File: /home/mmtprep/public_html/mathzen.mmtprep.com/assets/2N11-2-QbS843lR.js.map
{"version":3,"file":"2N11-2-QbS843lR.js","sources":["../../src/exercices/2e/2N11-2.js"],"sourcesContent":["import { crochetD, crochetG, intervalle } from '../../lib/2d/intervalles.js'\nimport { point } from '../../lib/2d/points.js'\nimport { segment } from '../../lib/2d/segmentsVecteurs.js'\nimport { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport Exercice from '../deprecatedExercice.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nimport { miseEnEvidence } from '../../lib/outils/embellissements'\n\nexport const titre = 'Use and understand the symbols $\\\\cup $ and $\\\\cap $ with the intervals of $\\\\mathbb{R}$'\n\n/**\n * @author Stéphane Guyon\n */\nexport const uuid = 'dc2a5'\nexport const ref = '2N11-2'\nexport default function UnionEtIntersectionIntervallesDeR () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.nbQuestions = 4\n this.nbCols = 2\n this.nbColsCorr = 2\n\n this.nouvelleVersion = function () {\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n const typesDeQuestionsDisponibles = [1, 2, 3, 4, 5, 6, 7, 8]; let typesDeQuestions\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n const X1 = point(0, 0)\n const X2 = point(12, 0)\n for (let i = 0, a, b, c, d, s, e, f, test, A, B, C, D, c1, c2, c3, c4, int, int1, int2, texte = '', texteCorr = '', cpt = 0; i < this.nbQuestions && cpt < 50;) {\n typesDeQuestions = listeTypeDeQuestions[i]\n test = randint(1, 6)\n // variables that alternate bracket openings\n switch (typesDeQuestions) {\n // Case by case, we define the type of numbers we want\n // How many digits? What values?\n case 1: // Intersection de deux intervalles fermés disjoints\n a = randint(1, 15)\n e = a + 1\n b = randint(e, 25)\n e = b + 1\n c = randint(e, 35)\n e = c + 1\n d = randint(e, 45)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(5, 0, b)\n C = point(6, 0, c)\n D = point(9, 0, d)\n if (test === 1) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else if (test === 5) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', 0)\n int2 = intervalle(C, D, 'blue', 0)\n\n texte = 'If possible, give a simplified writing of'\n texte += 'tupe' + typesDeQuestions\n if (test === 1) {\n texte += `$I=[${a},${b}]\\\\cap[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}]$. `\n } else if (test === 2) {\n texte += `$I=]${a},${b}]\\\\cap[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]${a},${b}]$ and in $[${c},${d}]$. `\n } else if (test === 3) {\n texte += `$I=[${a},${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $]${c},${d}]$. `\n } else if (test === 4) {\n texte += `$I=[${a},${b}]\\\\cap[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cap[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n } else {\n texte += `$I=]${a},${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n }\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += '<br>The two sets are disjoint, they have no element in common.<br>$I=\\\\emptyset$'\n break\n case 2: // Union de deux intervalles fermés disjoints\n a = randint(1, 15)\n e = a + 1\n b = randint(e, 25)\n e = b + 1\n c = randint(e, 35)\n e = c + 1\n d = randint(e, 45)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(5, 0, b)\n C = point(6, 0, c)\n D = point(9, 0, d)\n if (test === 1) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else if (test === 5) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', 0)\n int2 = intervalle(C, D, 'blue', 0)\n texte = 'If possible, give a simplified writing of'\n if (test === 1) {\n texte += `$I=[${a},${b}]\\\\cup[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$ or $[${c},${d}]$, or in both. `\n } else if (test === 2) {\n texte += `$I=]${a},${b}]\\\\cup[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]${a},${b}]$ or $[${c},${d}]$ , or in both. `\n } else if (test === 3) {\n texte += `$I=[${a},${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$or $]${c},${d}]$, or in both. `\n } else if (test === 4) {\n texte += `$I=[${a},${b}]\\\\cup[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$ or $[${c},${d}[$, or in both. `\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cup[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}[$ or $[${c},${d}[$, or in both. `\n } else {\n texte += `$I=]${a},${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]${a},${b}]$ or $]${c},${d}[$, or in both. `\n }\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n texteCorr += '<br>The two sets are disjoint, they have no element in common.<br>We cannot simplify the writing of $I$ which is therefore written'\n if (test === 1) {\n texteCorr += `$I=[${a},${b}]\\\\cup[${c},${d}]$`\n } else if (test === 2) {\n texteCorr += `$I=]${a},${b}]\\\\cup[${c},${d}]$`\n } else if (test === 3) {\n texteCorr += `$I=[${a},${b}]\\\\cup]${c},${d}]$`\n } else if (test === 4) {\n texteCorr += `$I=[${a},${b}]\\\\cup[${c},${d}[$`\n } else if (test === 5) {\n texteCorr += `$I=[${a},${b}[\\\\cup[${c},${d}[$`\n } else {\n texteCorr += `$I=]${a},${b}]\\\\cup]${c},${d}]$`\n }\n break\n case 3:// Intersection de deux intervalles fermés avec intervalle fermé en commun\n a = randint(1, 15)\n e = a + 4\n b = randint(29, 45)\n e = b - 1\n c = randint(16, e)\n e = b + 1\n d = randint(e, 65)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(6, 0, b)\n C = point(5, 0, c)\n D = point(9, 0, d)\n if (test === 1) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else if (test === 5) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', -0.1)\n int2 = intervalle(C, D, 'blue', 0.1)\n texte = 'If possible, give a simplified writing of'\n if (test === 1) {\n texte += `$I=[${a},${b}]\\\\cap[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=[${c},${b}]$`\n } else if (test === 2) {\n texte += `$I=]${a},${b}]\\\\cap[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]${a},${b}]$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=[${c},${b}]$`\n } else if (test === 3) {\n texte += `$I=[${a},${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $]${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=]${c},${b}]$`\n } else if (test === 4) {\n texte += `$I=[${a},${b}[\\\\cap]${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=]${c},${b}[$`\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cap[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=[${c},${b}[$`\n } else {\n texte += `$I=]${a},${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=]${c},${b}]$`\n }\n\n break\n case 4:// Union de deux intervalles fermés avec intervalle fermé en commun\n a = randint(1, 15)\n e = a + 4\n b = randint(29, 45)\n e = b - 1\n c = randint(16, e)\n e = b + 1\n d = randint(e, 65)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(6, 0, b)\n C = point(5, 0, c)\n D = point(9, 0, d)\n if (test === 1) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else if (test === 5) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', -0.1)\n int2 = intervalle(C, D, 'blue', 0.1)\n texte = 'If possible, give a simplified writing of'\n if (test === 1) {\n texte += `$I=[${a},${b}]\\\\cup[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$ or $[${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `$I=[${a},${d}]$`\n } else if (test === 2) {\n texte += `$I=]${a},${b}]\\\\cup[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]${a},${b}]$ or $[${c},${d}]$ , or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `$I=]${a},${d}]$`\n } else if (test === 3) {\n texte += `$I=[${a},${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$or $]${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `$I=[${a},${d}]$`\n } else if (test === 4) {\n texte += `$I=[${a},${b}[\\\\cup]${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}[$ or $]${c},${d}[$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `$I=[${a},${d}[$`\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cup[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}[$ or $[${c},${d}[$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `$I=[${a},${d}[$`\n } else {\n texte += `$I=]${a},${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]${a},${b}]$ or $]${c},${d}[$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `$I=]${a},${d}]$`\n }\n\n break\n case 5:// Intersection de deux intervalles fermés dont un inclus dans l'autre\n a = randint(1, 15)\n e = a + 15\n b = randint(e, 35)\n e = a + 1\n f = b - 10\n c = randint(e, f)\n e = c + 1\n d = randint(e, f)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(9, 0, b)\n C = point(5, 0, c)\n D = point(7, 0, d)\n if (test === 1) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else if (test === 5) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', -0.1)\n int2 = intervalle(C, D, 'blue', 0.1)\n texte = 'If possible, give a simplified writing of'\n\n if (test === 1) {\n texte += `$I=[${a},${b}] \\\\cap [${c},${d}].$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += `We observe that $[${c},${d}]\\\\subset [${a},${b}]$ therefore $I=[${c},${d}].$`\n } else if (test === 2) {\n texte += `$I=]${a},${b}]\\\\cap[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]${a},${b}]$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += `We observe that $[${c},${d}]\\\\subset ]${a},${b}]$ therefore $I=[${c},${d}].$`\n } else if (test === 3) {\n texte += `$I=[${a},${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $]${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += `We observe that $]${c},${d}]\\\\subset [${a},${b}]$ therefore $I=]${c},${d}].$`\n } else if (test === 4) {\n texte += `$I=[${a},${b}[\\\\cap]${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += `We observe that $]${c},${d}[\\\\subset [${a},${b}[$ therefore $I=]${c},${d}[.$`\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cap[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}[$ and in $[${c},${d}[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += `We observe that $[${c},${d}[\\\\subset [${a},${b}[$ therefore $I=[${c},${d}[.$`\n } else {\n texte += `$I=]${a},${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}]$ and in $[${c},${d}[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both blue and red.<br>'\n texteCorr += `We observe that $]${c},${d}]\\\\subset ]${a},${b}]$ therefore $I=]${c},${d}].$`\n }\n\n break\n case 6:// Union de deux intervalles fermés dont un inclus dans l'autre\n a = randint(1, 15)\n e = a + 15\n b = randint(e, 35)\n e = a + 1\n f = b - 10\n c = randint(e, f)\n e = c + 1\n d = randint(e, f)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(9, 0, b)\n C = point(5, 0, c)\n D = point(7, 0, d)\n if (test === 1) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n c1 = crochetD(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else if (test === 5) {\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetD(D, 'blue')\n } else {\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', -0.1)\n int2 = intervalle(C, D, 'blue', 0.1)\n texte = 'If possible, give a simplified writing of'\n\n if (test === 1) {\n texte += `$I=[${a},${b}]\\\\cup[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$ or $[${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n\n texteCorr += `We have $[${c},${d}]\\\\subset [${a},${b}]$ so $I=[${a},${b}]$`\n } else if (test === 2) {\n texte += `$I=]${a},${b}]\\\\cup[${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]${a},${b}]$ or $[${c},${d}]$ , or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n\n texteCorr += `We have $[${c},${d}]\\\\subset ]${a},${b}]$ so $I=]${a},${b}]$`\n } else if (test === 3) {\n texte += `$I=[${a},${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}]$or $]${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n\n texteCorr += `We have $]${c},${d}]\\\\subset [${a},${b}]$ so $I=[${a},${b}]$`\n } else if (test === 4) {\n texte += `$I=[${a},${b}[\\\\cup]${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}[$ or $]${c},${d}[$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n\n texteCorr += `We have $]${c},${d}[\\\\subset [${a},${b}[$ therefore $I=[${a},${b}[$`\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cup[${c},${d}[$`\n texteCorr = `<br>We are looking for the real numbers which are in $[${a},${b}[$ or $[${c},${d}[$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n\n texteCorr += `We have $[${c},${d}]\\\\subset [${a},${b}[$ so $I=[${a},${b}[$`\n } else {\n texte += `$I=]${a},${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]${a},${b}]$ or $]${c},${d}[$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n\n texteCorr += `We have $]${c},${d}]\\\\subset ]${a},${b}]$ so $I=]${a},${b}]$`\n }\n\n break\n case 7:// Intersection de deux intervalles avec infini\n a = randint(1, 15)\n e = a + 1\n b = randint(e, 25)\n e = b + 1\n c = randint(e, 35)\n e = c + 1\n d = randint(e, 45)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n B = point(5, 0, b)\n C = point(6, 0, c)\n D = point(10, 0, d)\n if (test === 1) {\n A = point(0, 0)\n D = point(10, 0, d)\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n A = point(0, 0)\n D = point(10, 0, d)\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n A = point(0, 0)\n D = point(10, 0, d)\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n A = point(0, 0, a)\n D = point(15, 0)\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n } else if (test === 5) {\n A = point(0, 0, a)\n D = point(15, 0)\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n } else {\n A = point(0, 0, a)\n D = point(15, 0)\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', 0)\n int2 = intervalle(C, D, 'blue', 0)\n\n texte = 'If possible, give a simplified writing of'\n if (test === 1) {\n texte += `$I=]-\\\\infty,${b}] \\\\cap [${c},${d}].$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]-\\\\infty,${b}]$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += 'We observe that the two intervals are disjoint so no real belongs to the two sets.<br>'\n texteCorr += '$I=\\\\emptyset$'\n } else if (test === 2) {\n texte += `$I=]-\\\\infty,${b}] \\\\cap [${c},${d}].$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]-\\\\infty,${b}]$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += 'We observe that the two intervals are disjoint so no real belongs to the two sets.<br>'\n texteCorr += '$I=\\\\emptyset$'\n } else if (test === 3) {\n texte += `$I=]-\\\\infty,${b}]\\\\cap]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]-\\\\infty,${b}]$ and in $]${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += 'We observe that the two intervals are disjoint so no real belongs to the two sets.<br>'\n texteCorr += '$I=\\\\emptyset$'\n } else if (test === 4) {\n texte += `$I=[${a},${b}[\\\\cap]${c},+\\\\infty[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}[$ and in $]${c},+\\\\infty[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += '$I=\\\\emptyset$'\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cap[${c},+\\\\infty[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $[${a},${b}[$ and in $[${c},+\\\\infty[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += '$I=\\\\emptyset$'\n } else {\n texte += `$I=]${a},${b}]\\\\cap]${c},+\\\\infty[$`\n texteCorr = `<br>We are looking for the real numbers which are both in $]${a},${b}]$ and in $]${c},+\\\\infty[$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += '$I=\\\\emptyset$'\n }\n break\n case 8:// Union de deux intervalles un fermé et l'autre semi fermé, et disjoints\n a = randint(1, 15)\n e = a + 1\n b = randint(e, 25)\n e = b + 1\n c = randint(e, 35)\n e = c + 1\n d = randint(e, 45)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n B = point(5, 0, b)\n C = point(6, 0, c)\n\n if (test === 1) {\n A = point(0, 0)\n D = point(10, 0, d)\n // c1 = hookG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 2) {\n A = point(0, 0)\n D = point(10, 0, d)\n // c1 = hookG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 3) {\n A = point(0, 0)\n D = point(10, 0, d)\n // c1 = hookG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetG(D, 'blue')\n } else if (test === 4) {\n A = point(0, 0, a)\n D = point(15, 0)\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n // c4 = hookD(D, 'blue')\n } else if (test === 5) {\n A = point(0, 0, a)\n D = point(15, 0)\n c1 = crochetD(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n // c4 = hookD(D, 'blue')\n } else {\n A = point(0, 0, a)\n D = point(15, 0)\n c1 = crochetG(A, 'red')\n c2 = crochetG(B, 'red')\n c3 = crochetG(C, 'blue')\n // c4 = hookD(D, 'blue')\n }\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', 0)\n int2 = intervalle(C, D, 'blue', 0)\n texte = 'If possible, give a simplified writing of'\n if (test === 1) {\n texte += `$I=]-\\\\infty,${b}] \\\\cup [${c},${d}].$`\n texteCorr = `<br>We are looking for the real numbers which are in $]-\\\\infty,${b}]$ or in $[${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red<br>'\n texteCorr += 'We observe that the two intervals are disjoint therefore <br>'\n texteCorr += `$I=]-\\\\infty,${b}] \\\\cup [${c},${d}]$`\n } else if (test === 2) {\n texte += `$I=]-\\\\infty,${b}] \\\\cup [${c},${d}].$`\n texteCorr = `<br>We are looking for the real numbers which are in $]-\\\\infty,${b}]$ or in $[${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red<br>'\n texteCorr += 'We observe that the two intervals are disjoint therefore <br>'\n texteCorr += `$I=]-\\\\infty,${b}] \\\\cup [${c},${d}]$`\n } else if (test === 3) {\n texte += `$I=]-\\\\infty,${b}]\\\\cup]${c},${d}]$`\n texteCorr = `<br>We are looking for the real numbers which are in $]-\\\\infty,${b}]$ or in $[${c},${d}]$, or in both. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n texteCorr += 'We observe that the two intervals are disjoint therefore <br>'\n texteCorr += `$I=]-\\\\infty,${b}] \\\\cup [${c},${d}]$`\n } else if (test === 4) {\n texte += `$I=[${a},${b}[\\\\cup]${c},+\\\\infty[$`\n texteCorr = '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n texteCorr += 'We observe that the two intervals are disjoint therefore <br>'\n texteCorr += `$I=[${a},${b}[\\\\cup]${c},+\\\\infty[$`\n } else if (test === 5) {\n texte += `$I=[${a},${b}[\\\\cup[${c},+\\\\infty[$`\n texteCorr = '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n texteCorr += 'We observe that the two intervals are disjoint therefore <br>'\n texteCorr += `$I=[${a},${b}[\\\\cup[${c},+\\\\infty[$`\n } else {\n texte += `$I=]${a},${b}]\\\\cup]${c},+\\\\infty[$`\n texteCorr = '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red.<br>'\n texteCorr += 'We observe that the two intervals are disjoint therefore <br>'\n texteCorr += `$I=[${a},${b}]\\\\cup]${c},+\\\\infty[$`\n }\n\n break\n case 9:\n a = randint(1, 15)\n e = a + 4\n b = randint(29, 45)\n e = b - 1\n c = randint(16, e)\n e = b + 1\n d = randint(e, 65)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(6, 0, b)\n C = point(5, 0, c)\n D = point(9, 0, d)\n c1 = crochetG(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetD(C, 'blue')\n c4 = crochetG(D, 'blue')\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', -0.1)\n int2 = intervalle(C, D, 'blue', 0.1)\n texte = `If possible, give a simplified writing of $I=]${a},${b}[ \\\\cap [${c},${d}].$`\n\n texteCorr = `<br>We are looking for the real numbers which are both in $]${a},${b}[$ and in $[${c},${d}]$. `\n texteCorr += '<br>We look at the part of the interval which is colored both in blue and in red:<br>'\n texteCorr += `$I=[${c},${b}[$`\n break\n case 10:\n a = randint(1, 15)\n e = a + 4\n b = randint(29, 45)\n e = b - 1\n c = randint(16, e)\n e = b + 1\n d = randint(e, 65)\n s = segment(0, 0, 10, 0)\n s.styleExtremites = '->'\n\n A = point(2, 0, a)\n B = point(6, 0, b)\n C = point(5, 0, c)\n D = point(9, 0, d)\n c1 = crochetG(A, 'red')\n c2 = crochetD(B, 'red')\n c3 = crochetG(C, 'blue')\n c4 = crochetD(D, 'blue')\n int = intervalle(X1, X2, 'black', 0)\n int1 = intervalle(A, B, 'red', -0.1)\n int2 = intervalle(C, D, 'blue', 0.1)\n texte = `If possible, give a simplified writing of $I=]${a},${b}[ \\\\cup ]${c},${d}[.$`\n\n texteCorr = `<br>We look for the real numbers which are in $]${a},${b}[$, or in $]${c},${d}[$. `\n texteCorr += '<br>We therefore look at the part of the interval which is colored, either in blue, or in red, or in blue and red:<br>'\n texteCorr += `$I=]${a},${d}[$`\n break\n }\n\n let aRemplacer = texteCorr.split('=')[1]\n aRemplacer = aRemplacer.replace('$', '')\n texteCorr = texteCorr.split('=')[0] + '=$'\n texteCorr += `$${miseEnEvidence(aRemplacer)}$. `\n\n texteCorr += mathalea2d({\n xmin: -2,\n ymin: -2,\n xmax: 15,\n ymax: 2\n }, int, int1, int2, c1, c2, c3, c4)\n if (this.listeQuestions.indexOf(texte) === -1) { // 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 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