end] -1 * -3 * * * [blank_start]-4[blank_end] * * * [blank_start]+2[blank_end] * * * [blank_start]+3[blank_end] * * * [blank_start]+0,3[blank_end]3

CÁLCULOS... ========== 6,7 x \(10^{-2}\) = [blank_start]0,067[blank_end] . . . . 2\(\frac{3}{4}\) = [blank_start]11/4[blank_end] \(\pi\) = [blank_start]3,14[blank_end] . . . . . 3\(\frac{1}{2}\) = [blank_start]7/2[blank_end] 9 – 5 = [blank_start]4[blank_end] . . . . . . \(\sqrt {16}\) = [blank_start]4[blank_end] \(\sqrt {36}\) = [blank_start]6[blank_end] . . . . . 3 x 2 = [blank_start]6[blank_end] \(\sqrt {49}\) = [blank_start]7[blank_end] . . . . . . \(2^3\) = [blank_start]8[blank_end] \(3^2\) = [blank_start]9[blank_end] . . . . . . . \(\sqrt {81}\) = [blank_start]9[blank_end] \(\frac{3}{5}\) de 20 = [blank_start]12[blank_end] . . . . . 7 + 5 = [blank_start]12[blank_end] \(\frac{2}{3}\) de 21 = [blank_start]14[blank_end] . . . \(\frac{1}{2}\) de 28 = [blank_start]14[blank_end] \(5^2\) = [blank_start]25[blank_end] . . . . . \(3^3\) = [blank_start]27[blank_end] \(2^5\) = [blank_start]32[blank_end] . . . . . \(\frac{3}{4}\) de 60 = [blank_start]45[blank_end] \(3^4\) = [blank_start]81[blank_end] . . . . \(5^3\) = [blank_start]125[blank_end] \(10^3\) = [blank_start]1.000[blank_end] . . . 2,07 x \(10^3\) = [blank_start]2.070[blank_end] \(\overline{X I V}\) = [blank_start]14.000[blank_end]

Descomposición FACTORIAL ... =========================== 4. 6 2 0 | [blank_start]2[blank_end] * * * * * 9. 4 5 0 | [blank_start]2[blank_end] 2. 3 1 0 | [blank_start]2[blank_end] * * * * * 4. 7 2 5 | [blank_start]3[blank_end] 1. 1 5 5 | [blank_start]3[blank_end] * * * * * 1. 5 7 5 | [blank_start]3[blank_end] * 3 8 5 | [blank_start]5[blank_end] * * * * * * 5 2 5 | [blank_start]3[blank_end] * * 7 7 | [blank_start]7[blank_end] * * * * * * 1 7 5 | [blank_start]5[blank_end] * * 1 1 | [blank_start]11[blank_end] * * * * * * 3 5 | [blank_start]5[blank_end] * * * 1 | * * * * * * * * * 7 | [blank_start]7[blank_end] * [blank_start]2[blank_end]² x [blank_start]3[blank_end] x [blank_start]5[blank_end] x [blank_start]7[blank_end] x [blank_start]11[blank_end] * * * 1 | * * * * * * * * * * [blank_start]2[blank_end] x [blank_start]3[blank_end]³ x [blank_start]5[blank_end]² x [blank_start]7[blank_end]

Descomposición FACTORIAL ... =========================== 3. 5 2 8 | [blank_start]2[blank_end] * * * * * 9. 4 5 0 | [blank_start]2[blank_end] * 1. [blank_start]764[blank_end] | [blank_start]2[blank_end] * * * * * 4. [blank_start]725[blank_end] | [blank_start]3[blank_end] * * [blank_start]882[blank_end] | [blank_start]2[blank_end] * * * * * *1. [blank_start]575[blank_end] | [blank_start]3[blank_end] * * [blank_start]441[blank_end] | [blank_start]3[blank_end] * * * * * * * [blank_start]525[blank_end] | [blank_start]3[blank_end] * * [blank_start]147[blank_end] | [blank_start]3[blank_end] * * * * * * * [blank_start]175[blank_end] | [blank_start]5[blank_end] * * *[blank_start]49[blank_end] | [blank_start]7[blank_end] * * * * * * * *[blank_start]35[blank_end] | [blank_start]5[blank_end] * * * *[blank_start]7[blank_end] | [blank_start]7[blank_end] * * * * * * * * [blank_start]7[blank_end] | [blank_start]7[blank_end] 3.528 = [blank_start]2[blank_end]³ x [blank_start]3[blank_end]² x [blank_start]7[blank_end]² 9.450 = [blank_start]2[blank_end] x [blank_start]3[blank_end]³ x [blank_start]5[blank_end]² x [blank_start]7[blank_end]

DESCOMPOSICIÓN en FACTORES PRIMOS... ================== 90 = [blank_start]2 · 3² · 5[blank_end] 100 = [blank_start]2² · 5²[blank_end] 120 = [blank_start]2³ · 3 · 5[blank_end] 150 = [blank_start]2 · 3 · 5²[blank_end] 180 = [blank_start]2² · 3² · 5[blank_end] 200 = [blank_start]2³ · 5²[blank_end] 225 = [blank_start]3² · 5²[blank_end] 250 = [blank_start]2 · 5³[blank_end]

DESCOMPOSICIÓN en FACTORES PRIMOS. … … … … [^=elevado a] ... ================================== 30 = 2^[blank_start]1[blank_end] x 3^[blank_start]1[blank_end] x 5^[blank_start]1[blank_end] x 7^[blank_start]0[blank_end] 32 = 2^[blank_start]5[blank_end] x 3^[blank_start]0[blank_end] x 5^[blank_start]0[blank_end] x 7^[blank_start]0[blank_end] 35 = 2^[blank_start]0[blank_end] x 3^[blank_start]0[blank_end] x 5^[blank_start]1[blank_end] x 7^[blank_start]1[blank_end] 40 = 2^[blank_start]3[blank_end] x 3^[blank_start]0[blank_end] x 5^[blank_start]1[blank_end] x 7^[blank_start]0[blank_end] 42 = 2^[blank_start]1[blank_end] x 3^[blank_start]1[blank_end] x 5^[blank_start]0[blank_end] x 7^[blank_start]1[blank_end] 45 = 2^[blank_start]0[blank_end] x 3^[blank_start]2[blank_end] x 5^[blank_start]1[blank_end] x 7^[blank_start]0[blank_end] 50 = 2^[blank_start]1[blank_end] x 3^[blank_start]0[blank_end] x 5^[blank_start]2[blank_end] x 7^[blank_start]0[blank_end] 54 = 2^[blank_start]1[blank_end] x 3^[blank_start]3[blank_end] x 5^[blank_start]0[blank_end] x 7^[blank_start]0[blank_end] 56 = 2^[blank_start]3[blank_end] x 3^[blank_start]0[blank_end] x 5^[blank_start]0[blank_end] x 7^[blank_start]1[blank_end] 60 = 2^[blank_start]2[blank_end] x 3^[blank_start]1[blank_end] x 5^[blank_start]1[blank_end] x 7^[blank_start]0[blank_end]

SISTEMA MÉTRICO DECIMAL... MEDIDA . . . . . EQUIV. . UNIDAD . . . ABREV. ========== ====== ========== ===== 2,074 metros = . 207,4 . [blank_start]centímetros[blank_end] . ([blank_start]cm[blank_end]) 2.074 metros = . 2,074 . [blank_start]kilómetros[blank_end] . . ([blank_start]km[blank_end]) 20,74 metros = . 2,074 . [blank_start]decámetros[blank_end] . ([blank_start]dam[blank_end]) 2,074 metros = . 2.074 . [blank_start]milímetros[blank_end] . . ([blank_start]mm[blank_end]) 207,4 metros = . 2,074 . [blank_start]hectómetros[blank_end] . ([blank_start]hm[blank_end]) 6.193 litros = . . .61,93 . [blank_start]hectolitros[blank_end] . . . ([blank_start]hl[blank_end]) 61,93 litros = . . .619,3 . [blank_start]decilitros[blank_end] . . . . ([blank_start]dl[blank_end]) 61,93 litros = . . .6.193 . [blank_start]centilitros[blank_end] . . . .([blank_start]cl[blank_end]) 528,7 gramos = 52,87 . [blank_start]decagramos[blank_end] . ([blank_start]dag[blank_end]) 52,87 kilos = . . .52.870 . [blank_start]gramos[blank_end] . . . . ([blank_start]g[blank_end]) 528,7 kilos = . . 5.287 . [blank_start]hectogramos[blank_end] . ([blank_start]hg[blank_end]) 5.287 kilos = . . 5,287 . [blank_start]toneladas[blank_end]. . . . ([blank_start]t[blank_end])

Las 2 y cuarto de la noche = . . . . . . . . . [blank_start]02:15[blank_end] Las 4 y media de la noche = . . . . . . . . . [blank_start]04:30[blank_end] Las 7 menos cuarto de la noche = . . . . [blank_start]06:45[blank_end] Las 9 y diez de la mañana = . . . . . . . . . .[blank_start]09:10[blank_end] Las 11 menos veinte de la mañana = . [blank_start]10:40[blank_end] Las 12 y cinco de la mañana = . . . . . . . [blank_start]12:05[blank_end] Las 2 y media de la tarde = . . . . . . . . . .[blank_start]14:30[blank_end] Las 5 menos diez de la tarde = . . . . . . [blank_start]16:50[blank_end] Las 6 y cinco de la tarde = . . . . . . . . . . [blank_start]18:05[blank_end] Las 7 y cuarto de la tarde = . . . . . . . . . [blank_start]19:15[blank_end] Las 11 menos cuarto de la noche = . . [blank_start]22:45[blank_end] Las 12 y veinte de la noche = . . . . . . . .[blank_start]00:20[blank_end]

RECTAS y ÁNGULOS...

CIRCUNFERENCIA y CÍRCULO: Elementos...

FIGURAS GEOMÉTRICAS...

ÁREAS de FIGURAS PLANAS * Fórmula de Herón ...

TEOREMA de PITÁGORAS ... ========================= Aplicación a triángulos [blank_start]rectángulos[blank_end]. La suma de los tres ángulos de un triángulo es [blank_start]180[blank_end]º. Los ángulos agudos son [blank_start]complementarios[blank_end] (suman 90º). Lados del ángulo recto: [blank_start]catetos[blank_end]. Lado opuesto al ángulo recto: [blank_start]hipotenusa[blank_end] ENUNCIADO: "La suma de los cuadrados de los [blank_start]catetos[blank_end] es igual al cuadrado de la [blank_start]hipotenusa[blank_end]". TEOREMA del CATETO: "El cuadrado de cada [blank_start]cateto[blank_end] es igual al producto de su proyección por la [blank_start]hipotenusa[blank_end]". TEOREMA de la ALTURA: "El cuadrado de la [blank_start]altura[blank_end] es igual al producto de las proyecciones de los [blank_start]catetos[blank_end]".

TEOREMA de TALES...

PLANO CARTESIANO...

… ... … [ y = 2x – 3 ] . [ y = x² + 3x – 5 ] . [ y = x³+2x²–3x–1 ] … … … ========= . ============= . =============== x=–2 => . . y= [blank_start]-7[blank_end] . . . . . . . y= [blank_start]-7[blank_end] . . . . . . . . . . y= [blank_start]5[blank_end] x=–1 => . . y= [blank_start]-5[blank_end] . . . . . . . y= [blank_start]-7[blank_end] . . . . . . . . . . y= [blank_start]3[blank_end] x=0 => . . . y= [blank_start]-3[blank_end] . . . . . . . y= [blank_start]-5[blank_end] . . . . . . . . . . y= [blank_start]-1[blank_end] x=1 => . . . y= [blank_start]-1[blank_end] . . . . . . . y= [blank_start]-1[blank_end] . . . . . . . . . . y= [blank_start]-1[blank_end] x=2 => . . . y= [blank_start]1[blank_end] . . . . . . . y= [blank_start]5[blank_end] . . . . . . . . . . . y= [blank_start]9[blank_end]

ÁLGEBRA. ECUACIONES ... ======================= [ 2x – 3 = 5 ] 2x = 5 + [blank_start]3[blank_end] // x = [blank_start]8[blank_end] / 2 // x = [blank_start]4[blank_end] . . . [ 3x – 1 = x + 9 ] 3x – [blank_start]x[blank_end] = 9 + [blank_start]1[blank_end] // [blank_start]2[blank_end]x = [blank_start]10[blank_end] x = 10 / [blank_start]2[blank_end] // x = [blank_start]5[blank_end] . . . [ 5 – x = 2 ] 5 – [blank_start]2[blank_end] = [blank_start]x[blank_end] // [blank_start]3[blank_end] = x . . . [ \(\frac {3x−1}{5}\) = 4 ] 3x – 1 = 4 · [blank_start]5[blank_end] // 3x = [blank_start]20[blank_end] + 1 x = 21 / [blank_start]3[blank_end] // x = [blank_start]7[blank_end] . . . [ \(\frac {3x}{2}\) + 4 = 7 ] . (Dos FORMAS): 3x + 4·[blank_start]2[blank_end] = 7·[blank_start]2[blank_end] . . . . . \(\frac {3x}{2}\) = 7 – [blank_start]4[blank_end] 3x = [blank_start]14[blank_end] – [blank_start]8[blank_end] . . . . . . . . 3x = [blank_start]3[blank_end] · [blank_start]2[blank_end] x = [blank_start]6[blank_end] / 3 . . . . . . . . . . 3x = [blank_start]6[blank_end] x = [blank_start]2[blank_end] . . . . . . . . . . . . x = 6 / [blank_start]3[blank_end] = [blank_start]2[blank_end] [ \(\frac {2x–1}{3}\) + \(\frac {x}{2}\) = 9 ] [blank_start]2[blank_end]· (2x–1) + [blank_start]3[blank_end] · x = 9 · [blank_start]6[blank_end] 4x – 2 + [blank_start]3x[blank_end] = [blank_start]54[blank_end] [blank_start]7x[blank_end] = 54 + 2 // x = 56 / [blank_start]7[blank_end] = [blank_start]8[blank_end]

EXPRESIONES ALGEBRAICAS... ========================= Diagonal del cuadrado de lado 'x' => [blank_start]x[blank_end] · \(\sqrt{2}\) Diagonal del rectángulo de lados 'x' 'y' => V¯([blank_start]x[blank_end]²+[blank_start]y[blank_end]²) Área del trapecio de dimensiones 'B' 'b' 'h' => ([blank_start]B[blank_end]+[blank_start]b[blank_end]) · [blank_start]h[blank_end]/[blank_start]2[blank_end] Longitud de un arco de radio 'x' y ángulo 'A'º => \(\pi\) · [blank_start]x[blank_end] · [blank_start]A[blank_end]/180 Área de corona circular entre circunferencias de radios 'R' 'r' => \(\pi\) · ([blank_start]R[blank_end]² – [blank_start]r[blank_end]²) Producto de dos números impares consecutivos => ([blank_start]2x[blank_end]–1) · ([blank_start]2x[blank_end]+1) = [blank_start]4x[blank_end]²–[blank_start]1[blank_end]

FACTORIZACIÓN ALGEBRAICA ... ========================== Sacar factor común: 6x² + 9x – 5 ... => ... [[blank_start]3x[blank_end]] · ([blank_start]2x+3[blank_end]) – 5 2x²y – 3xy² + xy ... => ... [[blank_start]xy[blank_end]] · ([blank_start]2x-3y+1[blank_end]) Cuadrado de suma y resta: x² + 10x + 25 ... => ... ([blank_start]x+5[blank_end]) · (x+5) = (x+5)² 4x² – 12x + 9 ... => ... ([blank_start]2x-3[blank_end]) · (2x-3) = (2x-3)² Suma por diferencia: 9x² – 36 ... => ... ([blank_start]3x+6[blank_end]) · ([blank_start]3x-6[blank_end]) 25x² – 4y² ... => ... ([blank_start]5x+2y[blank_end]) · ([blank_start]5x-2y[blank_end]) Ecuación cuadrada: 2x² + x – 3 = 0 . . . Soluciones: 1 y -3/2 2x² + x – 3 ... => ... ([blank_start]x-1[blank_end]) · ([blank_start]2x+3[blank_end]) Otros factores (Regla de Ruffini): 6x³+5x²–17x–6 ... => ... = (x+2) · ([blank_start]6x²-7x-3[blank_end]) . . . (x+2) · ([blank_start]2x-3[blank_end]) · (3x+1)

ECUACIONES RACIONALES. Ejemplos ...

TÉRMINO de una SUCESIÓN... ======================== 5º de [3n²-5] = [blank_start]70[blank_end] 4º de [2n+3] = [blank_start]11[blank_end] 2º de [n³/2] = [blank_start]4[blank_end] 6º de [3n/2] = [blank_start]9[blank_end] 3º de [2n³-8] = [blank_start]46[blank_end] 5º de [(n²+3)/2] = [blank_start]14[blank_end]

ESTADÍSTICA: Datos de un examen de los 50 alumnos de una clase... . x . . fi . . Fi . . f% . . F% . . x·fi === === === === ==== ==== . 0 . . 1 . . 1 . . . 2 . . . 2 . . . [blank_start]0[blank_end] . 1 . . 3 . . 4 . . . 6 . . . 8 . . . [blank_start]3[blank_end] . 2 . . 2 . . 6 . . . [blank_start]4[blank_end] . . 12 . . .[blank_start]4[blank_end] . 3 . . 4 . .10 . . .[blank_start]8[blank_end] . . [blank_start]20[blank_end] . .[blank_start]12[blank_end] . 4 . . 5 . .[blank_start]15[blank_end] . .10 . . 30 . . [blank_start]20[blank_end] . 5 . . 7 . .22 . . [blank_start]14[blank_end] . .44 . .[blank_start]35[blank_end] . 6 . .11 . 33 . . [blank_start]22[blank_end] . .66 . .[blank_start]66[blank_end] . 7 . . 8 . .[blank_start]41[blank_end] . .16 . .[blank_start]82[blank_end] . . [blank_start]56[blank_end] . 8 . . 4 . .45 . . 8 . . .[blank_start]90[blank_end] . . [blank_start]32[blank_end] . 9 . . 3 . .[blank_start]48[blank_end] . . 6 . . .96 . . [blank_start]27[blank_end] .10 . .2 . .50 . . 4 . .100 . . [blank_start]20[blank_end] . . . === . . . . === . . . . . ==== . . . . 50 . . . . 100 . . . . . . [blank_start]275[blank_end] ====================== MEDIA => [blank_start]275[blank_end] / [blank_start]50[blank_end] = [blank_start]5,5[blank_end] MEDIANA => [blank_start]5[blank_end]+3/11 MODA => [blank_start]6[blank_end]

Sistema BINARIO { 32 ~ 16 ~ 8 ~ 4 ~ 2 ~ 1 } ...

A modo de REGLA de TRES ... ========================== 4 es a CUATRO, como 9 es a [blank_start]NUEVE[blank_end]. - - - - - - - - - - - - m² es a m³, como SUPERFICIE es a [blank_start]VOLUMEN[blank_end]. 10 es a DIEZ, como 20 es a [blank_start]VEINTE[blank_end]. - - - - - - - - - - - - - METRO es a KILÓMETRO, como KILO es a [blank_start]TONELADA[blank_end]. 9° es a NOVENO, como 20° es a [blank_start]VIGÉSIMO[blank_end]. - - - - - - -METRO es a CENTÍMETRO, como EURO es a [blank_start]CÉNTIMO[blank_end]. 7° es a SÉPTIMO, como 12° es a [blank_start]DUODÉCIMO[blank_end]. - - - - TIEMPO es a HORA, como ÁNGULO es a [blank_start]GRADO[blank_end]. 1/4 es a UN CUARTO, como 1/2 es a UN [blank_start]MEDIO[blank_end]. - - - 15 h es a 15 HORAS, como 15° es a 15 [blank_start]GRADOS[blank_end]. N² es a N³ , como CUADRADO es a [blank_start]CUBO[blank_end]. - - - - - - - - 45º es a AGUDO, como 135º es a [blank_start]OBTUSO[blank_end]. 1ª es a DÉCIMAS, como 3ª es a [blank_start]MILÉSIMAS[blank_end]. - - - - - - - ROTACIÓN es a DÍA, como TRASLACIÓN es a [blank_start]AÑO[blank_end]. 3² es a POTENCIA, como 3/4 es a [blank_start]FRACCIÓN[blank_end]. - - - - - CIRCUNFERENCIA es a ARCO, como RECTA es a [blank_start]SEGMENTO[blank_end]. x es a MULTIPLICAR, como : es a [blank_start]DIVIDIR[blank_end]. - - - - - - - -NIVEL es a HORIZONTAL, como PLOMADA es a [blank_start]VERTICAL[blank_end]. x es A MULTIPLICAR, como + es a [blank_start]SUMAR[blank_end]. - - - - - - - 3 es a TRIÁNGULO, como 6 es a [blank_start]HEXÁGONO[blank_end]. F es a LETRA, como 5 es a [blank_start]CIFRA[blank_end]. - - - - - - - - - - - - - - PERÍMETRO es a POLÍGONO, como CIRCUNFERENCIA es a [blank_start]CÍRCULO[blank_end]. ROMA es a PALABRA, como 7.541 es a [blank_start]CANTIDAD[blank_end]. - - - - - - - - - - - CILINDRO es a CONO, como PRISMA es a [blank_start]PIRÁMIDE[blank_end]. RESTA es a DIFERENCIA, como MULTIPLICACIÓN es a [blank_start]PRODUCTO[blank_end]. - BORDE es a ARISTA, como ESQUINA es a [blank_start]VÉRTICE[blank_end]. SUMAR es a TOTAL, como DIVIDIR es a [blank_start]COCIENTE[blank_end]. - - - - - - - - - - - - ÁREA es a HECTÁREA, como AÑO es a [blank_start]SIGLO[blank_end]. SUMA es a SUMANDOS, como MULTIPLICACIÓN es a [blank_start]FACTORES[blank_end]. - - SEGUNDO es a MINUTO, como MINUTO es a [blank_start]HORA[blank_end].

SUDOKU [P] [E] [L] [O] [T] [A] ...

SUDOKU...

PORCENTAJES... Un ciclista ha recorrido 18 km de una etapa que tiene 150 km en total. ¿Qué porcentaje le queda por recorrer? ... 18 de 150 => 1.800/150 = 12% ha recorrido ... 100–12 = 88% queda por recorrer. Una magdalena contiene 24 gramos de harina, que representan el 40% de su peso total. ¿Cuánto pesará una bolsa con una docena? ... 40% de P = 24 g => P = 2.400/40 = 60 g pesa cada una. ... 60 x 12 = 720 g pesará una docena. Queremos comprar unos pantalones que tienen un 20% de descuento. Si su precio final después de la rebaja es 27,2 €, ¿cuánto costaban los pantalones antes de ser rebajados? ... Ha pagado el 80%. => 27,2x100/80 = 34 € ers su precio inicial. Una panadería ha vendido 340 barras de pan de las 500 barras que habían preparado. ¿Qué porcentaje se ha vendido? ¿Qué porcentaje ha quedado sin vender? ... 340 de 500 => 340x100/500 = 68% ha vendido. ... 100 – 68 = 32% sin vender. Este año pagamos 252 € de IBI tras una subida del 5%. ¿Cuánto pagamos el año pasado, antes de la subida? ... El 105% de P = 254,6 => 252x100/105 = 240 € el año pasado. A fecha actual, el agua embalsada en Córdoba es de 2000 hm3, lo que supone un 70% de la capacidad total. ¿Cuál es la capacidad total de los embalses de Córdoba?

. . . = P O R C E N T A J E S = . . . . . . . =================== . . . . 4% de 25 = [blank_start]1[blank_end] . . . . 10% de 40 = [blank_start]4[blank_end] 5% de 60 = [blank_start]3[blank_end] . . . . 15% de 60 = [blank_start]9[blank_end] 8% de 75 = [blank_start]6[blank_end] . . . 25% de 200 = [blank_start]50[blank_end] 6 de 15 = [blank_start]40[blank_end]% . . . 12 de 20 = [blank_start]60[blank_end]% 9 de 30 = [blank_start]30[blank_end]% . . . 6 de 120 = [blank_start]5[blank_end]%

PORCENTAJES... ============ Un ciclista ha recorrido 18 km de una etapa de 150 km. ¿Qué porcentaje le queda por recorrer? ... 18 de 150 >>> 18x100/[blank_start]150[blank_end] = [blank_start]12[blank_end]% ha recorrido ... 100–[blank_start]12[blank_end] = [blank_start]88[blank_end]% queda por recorrer. Una magdalena contiene 24 gramos de harina, que es el 40% de su peso total. ¿Cuánto pesará una bolsa con una docena? ... 40% de P = 24 g >>> P = [blank_start]24[blank_end]x100/[blank_start]40[blank_end] = [blank_start]60[blank_end] g pesa cada una. ... 60 x [blank_start]12[blank_end] = [blank_start]720[blank_end] g pesará una docena. Una prenda con un 20% de descuento, me costó 27,2 €. ¿Cuánto costaba antes de la rebaja? ... Ha pagado el: 100–20 = [blank_start]80[blank_end]% >>> 27,2x[blank_start]100[blank_end]/[blank_start]80[blank_end] = [blank_start]34[blank_end] € era su precio inicial. Se han vendido 340 panes de los 500 que se habían preparado. ¿Qué porcentaje se ha vendido? ¿Qué porcentaje ha quedado sin vender? ... 340 de 500 >>> 340x100/500 = [blank_start]68[blank_end]% ha vendido. ... 100 – [blank_start]68[blank_end] = [blank_start]32[blank_end]% sin vender. Este año pagamos 252 € de IBI tras una subida del 5%. ¿Cuánto pagamos el año pasado, antes de la subida? ... El 100+5 = [blank_start]105[blank_end]% de P = 252 >>> 252x100/[blank_start]105[blank_end] = [blank_start]240[blank_end] € el año pasado. Un embalse contiene 644 hm³ de agua, que es un 70% de la capacidad total. ¿Cuál es la capacidad total del embalse? ... 70% de T = [blank_start]644[blank_end] >>> [blank_start]644[blank_end]x100/[blank_start]70[blank_end] = [blank_start]920[blank_end] hm³ lleno.

SISTEMAS de NUMERACIÓN... NÚMERO: 1 2 0 ============= En base 2 => [120/2] = [blank_start]60[blank_end](0)/2 = [blank_start]30[blank_end](0)/2 = [blank_start]15[blank_end](0)/2 = [blank_start]7[blank_end](1)/2 = [blank_start]3[blank_end](1)/2 = [blank_start]1[blank_end](1) ... >>> 1111000 En base 5 => [120/5] = 24([blank_start]0[blank_end])/5 = 4([blank_start]4[blank_end]) ... >>> [blank_start]440[blank_end] En base 9 => [120/9] = [blank_start]13[blank_end]([blank_start]3[blank_end])/9 = [blank_start]1[blank_end]([blank_start]4[blank_end]) ... >>> [blank_start]143[blank_end]

SISTEMAS de NUMERACIÓN. PASO a BASE DECIMAL ... ==================== 100110 en base 2 => 0+1·[blank_start]2[blank_end]+1·[blank_start]4[blank_end]+0·[blank_start]8[blank_end]+0·[blank_start]16[blank_end]+1·[blank_start]32[blank_end] = [blank_start]38[blank_end] 2031 en base 4 => [blank_start]1[blank_end]+[blank_start]3[blank_end]·4+[blank_start]0[blank_end]·16+[blank_start]2[blank_end]·64 = [blank_start]141[blank_end] 1507 en base 8 => 7+0·[blank_start]8[blank_end]+5·[blank_start]64[blank_end]+1·[blank_start]512[blank_end] = [blank_start]839[blank_end]

CÁLCULOS en CADENA ...

. . . . . . . = Á L G E B R A = . . . . . . . =========================== x–3=0 > x=[blank_start]3[blank_end] . . . . . . . x+5=3 > x=[blank_start]-2[blank_end] 3+x=5 > x=[blank_start]2[blank_end] . . . . . . . 2=x–3 > x=[blank_start]5[blank_end] x/2=3 > x=[blank_start]6[blank_end] . . . . . . . x/3+2=5 > x=[blank_start]9[blank_end] 2x=6 > x=[blank_start]3[blank_end] . . . . . . . . 2x+3=7 > x=[blank_start]2[blank_end] 2x–1=5 > x=[blank_start]3[blank_end] . . . . . . 3x=9 > x=[blank_start]3[blank_end] 3x+2=5 > x=[blank_start]1[blank_end] . . . . . . 3x–5=4 > x=[blank_start]3[blank_end] 2x/3=4 > x=[blank_start]6[blank_end] . . . . . . . 3x/2=6 > x=[blank_start]4[blank_end] 2x/5+1=3 > x=[blank_start]5[blank_end] . . . . . 3x/4–5=1 > x=[blank_start]8[blank_end] x²=9x4 > x=+–[blank_start]6[blank_end] . . . . . x²+5=9 > x=+–[blank_start]2[blank_end] x²–3=6 > x=+–[blank_start]3[blank_end] . . . . . 2x²/3=6 > x=+–[blank_start]3[blank_end] 3x²/2–5=1 > x=+–[blank_start]2[blank_end] . . 2x–3=x+1 > x=[blank_start]4[blank_end] x=3x–6 > x=[blank_start]3[blank_end] . . . . . . (2x–3)/5=x > x=[blank_start]-1[blank_end] x³=54/2 > x=[blank_start]3[blank_end] . . . . . 3x/5=(x+3)/2 > x=[blank_start]15[blank_end]

ECUACIÓN RACIONAL ...

CÁLCULO MENTAL ... ================= 9x7 =[blank_start]63[blank_end]– 5 =[blank_start]58[blank_end]/ 2 =[blank_start]29[blank_end]– 4 =[blank_start]25[blank_end]√¯=[blank_start]5[blank_end]x 8 =[blank_start]40[blank_end] 8+7 =[blank_start]15[blank_end]/ 3 =[blank_start]5[blank_end]x 9 =[blank_start]45[blank_end]+ 4 =[blank_start]49[blank_end]√¯=[blank_start]7[blank_end]x 3 =[blank_start]21[blank_end] 7–3 =[blank_start]4[blank_end]² =[blank_start]16[blank_end]x 4 =[blank_start]64[blank_end]√¯=[blank_start]8[blank_end]x 7 =[blank_start]56[blank_end]– 15 =[blank_start]41[blank_end] 6x7 =[blank_start]42[blank_end]/ 2 =[blank_start]21[blank_end]/7 =[blank_start]3[blank_end]³ = [blank_start]27[blank_end]x 2 =[blank_start]54[blank_end]/ 6 =[blank_start]9[blank_end]

ÁLGEBRA ...

CÁLCULOS VARIADOS [&=infinito] [Hasta 2 cifras decimales] ...

NÚMEROS ENTEROS ...

NÚMEROS ROMANOS... =================== [blank_start]IX[blank_end] [blank_start]XIV[blank_end] [blank_start]XXVI[blank_end] [blank_start]XLII[blank_end] [blank_start]LIV[blank_end] [blank_start]LXIX[blank_end] [blank_start]XCV[blank_end] [blank_start]XCIX[blank_end] [blank_start]CXIX[blank_end] [blank_start]CXLI[blank_end] [blank_start]CCXC[blank_end] [blank_start]CDXV[blank_end] [blank_start]CDXCIII[blank_end] [blank_start]DXXX[blank_end] [blank_start]DXLV[blank_end] [blank_start]DCXIX[blank_end] [blank_start]CMLXXX[blank_end] [blank_start]CMXCIX[blank_end]