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{"version":3,"file":"2N32-2-zu8D7FnT.js","sources":["../../src/exercices/2e/2N32-2.js"],"sourcesContent":["import { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { ecritureAlgebrique, ecritureParentheseSiNegatif, rienSi1 } from '../../lib/outils/ecritures.js'\nimport Exercice from '../Exercice.js'\nimport { abs } from '../../lib/outils/nombres.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { propositionsQcm } from '../../lib/interactif/qcm.js'\nexport const titre = 'Connaître les propriétés calculatoires des racines carrées'\nexport const interactifReady = true\nexport const interactifType = 'qcm'\nexport const dateDeModifImportante = '13/12/2023'\n/**\n * 2N32-2, ex 2N10-1\n * @author Stéphane Guyon modif Gilles Mora\n */\nexport const uuid = '99b29'\nexport const ref = '2N32-2'\nexport default function Proprietesracinecarree () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.nbQuestions = 2\n this.nbCols = 2\n this.nbColsCorr = 1\n this.sup = 1 //\n this.nouvelleVersion = function () {\n this.consigne = this.interactif ? `Indiquer l'écriture simplifiée ${this.nbQuestions === 1 ? 'du calcul suivant.' : 'des calculs suivants.'}` : `Donner, si possible, une écriture simplifiée ${this.nbQuestions === 1 ? 'du calcul suivant.' : 'des calculs suivants.'}`\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n const typesDeQuestionsDisponibles = [1, 2, 3, 4, 5, 6, 7]; let typesDeQuestions//,\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n for (let i = 0, a, b, c, d, e, monQcm, texte, texteCorr, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n typesDeQuestions = listeTypeDeQuestions[i]\n switch (typesDeQuestions) {\n // Cas par cas, on définit le type de nombres que l'on souhaite\n // Combien de chiffres ? Quelles valeurs ?\n case 1:// calcul de (a sqrt b)²\n a = randint(2, 9) * choice([-1, 1])\n b = randint(2, 11, [4, 8, 9])\n c = a * a * b\n d = a * a\n texte = `$\\\\left(${a} \\\\sqrt{${b}}\\\\right)^{2}$`\n texteCorr = `$\\\\left(${a} \\\\sqrt{${b}}\\\\right)^{2}=${ecritureParentheseSiNegatif(a)}^{2}\\\\times \\\\left(\\\\sqrt{${b}}\\\\right)^{2}$\n $\\\\phantom{\\\\left(${a} \\\\sqrt{${b}}\\\\right)^{2}}$<br>\n $\\\\phantom{\\\\left(${a} \\\\sqrt{${b}}\\\\right)^{2}}=${d}\\\\times ${b}$<br>\n $\\\\phantom{\\\\left(${a} \\\\sqrt{${b}}\\\\right)^{2}}=${c}$`\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$${c}$`,\n statut: true\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: false\n },\n {\n texte: `$${a ** 2} \\\\sqrt{${b}}$`,\n statut: false\n },\n {\n texte: `$${abs(a) * b} $`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n case 2:// calcul de (a sqrt b)*c sqrt b\n\n a = randint(2, 9) * choice([-1, 1])\n c = randint(2, 9) * choice([-1, 1])\n d = randint(2, 9) * choice([-1, 1])\n b = randint(2, 11, [4, 8, 9])\n e = c * d\n\n texte = `$${c} \\\\sqrt{${b}}\\\\times ${ecritureParentheseSiNegatif(d)}\\\\sqrt{${b}}$`\n texteCorr = `$ ${c} \\\\sqrt{${b}}\\\\times ${ecritureParentheseSiNegatif(d)} \\\\sqrt{${b}}=${c}\\\\times ${ecritureParentheseSiNegatif(d)} \\\\sqrt{${b}} \\\\times \\\\sqrt{${b}}$<br>\n $\\\\phantom{${c} \\\\sqrt{${b}}\\\\times ${ecritureParentheseSiNegatif(d)} \\\\sqrt{${b}}}=${e}\\\\times ${b}$<br>\n $\\\\phantom{${c} \\\\sqrt{${b}}\\\\times ${ecritureParentheseSiNegatif(d)} \\\\sqrt{${b}}}=${e * b}$`\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$${e * b}$`,\n statut: true\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: false\n },\n {\n texte: `$${e} \\\\sqrt{${b}}$`,\n statut: false\n },\n {\n texte: `$${-e} \\\\sqrt{${b}}$`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n case 3:// calcul de (a sqrt b)*(c + d sqrt b)\n a = randint(2, 9) * choice([-1, 1])\n c = randint(3, 9) * choice([-1, 1])\n d = randint(2, 9) * choice([-1, 1])\n b = randint(2, 11, [4, 8, 9])\n e = c * d\n\n texte = `$ ${a} \\\\sqrt{${b}}\\\\left( ${c} ${ecritureAlgebrique(d)}\\\\sqrt{${b}}\\\\right)$`\n texteCorr = `$${a} \\\\sqrt{${b}}\\\\left( ${c} ${ecritureAlgebrique(d)}\\\\sqrt{${b}}\\\\right)=\n ${a} \\\\sqrt{${b}}\\\\times ${ecritureParentheseSiNegatif(c)}${ecritureAlgebrique(a)} \\\\sqrt{${b}}\\\\times ${ecritureParentheseSiNegatif(d)}\\\\sqrt{${b}}$<br>\n $\\\\phantom{${a} \\\\sqrt{${b}}\\\\left( ${c} ${ecritureAlgebrique(d)}\\\\sqrt{${b}}\\\\right)}=${a * c}\\\\sqrt{${b}}${ecritureAlgebrique(a)}\\\\times ${ecritureParentheseSiNegatif(d)}\\\\times ${b}$<br>\n $\\\\phantom{${a} \\\\sqrt{${b}}\\\\left( ${c} ${ecritureAlgebrique(d)}\\\\sqrt{${b}}\\\\right)}=${a * c}\\\\sqrt{${b}}${ecritureAlgebrique(a * d * b)}$`\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$${a * c}\\\\sqrt{${b}}${ecritureAlgebrique(a * d * b)}$`,\n statut: true\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: false\n },\n {\n texte: `$${a * c}\\\\sqrt{${b}}${ecritureAlgebrique(-a * d * b)}$`,\n statut: false\n },\n {\n texte: `$${rienSi1(a + c)}\\\\sqrt{${b}}${ecritureAlgebrique(a * d * b)}$`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n case 4:// calcul de sqrt b + sqrt c\n\n a = randint(2, 9)\n\n d = randint(2, 9)\n b = randint(2, 11, [4, 8, 9])\n c = randint(2, 19, [4, 8, 9, 12, 16, 18, b])\n e = c * d\n\n texte = `$\\\\sqrt{${b}}+\\\\sqrt{${c}}$`\n texteCorr = `$ \\\\sqrt{${b}}+\\\\sqrt{${c}}$ n'est pas simplifiable`\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$\\\\sqrt{${b + c}}$`,\n statut: false\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: true\n },\n {\n texte: `$\\\\sqrt{${b * c}}$`,\n statut: false\n },\n {\n texte: `$${b + c}$`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n case 5:// calcul de sqrt b² + sqrt c²\n\n b = randint(2, 11)\n c = randint(2, 11, [b])\n e = c * d\n\n texte = `$ \\\\sqrt{${b * b}}+\\\\sqrt{${c * c}}$`\n texteCorr = `$ \\\\sqrt{${b * b}}+\\\\sqrt{${c * c}}=${b}+${c}=${b + c}$ `\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$\\\\sqrt{${b + c}}$`,\n statut: false\n },\n {\n texte: `$${b + c}$`,\n statut: true\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: false\n },\n {\n texte: `$\\\\sqrt{${b * b + c * c}}$`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n case 6:// calcul de sqrt (b²c/c)\n\n b = randint(2, 11)\n c = randint(2, 7, [b])\n d = b * b * c\n\n texte = `$ \\\\sqrt{\\\\dfrac{${d}}{${c}}}$`\n texteCorr = `$ \\\\sqrt{\\\\dfrac{${d}}{${c}}}= \\\\sqrt{\\\\dfrac{${b}^{2}\\\\times${c}}{${c}}}$<br>\n $\\\\phantom{\\\\sqrt{\\\\dfrac{${d}}{${c}}}}=\\\\sqrt{${b}^{2}}$<br>\n $\\\\phantom{\\\\sqrt{\\\\dfrac{${d}}{${c}}}}=${b}$ `\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$\\\\sqrt{${b}}$`,\n statut: false\n },\n {\n texte: `$${b}$`,\n statut: true\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: false\n },\n {\n texte: `$${b ** 2}$`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n case 7:// calcul de sqrt b * sqrt c\n\n b = randint(2, 11, [4, 9])\n c = randint(2, 10, [4, 9])\n d = b * c\n while (d === 4 || d === 9 || d === 16 || d === 25 || d === 36 || d === 49 || d === 64 || d === 81 || d === 100) {\n b = randint(2, 11, [4, 9])\n c = randint(2, 10, [b])\n d = b * c\n }\n texte = `$ \\\\sqrt{${d}}\\\\times \\\\sqrt{${c}}$`\n texteCorr = `$ \\\\sqrt{${d}}\\\\times \\\\sqrt{${c}}=\\\\sqrt{${d}\\\\times${c}}$<br>\n $\\\\phantom{\\\\sqrt{${d}}\\\\times \\\\sqrt{${c}}}=\\\\sqrt{${b}\\\\times${c}\\\\times${c}}$<br>\n $\\\\phantom{\\\\sqrt{${d}}\\\\times \\\\sqrt{${c}}}=${c}\\\\sqrt{${b}}$ `\n if (this.interactif) {\n this.autoCorrection[i] = {\n enonce: texte,\n options: { horizontal: true },\n propositions: [\n {\n texte: `$${c * b}$`,\n statut: false\n },\n {\n texte: `$${c}\\\\sqrt{${b}}$`,\n statut: true\n },\n {\n texte: 'On ne peut pas simplifier',\n statut: false\n },\n {\n texte: `$${b}\\\\sqrt{${c}}$`,\n statut: false\n }\n ]\n }\n monQcm = propositionsQcm(this, i)\n texte += monQcm.texte\n }\n break\n }\n if (this.listeQuestions.indexOf(texte) === -1) { // Si la question n'a jamais été posée, 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