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{"version":3,"file":"2F20-2-qscNmOra.js","sources":["../../src/exercices/2e/2F20-2.js"],"sourcesContent":["import { choice, combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { miseEnEvidence } from '../../lib/outils/embellissements'\nimport { simplificationDeFractionAvecEtapes } from '../../lib/outils/deprecatedFractions.js'\nimport {\n ecritureAlgebrique,\n ecritureParentheseSiNegatif,\n reduireAxPlusB,\n reduirePolynomeDegre3, rienSi1\n} from '../../lib/outils/ecritures'\nimport { ajouteChampTexteMathLive } from '../../lib/interactif/questionMathLive.js'\nimport { texteCentre } from '../../lib/format/miseEnPage.js'\nimport { sp } from '../../lib/outils/outilString.js'\nimport { pgcd } from '../../lib/outils/primalite'\nimport Exercice from '../deprecatedExercice.js'\nimport FractionEtendue from '../../modules/FractionEtendue.js'\nimport { fraction, obtenirListeFractionsIrreductibles, obtenirListeFractionsIrreductiblesFaciles } from '../../modules/fractions.js'\nimport {\n listeQuestionsToContenu, randint\n} from '../../modules/outils.js'\nimport { setReponse } from '../../lib/interactif/gestionInteractif.js'\nexport const titre = 'Calculate coordinates of points belonging to a curve knowing the abscissa or the ordinate'\nexport const interactifReady = true\nexport const interactifType = 'mathLive'\nexport const dateDePublication = '24/09/2022'\nexport const dateDeModifImportante = '07/11/2023'\n/**\n* Répondre à des questions sur les fonctions.\n* @author Gilles Mora\n*/\n\nexport const uuid = 'ec059'\nexport const ref = '2F20-2'\nexport default function CalculPointSurCourbe () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.sup = 1\n this.sup2 = 1\n this.consigne = ''\n this.spacing = 1\n this.nbQuestions = 2\n this.nbQuestionsModifiable = true\n this.nouvelleVersion = function () {\n this.autoCorrection = []\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n let typesDeQuestionsDisponibles\n switch (this.sup) {\n case 1:\n typesDeQuestionsDisponibles = ['refined']\n break\n case 2:\n typesDeQuestionsDisponibles = ['polynomial']\n break\n case 3:\n typesDeQuestionsDisponibles = ['a/x+b']\n break\n case 4:\n typesDeQuestionsDisponibles = ['refined', 'polynomial', 'a/x+b']\n break\n\n //\n }\n const listeTypeDeQuestions = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n let sousChoix\n if (this.sup2 === 1) {\n sousChoix = combinaisonListes([0], this.nbQuestions) // pour choisir aléatoirement des questions dans chaque catégorie\n } else if (this.sup2 === 2) {\n sousChoix = combinaisonListes([1], this.nbQuestions)\n } else {\n sousChoix = combinaisonListes([0, 1], this.nbQuestions)\n }\n\n const nomF = [\n ['f'], ['g'], ['h'], ['u'],\n ['v'], ['w']\n ]\n const pointM = [\n ['M'], ['N'], ['P'], ['R'],\n ['S'], ['T']\n ]\n for (let i = 0, texte, texteCorr, nom, point, x, y, a, b, c, abs, f, ord, f1, fa, fb, fractionA, fractionB, fractionC, fractionb, fractionb2, fractionc, enonce, correction, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n // we only choose numbers between 1 and 20\n x = randint(-9, 9, [0, 1, -1])\n y = randint(-9, 9, [x, 0])\n\n switch (listeTypeDeQuestions[i]) {\n case 'refined':\n switch (sousChoix[i]) { // sousChoix[i]\n case 0:\n a = randint(-12, 12, [0, 1])\n b = randint(-12, 12, 0)\n abs = randint(-12, 12, 0)\n ord = a * abs + b\n nom = choice(nomF)\n point = choice(pointM)\n if (choice([true, false])) {\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduireAxPlusB(a, b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>$${point}$ is the point of $\\\\mathscr{C}$ with abscissa $${abs}$. <br>What is its ordinate?`\n correction = `Since the point $${point}$ belongs to $\\\\mathscr{C}$, its ordinate is the image of its abscissa.<br>$${nom}(${abs})=${a}\\\\times ${ecritureParentheseSiNegatif(abs)}${ecritureAlgebrique(b)}=${ord}$.<br>The ordinate of the point $${point}$ is $${ord}$. `\n\n setReponse(this, i, ord)\n } else {\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduireAxPlusB(a, b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>$${point}$ is the point of $\\\\mathscr{C}$ with ordinate $${ord}$.<br>What is its abscissa?`\n correction = `$${nom}$ is an affine function (non-constant), so there exists a unique point whose ordinate is $${ord}$.<br>Since the point $${point}$ belongs to $\\\\mathscr{C}$, its abscissa is the antecedent of its ordinate.<br>We therefore look for $x$ such that $${nom}(x)=${ord}$, that is to say $${reduireAxPlusB(a, b)}=${ord}$.<br>`\n if (b < 0) {\n correction += `\n $\\\\begin{aligned}\n ${reduireAxPlusB(a, b)}&=${ord}\\\\\\\\\n ${reduireAxPlusB(a, b)}+${miseEnEvidence(-b)}&=${ord}+${miseEnEvidence(-b)}\\\\\\\\\n ${a}x&=${ord - b} \\\\\\\\\n x&=\\\\dfrac{${ord - b}}{${a}} \\\\\\\\\n x&=${abs}\n \\\\end{aligned}$<br>`\n } else {\n correction += `\n $\\\\begin{aligned}\n ${reduireAxPlusB(a, b)}&=${ord}\\\\\\\\\n ${reduireAxPlusB(a, b)}-${miseEnEvidence(b)}&=${ord}-${miseEnEvidence(b)}\\\\\\\\\n ${a}x&=${ord - b} \\\\\\\\\n x&=\\\\dfrac{${ord - b}}{${a}} \\\\\\\\\n x&=${abs}\n \\\\end{aligned}$<br>`\n }\n correction += `The abscissa of the point $${point}$ is $${abs}$. `\n setReponse(this, i, abs)\n }\n\n break\n case 1:\n a = randint(-10, 10, [0, 1])\n b = randint(-10, 10, 0)\n f = choice(obtenirListeFractionsIrreductibles())\n f1 = new FractionEtendue(a * f.n + b * f.d, f.d)// ordonnée du point\n fractionb = new FractionEtendue(b * f1.d, f1.d)\n fractionA = new FractionEtendue(f.n - b * f.d, f.d)\n fractionB = new FractionEtendue(b * f.d, f.d)\n fractionC = new FractionEtendue(f.n - b * f.d, a * f.d)// abscisse du point\n nom = choice(nomF)\n point = choice(pointM)\n if (choice([true, false])) {\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduireAxPlusB(a, b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>$${point}$ is the point of $\\\\mathscr{C}$ with abscissa $${f.texFraction}$.<br>What is its ordinate?`\n correction = `Since the point $${point}$ belongs to $\\\\mathscr{C}$, its ordinate is the image of its abscissa.<br>$${nom}\\\\left(${f.texFraction}\\\\right)=$`\n if (a === -1 || a === 1) {\n correction += `$${rienSi1(a)}${f.texFraction}${ecritureAlgebrique(b)}=${rienSi1(a)}${f.texFraction}${fractionb.ecritureAlgebrique} =\\\\dfrac{${rienSi1(a)}${f.n}${ecritureAlgebrique(b * f.d)}}{${f.d}}=${f1.texFraction}${simplificationDeFractionAvecEtapes(a * f.n + b * f.d, f.d)}$.<br>The ordinate of point $${point}$ is $${f1.texFractionSimplifiee}$. `\n } else {\n correction += `$${a}\\\\times ${f.texFraction}${ecritureAlgebrique(b)}=${a}\\\\times${f.texFraction}${fractionb.ecritureAlgebrique} =\\\\dfrac{${a}\\\\times${f.n}${ecritureAlgebrique(b * f.d)}}{${f.d}}=${f1.texFraction}${simplificationDeFractionAvecEtapes(a * f.n + b * f.d, f.d)}$.<br>The ordinate of the point $${point}$ is $${f1.texFractionSimplifiee}$. `\n }\n setReponse(this, i, f1, { formatInteractif: 'fractionEqual' })\n } else {\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduireAxPlusB(a, b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>$${point}$ is the point of $\\\\mathscr{C}$ with ordinate $${f.texFraction}$. <br>What is its abscissa?`\n\n correction = `$${nom}$ is an affine function (non-constant), so there exists a unique point whose ordinate is $${f.texFraction}$.<br>Since the point $${point}$ belongs to $\\\\mathscr{C}$, its abscissa is the antecedent of its ordinate.<br>We therefore look for $x$ such that $${nom}(x)=${f.texFraction}$, that is to say $${reduireAxPlusB(a, b)}=${f.texFraction}$.<br>`\n if (b < 0) {\n correction += `\n $\\\\begin{aligned}\n ${reduireAxPlusB(a, b)}&=${f.texFraction}\\\\\\\\\n ${reduireAxPlusB(a, b)}+${miseEnEvidence(-b)}&=${f.texFraction}+${miseEnEvidence(-b)}\\\\\\\\\n ${a}x&=${f.texFraction}+${fractionB.oppose().texFraction} \\\\\\\\\n ${a}x&=${fractionA.texFraction}\\\\\\\\\n ${a}x\\\\div${miseEnEvidence(ecritureParentheseSiNegatif(a))} &=${fractionA.texFraction}\\\\div${miseEnEvidence(ecritureParentheseSiNegatif(a))} \\\\\\\\\n x&=${fractionC.texFraction}${fractionC.texSimplificationAvecEtapes()}\n \\\\end{aligned}$<br>`\n } else {\n correction += `\n $\\\\begin{aligned}\n ${reduireAxPlusB(a, b)}&=${f.texFraction}\\\\\\\\\n ${reduireAxPlusB(a, b)}-${miseEnEvidence(b)}&=${f.texFraction}-${miseEnEvidence(b)}\\\\\\\\\n ${a}x&=${f.texFraction}-${fractionB.texFraction} \\\\\\\\\n ${a}x&=${fractionA.texFraction}\\\\\\\\\n ${a}x\\\\div${miseEnEvidence(ecritureParentheseSiNegatif(a))} &=${fractionA.texFraction}\\\\div${miseEnEvidence(ecritureParentheseSiNegatif(a))} \\\\\\\\\n x&=${fractionC.texFraction}${fractionC.texSimplificationAvecEtapes()}\n \\\\end{aligned}$<br>`\n }\n correction += `The abscissa of the point $${point}$ is $${fractionC.texFractionSimplifiee}$. `\n setReponse(this, i, fractionC, { formatInteractif: 'fractionEqual' })\n }\n\n break\n }\n\n break\n case 'polynomial':\n switch (sousChoix[i]) { // ax^2+bx+c\n case 0:\n if (choice([true, false])) {\n a = randint(-10, 10, 0)\n b = randint(-10, 10, 0)\n c = randint(-10, 10)\n abs = randint(-9, 9)\n ord = a * abs ** 2 + b * abs + c\n nom = choice(nomF)\n point = choice(pointM)\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduirePolynomeDegre3(0, a, b, c)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>$${point}$ is the point of $\\\\mathscr{C}$ with abscissa $${abs}$. <br>What is its ordinate?`\n\n correction = `Since the point $${point}$ belongs to $\\\\mathscr{C}$, its ordinate is the image of its abscissa.<br>`\n if (a !== 1) {\n correction += `$${nom}(${abs})=${a}\\\\times ${ecritureParentheseSiNegatif(abs)}^2${ecritureAlgebrique(b)}\\\\times${ecritureParentheseSiNegatif(abs)}${c === 0 ? '' : `${ecritureAlgebrique(c)}`}=${a * abs ** 2}${ecritureAlgebrique(b * abs)}${c === 0 ? '' : `${ecritureAlgebrique(c)}`}=${ord}$.<br>The ordinate of the point $${point}$ is $${ord}$. `\n } else {\n correction += `$${nom}(${abs})= ${ecritureParentheseSiNegatif(abs)}^2${ecritureAlgebrique(b)}\\\\times${ecritureParentheseSiNegatif(abs)}${c === 0 ? '' : `${ecritureAlgebrique(c)}`}=${a * abs ** 2}${ecritureAlgebrique(b * abs)}${c === 0 ? '' : `${ecritureAlgebrique(c)}`}=${ord}$.<br>The ordinate of the point $${point}$ is $${ord}$. `\n }\n setReponse(this, i, ord)\n } else {\n a = randint(-10, 10, 0)\n b = randint(-10, 10, 0)\n c = randint(-10, 10, 0)\n abs = randint(-9, 16)\n ord = a * abs + c\n nom = choice(nomF)\n point = choice(pointM)\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduirePolynomeDegre3(0, a, 0, c)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>Are there points of $\\\\mathscr{C}$ with ordinate $${ord}$? <br>If yes, what are the possible x-coordinates of these points?`\n if (this.interactif) {\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduirePolynomeDegre3(0, a, 0, c)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>Are there points of $\\\\mathscr{C}$ with ordinate $${ord}$? <br>If yes, what are the possible x-coordinates of these points?<br>Write the values in ascending order separated by a semicolon or \"None\" if there is none. `\n }\n\n correction = ` If a point of $\\\\mathscr{C}$ has $${ord}$ as ordinate, its abscissa is an antecedent of $${ord}$.<br>`\n\n correction += ` We therefore look for $x$ such that $${nom}(x)=${ord}$, that is to say $${reduirePolynomeDegre3(0, a, 0, c)}=${ord}$.<br>We solve this equation by isolating the square, that is to say by writing it $x^2=${abs}$. <br>`\n if (abs === 0) {\n correction += ` This equation has only one solution: $0$.<br>We deduce that there exists a unique point of $\\\\mathscr{C}$ with $${ord}$ as its ordinate: its abscissa is $0$. `\n setReponse(this, i, 0)\n }\n if (abs < 0) {\n correction += ` This equation has no solution.<br>We deduce that there is no point in $\\\\mathscr{C}$ with $${ord}$ as ordinate. `\n setReponse(this, i, ['None', 'none'], { formatInteractif: 'text' })\n }\n if (abs > 0) {\n if (abs === 1 || abs === 4 || abs === 9 || abs === 16) {\n correction += ` This equation has two solutions: $-\\\\sqrt{${abs}}=-${Math.sqrt(abs)}$ and $\\\\sqrt{${abs}}=${Math.sqrt(abs)}$.<br>We deduce that there exist two points of $\\\\mathscr{C} $ having as ordinate $${ord}$.<br>The abscissa of these points are: $-${Math.sqrt(abs)}$ and $${Math.sqrt(abs)}$. `\n setReponse(this, i, [`-${Math.sqrt(abs)},${Math.sqrt(abs)}`])\n } else {\n correction += ` This equation has two solutions: $-\\\\sqrt{${abs}}$ and $\\\\sqrt{${abs}}$.<br>We deduce that there exist two points of $\\\\mathscr{C}$ with ordinate $ ${ord}$.<br>The abscissa of these points are: $-\\\\sqrt{${abs}}$ and $\\\\sqrt{${abs}}$. `\n setReponse(this, i, [`-\\\\sqrt{${abs}};\\\\sqrt{${abs}}`])\n }\n }\n }\n\n break\n\n case 1:// ax^2+bx+c\n a = randint(-2, 2, 0)\n b = randint(-3, 3)\n c = randint(-2, 2, 0)\n f = choice(obtenirListeFractionsIrreductiblesFaciles())\n f1 = fraction(a * f.n ** 2 + b * f.n * f.d + c * f.d ** 2, f.d ** 2)// ordonnée de A\n nom = choice(nomF)\n point = choice(pointM)\n fractionb = new FractionEtendue(b * f.n, f.d)\n fractionb2 = new FractionEtendue(b * f.n * f.d, f.d ** 2)\n fractionc = new FractionEtendue(c * f.d ** 2, f.d ** 2)\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}$ by:${texteCentre(`$${nom}(x)=${reduirePolynomeDegre3(0, a, b, c)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference .<br>$${point}$ is the point of $\\\\mathscr{C}$ with abscissa $${f.texFraction}$. <br>What is its ordinate?`\n correction = `Since the point $${point}$ belongs to $\\\\mathscr{C}$, its ordinate is the image of its abscissa.<br>`\n if (a !== 1) {\n if (b === 0) {\n correction += `\n $${nom}\\\\left(${f.texFraction}\\\\right)=${a}\\\\times \\\\left(${f.texFraction}\\\\right)^2${ecritureAlgebrique(c)}\n =\\\\dfrac{${a}\\\\times ${f.n ** 2}}{${f.d ** 2}}${ecritureAlgebrique(c)}\n =\\\\dfrac{${a * f.n ** 2}}{${f.d ** 2}}${fractionc.ecritureAlgebrique}\n = ${f1.texFractionSimplifiee}$`\n } else {\n correction += `\n $${nom}\\\\left(${f.texFraction}\\\\right)=${a}\\\\times \\\\left(${f.texFraction}\\\\right)^2${ecritureAlgebrique(b)}\\\\times${f.texFraction}${ecritureAlgebrique(c)}\n =\\\\dfrac{${a}\\\\times ${f.n ** 2}}{${f.d ** 2}}${fractionb.ecritureAlgebrique}${ecritureAlgebrique(c)}\n =\\\\dfrac{${a * f.n ** 2}}{${f.d ** 2}}${fractionb2.ecritureAlgebrique}${fractionc.ecritureAlgebrique}\n =${f1.texFractionSimplifiee}$`\n }\n } else {\n if (b === 0) {\n correction += `$${nom}\\\\left(${f.texFraction}\\\\right)=\\\\left(${f.texFraction}\\\\right)^2${ecritureAlgebrique(c)}=\\\\dfrac{${f.n ** 2}}{${f.d ** 2}}${ecritureAlgebrique(c)}=\\\\dfrac{${f.n ** 2}}{${f.d ** 2}}${fractionc.ecritureAlgebrique}=${f1.texFractionSimplifiee}$`\n } else {\n correction += `$${nom}\\\\left(${f.texFraction}\\\\right)=\\\\left(${f.texFraction}\\\\right)^2${ecritureAlgebrique(b)}\\\\times${f.texFraction}${ecritureAlgebrique(c)}=\\\\dfrac{ ${f.n ** 2}}{${f.d ** 2}}${fractionb.ecritureAlgebrique}${ecritureAlgebrique(c)}=\\\\dfrac{${a * f.n ** 2}}{${f.d ** 2}}${fractionb2.ecritureAlgebrique}${fractionc.ecritureAlgebrique}=${f1.texFractionSimplifiee} $`\n }\n }\n correction += `<br> The ordinate of the point $${point}$ is $${f1.texFractionSimplifiee}$. `\n setReponse(this, i, f1, { formatInteractif: 'fractionEqual' })\n break\n }\n\n break\n\n case 'a/x+b':\n\n switch (sousChoix[i]) { // sousChoix[i] = randint(0, 5)\n case 0:\n if (choice([true, false])) {\n a = randint(-9, 9, 0)\n b = randint(-9, 9, 0)\n abs = randint(-9, 9, [0, 1, -1])\n nom = choice(nomF)\n point = choice(pointM)\n while (pgcd(a, abs) !== 1) { a = randint(-9, 9, 0) }\n f1 = new FractionEtendue(a + b * abs, abs)// ordonnée de A\n fa = new FractionEtendue(a, abs)\n fb = new FractionEtendue(b * abs, abs)\n\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}^*$ by:${texteCentre(`$${nom}(x)=\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference frame.<br>$${point}$ is the point of $\\\\mathscr{C}$ with abscissa $${abs}$. <br>What is its ordinate?`\n\n correction = `Since the point $${point}$ belongs to $\\\\mathscr{C}$, its ordinate is the image of its abscissa.<br>$${nom}(${abs})=\\\\dfrac{${a}}{${abs}}${ecritureAlgebrique(b)}=${fa.texFractionSimplifiee}${ecritureAlgebrique(b)}=${fa.texFractionSimplifiee}${fb.ecritureAlgebrique} =${f1.texFractionSimplifiee}$<br>The ordinate of the point $${point}$ is $${f1.texFractionSimplifiee}$. `\n setReponse(this, i, f1, { formatInteractif: 'fractionEqual' })\n } else {\n a = randint(-10, 10, 0)\n b = randint(-9, 9, 0)\n ord = randint(-9, 9, [0, 1, -1, b])\n nom = choice(nomF)\n point = choice(pointM)\n f1 = new FractionEtendue(a, ord - b)\n\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}^*$ by:${texteCentre(`$${nom}(x)=\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a coordinate system.<br>Are there points of $\\\\mathscr{C}$ with ordinate $${ord}$? <br>If yes, what are the possible x-coordinates of these points?`\n\n correction = ` If a point of $\\\\mathscr{C}$ has $${ord}$ as ordinate, its abscissa is an antecedent of $${ord}$.<br>`\n\n correction += ` We therefore look for $x$ such that $${nom}(x)=${ord}$, that is to say $\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}=${ord}$.<br>`\n\n correction += `For $x\\\\neq 0$, <br>$\\\\begin{aligned}\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}&=${ord}\\\\\\\\\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}${miseEnEvidence(ecritureAlgebrique(-b))}&=${ord}${miseEnEvidence(ecritureAlgebrique(-b))}\\\\\\\\\\\\dfrac{${a}}{x}&=${ord - b}\\\\\\\\x\\\\times${ecritureParentheseSiNegatif(ord - b)} &=${a} ${sp(4)}{\\\\text{(Cross product)}}\\\\\\\\x&=${f1.texFraction}${f1.texSimplificationAvecEtapes()}\\\\\\\\\\\\ end{aligned}$<br>A single point of $\\\\mathscr{C}$ has ordinate $${ord}$. Its abscissa is $${f1.texFractionSimplifiee}$. `\n setReponse(this, i, f1, { formatInteractif: 'fractionEqual' })\n }\n\n break\n\n case 1:\n if (choice([true, false])) {\n a = randint(-9, 9, 0)\n b = randint(-9, 9, 0)\n abs = choice(obtenirListeFractionsIrreductiblesFaciles())\n\n f1 = new FractionEtendue(a * abs.d + b * abs.n, abs.n)// ordonnée de A\n fa = new FractionEtendue(a * abs.d, abs.n)\n fb = new FractionEtendue(b * abs.n, abs.n)\n\n nom = choice(nomF)\n point = choice(pointM)\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}^*$ by:${texteCentre(`$${nom}(x)=\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a reference frame.<br>$${point}$ is the point of $\\\\mathscr{C}$ with abscissa $${abs.texFraction}$.<br>What is its ordinate?`\n\n correction = `Since the point $${point}$ belongs to $\\\\mathscr{C}$, its ordinate is the image of its abscissa.<br>$${nom}\\\\left(${abs.texFraction}\\\\right)=\\\\dfrac{${a}}{${abs.texFraction} }${ecritureAlgebrique(b)}=${a}\\\\times \\\\dfrac{${abs.d}}{${abs.n}}${ecritureAlgebrique(b)}=${fa.texFractionSimplifiee}${ecritureAlgebrique(b)}=${f1.texFractionSimplifiee}$<br>The ordinate of the point $${point}$ is $${f1.texFractionSimplifiee}$. `\n setReponse(this, i, f1, { formatInteractif: 'fractionEqual' })\n } else {\n a = randint(-9, 9, 0)\n b = randint(-9, 9, 0)\n ord = choice(obtenirListeFractionsIrreductiblesFaciles())\n fa = fraction(ord.n - b * ord.d, ord.d)\n f1 = fraction(a * ord.d, ord.n - b * ord.d)\n nom = choice(nomF)\n point = choice(pointM)\n enonce = `Let $${nom}$ be the function defined on $\\\\mathbb{R}^*$ by:${texteCentre(`$${nom}(x)=\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}$`)}We note $\\\\mathscr{C}$ the curve representative of the function $${nom}$ in a coordinate system.<br>Are there points of $\\\\mathscr{C}$ with ordinate $${ord.texFraction}$? <br>If yes, what are the possible x-coordinates of these points?`\n\n correction = ` If a point of $\\\\mathscr{C}$ has $${ord.texFraction}$ as ordinate, its abscissa is an antecedent of $${ord.texFraction}$.<br>`\n\n correction += ` We therefore look for $x$ such that $${nom}(x)=${ord.texFraction}$, that is to say $\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}=${ord.texFraction}$.<br>`\n\n correction += `For $x\\\\neq 0$, <br>$\\\\begin{aligned}\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}&=${ord.texFraction}\\\\\\\\\\\\dfrac{${a}}{x}${ecritureAlgebrique(b)}${miseEnEvidence(ecritureAlgebrique(-b))}&=${ord.texFraction}${miseEnEvidence(ecritureAlgebrique(-b))}\\\\\\\\\\\\dfrac{${a}}{x}&=${fa.texFraction}\\\\\\\\x\\\\times${ecritureParentheseSiNegatif(ord.n - b * ord.d)} &=${a}\\\\times ${ord.d} ${sp(4)}{\\\\text{(Cross product)}}\\\\\\\\x&=${f1.texFraction}${f1.texSimplificationAvecEtapes()}\\\\ end{aligned}$<br>A single point of $\\\\mathscr{C}$ has ordinate $${ord.texFraction}$. Its abscissa is $${f1.texFractionSimplifiee}$. `\n setReponse(this, i, f1, { formatInteractif: 'fractionEqual' })\n }\n\n break\n }\n break\n }\n\n texte = enonce\n texte += ' ' + ajouteChampTexteMathLive(this, i, 'inline width01 keyboardBase alphanumeric')\n // text += ' ' + addMathLiveTextField(this, i)\n texteCorr = correction\n\n if (this.questionJamaisPosee(i, listeTypeDeQuestions[i], x, y, sousChoix[i])) {\n // If the question has never been asked, we create another one\n this.listeQuestions.push(texte)\n this.listeCorrections.push(texteCorr)\n i++\n }\n cpt++\n }\n listeQuestionsToContenu(this)\n }\n this.besoinFormulaireNumerique = [\n 'Choice of questions',\n 4,\n '1: Affine function\\n2: Polynomial of degree 2 \\n3: Function a/x+b \\n4: Combination'\n ]\n this.besoinFormulaire2Numerique = ['Choice of questions', 3, '1: Integer values\\n2: Fractional values\\n3: 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