File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/2N41-5-cisWEHxA.js.map
{"version":3,"file":"2N41-5-cisWEHxA.js","sources":["../../src/exercices/2e/2N41-5.js"],"sourcesContent":["import { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { pgcd } from '../../lib/outils/primalite.js'\nimport Exercice from '../Exercice.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { remplisLesBlancs } from '../../lib/interactif/questionMathLive.js'\nimport { context } from '../../modules/context.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\nimport { miseEnEvidence } from '../../lib/outils/embellissements'\nimport { fraction } from '../../modules/fractions.js'\nimport { developpementCompare } from '../../lib/interactif/mathLive.js'\n\nexport const titre = 'Développer $(a-b)^2$'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\n/**\n * Développer (a-b)²\n * @author Matthieu Devillers\n */\nexport const uuid = '5a4ad'\nexport const ref = '2N41-5'\n\nexport default function DevelopperIdentitesRemarquables4 () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.interactifReady = interactifReady\n this.interactifType = interactifType\n this.correctionDetailleeDisponible = true\n context.isHtml ? (this.spacingCorr = 3) : (this.spacingCorr = 2)\n if (!context.isHtml) {\n this.correctionDetaillee = false\n }\n this.consigne = 'Développer puis réduire les expressions suivantes.'\n this.nbCols = 1\n this.nbColsCorr = 1\n this.spacing = 1\n this.spacingCorr = 1\n this.nbQuestions = 4\n this.sup = 5\n this.nouvelleVersion = function () {\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n const listeFractions = [\n [1, 2],\n [1, 3],\n [2, 3],\n [1, 4],\n [3, 4],\n [1, 5],\n [2, 5],\n [3, 5],\n [4, 5],\n [1, 6],\n [5, 6],\n [1, 7],\n [2, 7],\n [3, 7],\n [4, 7],\n [5, 7],\n [6, 7],\n [1, 8],\n [3, 8],\n [5, 8],\n [7, 8],\n [1, 9],\n [2, 9],\n [4, 9],\n [5, 9],\n [7, 9],\n [8, 9],\n [1, 10],\n [3, 10],\n [7, 10],\n [9, 10]\n ]\n let typesDeQuestionsDisponibles = []\n if (this.sup === 1) {\n typesDeQuestionsDisponibles = [1] // coef de x = 1\n } else if (this.sup === 2) {\n typesDeQuestionsDisponibles = [2] // coef de x > 1\n } else if (this.sup === 3) {\n typesDeQuestionsDisponibles = [3] // coef de x positif, difference au carrée.\n } else if (this.sup === 4) {\n typesDeQuestionsDisponibles = [4] // coefficients rationnels\n } else {\n typesDeQuestionsDisponibles = [1, 2, 3, 4]\n } // mélange des questions\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0, texte, texteCorr, texteCorr2, cpt = 0, a, b, typesDeQuestions; i < this.nbQuestions && cpt < 50;) {\n typesDeQuestions = listeTypeDeQuestions[i]\n a = randint(1, 12)\n b = randint(2, 12)\n const uneFraction = choice(listeFractions)\n const ns = uneFraction[0]\n const ds = uneFraction[1]\n const dfrac = fraction(ns, ds).texFraction\n const dfrac2 = fraction(ns * ns, ds * ds).texFraction\n const dbleProdFrac = fraction(2 * ns * a, ds).texFraction\n const dbleProdFracRed = fraction(2 * ns * a, ds).simplifie().texFraction\n texteCorr = ''\n texteCorr2 = ''\n switch (typesDeQuestions) {\n case 1:\n texte = `$\\\\left(x-${a}\\\\right)^2$` // (x-a)^2\n if (this.correctionDetaillee) {\n texteCorr += `On développe l'expression en utilisant l'identité remarquable $(a-b)^2=a^2-2ab+b^2$, avec $\\\\color{blue} a = x\\\\color{black}$ et $\\\\color{green} b = ${a} \\\\color{black} $ : <br> <br>`\n texteCorr += `$\\\\left(\\\\color{blue}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2=\\\\color{blue}x\\\\color{black}^2-2 \\\\times \\\\color{blue}x \\\\color{black}\\\\times \\\\color{green}${a} \\\\color{black}+ \\\\color{green}${a}\\\\color{black}^2$ <br>`\n texteCorr += `$\\\\phantom{\\\\left(\\\\color{blue}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2} = x^2-${2 * a}x+${a * a}$`\n } else {\n texteCorr += `$\\\\left(x+${a} \\\\right)^2=x^2-${2 * a}x+${a * a}$`\n }\n setReponse(this, i, { reponse: { value: `x^2-${2 * a}x+${a * a}`, compare: developpementCompare } }, { formatInteractif: 'fillInTheBlank' })\n break\n case 2:\n texte = `$\\\\left(${b}x-${a}\\\\right)^2$` // b>1\n if (this.correctionDetaillee) {\n texteCorr += `On développe l'expression en utilisant l'identité remarquable $(a-b)^2=a^2-2ab+b^2$, avec $\\\\color{blue} a = ${b}x\\\\color{black}$ et $\\\\color{green} b = ${a} \\\\color{black} $ : <br> <br>`\n texteCorr += `$\\\\left(\\\\color{blue}${b}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2 = \\\\left(\\\\color{blue}${b}x\\\\color{black}\\\\right)^2 - 2 \\\\times \\\\color{blue}${b}x\\\\color{black} \\\\times \\\\color{green}${a} + ${a}\\\\color{black}^2$ <br>`\n texteCorr += `$\\\\phantom{\\\\left(\\\\color{blue}${b}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2} = ${b * b}x^2-${2 * b * a}x+${a * a}$`\n } else {\n texteCorr += `$\\\\left(${b}x+${a}\\\\right)^2 = ${b * b}x^2-${2 * b * a}x+${a * a}$`\n }\n setReponse(this, i, { reponse: { value: `${b * b}x^2-${2 * b * a}x+${a * a}`, compare: developpementCompare } }, { formatInteractif: 'fillInTheBlank' })\n break\n case 3:\n b = -b\n texte = `$\\\\left(${b}x+${a}\\\\right)^2$` // b>1\n if (this.correctionDetaillee) {\n texteCorr += `On remarque que : $\\\\left(${b}x+${a}\\\\right)^2 = \\\\left(${a}-${-b}x\\\\right)^2$ <br>`\n texteCorr += `Et on développe l'expression en utilisant l'identité remarquable $\\\\left(a-b\\\\right)^2=a^2-2ab+b^2$, avec $\\\\color{blue} a = ${a}\\\\color{black}$ et $\\\\color{green} b = ${-b}x \\\\color{black} $ : <br> <br>`\n texteCorr += `$\\\\left(\\\\color{green}${b}x\\\\color{black}+\\\\color{blue}${a}\\\\color{black}\\\\right)^2 = \\\\left(\\\\color{blue}${a}\\\\color{black}-\\\\color{green}${-b}x\\\\color{black}\\\\right)^2 $ <br>`\n texteCorr += `$\\\\phantom{\\\\left(\\\\color{blue}${b}x\\\\color{black}+\\\\color{green}${a}\\\\color{black}\\\\right)^2} = \\\\color{blue}${a}\\\\color{black}^2 - 2 \\\\times \\\\color{blue}${a}\\\\color{black} \\\\times \\\\color{green}${-b}x \\\\color{black} + \\\\left(\\\\color{green} ${-b}x\\\\color{black}\\\\right)^2$ <br>`\n texteCorr += `$\\\\phantom{\\\\left(\\\\color{blue}${b}x\\\\color{black}+\\\\color{green}${a}\\\\color{black}\\\\right)^2} = ${a * a} -${2 * (-b) * a}x+${b * b}x^2$ <br>`\n texteCorr += `$\\\\phantom{\\\\left(\\\\color{blue}${b}x\\\\color{black}+\\\\color{green}${a}\\\\color{black}\\\\right)^2} = ${b * b}x^2-${2 * (-b) * a}x+${a * a}$`\n texteCorr2 += `<br><br> Autre méthode possible : développer en utilisant $\\\\left(a+b\\\\right)^2$ avec $a = ${b}x$ et $ b = ${a} $. <br>`\n } else {\n texteCorr = texte + `$= ${b * b}x^2-${2 * (-b) * a}x+${a * a}$`\n }\n\n setReponse(this, i, { reponse: { value: `${b * b}x^2-${2 * (-b) * a}x+${a * a}`, compare: developpementCompare } }, { formatInteractif: 'fillInTheBlank' })\n break\n case 4:\n texte = `$\\\\left(${dfrac}x-${a}\\\\right)^2$`\n if (this.correctionDetaillee) {\n texteCorr += `On développe l'expression en utilisant l'identité remarquable $(a-b)^2=a^2-2ab+b^2$, avec $\\\\color{blue} a = ${dfrac}x\\\\color{black}$ et $\\\\color{green} b = ${a} \\\\color{black} $ : <br> <br>`\n texteCorr += `$\\\\left(\\\\color{blue}${dfrac}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2 = \\\\left(\\\\color{blue}${dfrac}x\\\\color{black}\\\\right)^2 - 2 \\\\times \\\\color{blue}${dfrac}x\\\\color{black} \\\\times \\\\color{green}${a} + ${a}\\\\color{black}^2 $ <br><br>`\n texteCorr += `$\\\\phantom{\\\\left(\\\\color{blue}${dfrac}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2} = ${dfrac2}x^2-${dbleProdFrac}x+${a * a}$`\n if (pgcd(ns, ds) !== 1 || pgcd(2 * ns * a, ds) !== 1) {\n texteCorr += `<br><br>$\\\\phantom{\\\\left(\\\\color{blue}${dfrac}x\\\\color{black}-\\\\color{green}${a}\\\\color{black}\\\\right)^2} = ${dfrac2}x^2-${dbleProdFracRed}x+${a * a}$`\n }\n } else {\n texteCorr = texte + `$= ${dfrac2}x^2-${dbleProdFracRed}x+${a * a}$`\n }\n setReponse(this, i, { reponse: { value: `${dfrac2}x^2-${dbleProdFrac}x+${a * a}`, compare: developpementCompare } }, { formatInteractif: 'fillInTheBlank' })\n break\n }\n\n // Uniformisation : Mise en place de la réponse attendue en interactif en orange et gras\n const textCorrSplit = texteCorr.split('=')\n let aRemplacer = textCorrSplit[textCorrSplit.length - 1]\n aRemplacer = aRemplacer.replace('$', '')\n\n texteCorr = ''\n for (let ee = 0; ee < textCorrSplit.length - 1; ee++) {\n texteCorr += textCorrSplit[ee] + '='\n }\n texteCorr += `$ $${miseEnEvidence(aRemplacer)}$`\n // Fin de cette uniformisation\n\n texteCorr += texteCorr2\n if (this.interactif) texte += remplisLesBlancs(this, i, '=%{reponse}', 'inline', '\\\\ldots\\\\ldots')\n if (this.questionJamaisPosee(i, a, b, ns, ds, typesDeQuestions)) {\n // Si la question n'a jamais été posée, on en créé une autre\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n }\n this.besoinFormulaireNumerique = ['Niveau de difficulté', 5, '1 : Coefficient de x égal à 1\\n 2 : 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