https://mathalea.fr/alea/assets/1A-C01-1-BcQrBftq.js

1import{a8 as T,K as q,d as K,i as t,g as I,t as r,O as A}from"./main-DH_YCWhC.js";/* empty css                         */import"./vendors/svelte-Bwj9ksTZ.js";import"./vendors/clsx-B-dksMZM.js";import"./vendors/esm-env-rsSWfq8L.js";import"./vendors/ua-parser-js-CdzcYDua.js";import"./vendors/apigeom-gBVORf3O.js";import"./vendors/katex-WsJDI_Zh.js";import"./vendors/xstate-Br8Re68l.js";import"./vendors/decimal.js-CNo3oIkL.js";import"./vendors/seedrandom-BYm4YTZX.js";import"./json/referentielStaticCH-CsB2sKLl.js";import"./json/referentielStaticFR-BpfcFBXH.js";import"./json/referentielStaticFRSessions-C16kvIal.js";import"./json/uuidsToUrlFR-DwveZ5MS.js";import"./vendors/mathlive-BBnTWQtg.js";import"./vendors/cortex-js_compute-engine-DypxK7Yf.js";import"./vendors/tex2typst-jlGLuCVx.js";import"./vendors/bugsnag_js-BYNXup-q.js";import"./vendors/bugsnag_browser-7_9w3i51.js";import"./vendors/jszip-CpCWtGZo.js";import"./json/ffjm.manifest-DtGgQ479.js";import"./index-DO4bxqzJ.js";import"./json/codeToLevelList-DBeELuO9.js";import"./json/codeToThemeList-Cl5sdfh8.js";import"./vendors/mixer_postmessage-rpc-JyZjM7pP.js";import"./vendors/eventemitter3-COjgItKg.js";import"./vendors/scratch2latex_scratch-core-SbdipC3l.js";import"./vendors/scratchblocks-C-s4qXfm.js";import"./json/refToUuidFR-DzGfFEU7.js";import"./json/refToUuidCH-amvDyhPQ.js";import"./json/referentielProfs-ZwqeFyNA.js";import"./json/uuidsRessources-DqCZDv09.js";import"./json/referentielBibliotheque-DwOqc9UA.js";import"./vendors/driver.js-CZ6E8Gep.js";import"./vendors/nunjucks-DPriE1Ie.js";import"./json/levelsThemesList-Bz_mwHyD.js";import"./json/levelsThemesListCH-DcH6YiLq.js";import"./json/referentiel2022CH--wUaSP5t.js";import"./json/referentiel2022FR-BXr5KUOC.js";import"./json/referentielGeometrieDynamique-DJ2qVZRa.js";import"./json/referentielRessources-DX6TJgTJ.js";import"./json/referentielsActivation-C_LdcjYr.js";import"./vendors/qrcode-Cm0245TE.js";import"./vendors/dijkstrajs-COg3n3zL.js";import"./vendors/codemirror_commands-CWGMp9X1.js";import"./vendors/codemirror_state-Cx7HU1Zt.js";import"./vendors/marijn_find-cluster-break-D2nwzJv4.js";import"./vendors/codemirror_view-Tb1Gu_Mm.js";import"./vendors/style-mod-Bs6eFhZE.js";import"./vendors/w3c-keyname-Vcq4gwWv.js";import"./vendors/crelt-C8TCjufn.js";import"./vendors/codemirror_language-DaAstm-P.js";import"./vendors/lezer_common-DhRCl6En.js";import"./vendors/lezer_highlight-B4Mv6ylJ.js";import"./vendors/codemirror_legacy-modes-B5BjspY4.js";import"./vendors/codemirror_search-dmKh6PUF.js";import"./vendors/codemirror_theme-one-dark-BrRIqWoF.js";import"./json/referentielAppsTierce-CsUCmKVo.js";import"./json/mobileMenu-DXeVrjL_.js";import"./vendors/sortablejs-BzJVkfZx.js";import"./json/carouselContent--2Fj10Gb.js";import"./json/codeToLevelListCH-iYbfof6A.js";import"./json/quickLinks-BIX1zke_.js";import"./vendors/myriaddreamin_typst.ts-C0zVWBvA.js";import"./vendors/myriaddreamin_typst-ts-web-compiler-DOxzHalq.js";import"./vendors/myriaddreamin_typst-ts-renderer-DoiTUA5o.js";import"./json/quizzBackgrounds-C1JhySzk.js";import"./vendors/socket.io-client-BF4DEest.js";import"./vendors/engine.io-client-QJOhq_6L.js";import"./vendors/engine.io-parser-DPmA-eyr.js";import"./vendors/socket.io_component-emitter-Dkula2eQ.js";import"./vendors/socket.io-parser-DxYZWorP.js";const Zt="7f979",ti={"fr-fr":["1A-C01-1"],"fr-ch":[]},ii=!0,oi=!0,ri="qcmMono",ei="Comparer deux nombres",si="02/09/2025",ni="02/10/2026";class ci extends T{constructor(){super(),this.typeExercice="simple",this.nbQuestions=1,this.spacing=1.5,this.spacingCorr=1.5,this.formatChampTexte=q.clavierDeBase,this.versionQcmDisponible=!0,this.versionQcm=!1,this.tip=`
2  <p style="margin: 0 0 10px 0;">
3    Il faut penser aux fonctions de référence, en particulier :
4  </p>
5  <ul style="list-style-type: disc; padding-left: 1.5em; margin: 0 0 14px 0; line-height: 2;">
6    <li>utiliser les variations de la <strong>fonction carré</strong> ;</li>
7    <li>utiliser les variations de la <strong>fonction inverse</strong>.</li>
8  </ul>
9  <a href="https://podeduc.apps.education.fr/video/143477-indice-automatisme-1-c01-1mp4/?is_iframe=true&autoplay=true" target="_blank"
10     style="display:inline-flex; align-items:center; gap:6px;
11            padding:6px 14px; border:1px solid #b3cde8; border-radius:6px;
12            font-size:13px; font-weight:500;

12 color:#1a5fa8;
13            background:#e8f1fb; text-decoration:none;">
14    ▶ Voir la vidéo explicative
15  </a>`}nouvelleVersion(){K.isAmc&&(this.versionQcm=!0);const l=this.quotaChoice("type",[1,2,3,4]),x=t(1,5)+t(1,9)/10+t(1,9)/100,L=x+t(1,9)/100,b=t(1,5)+t(1,9)/10+t(1,9)/100,D=b+t(1,9)/10+t(1,9)/100,y=t(1,5)+t(1,9)/10+t(1,9)/100,E=y+t(1,9)/10+t(1,9)/100,v=t(1,5)+t(1,9)/10+t(1,9)/100,Q=v+t(1,9)/10+t(1,9)/100,C=I([!0,!1]),n=r(-x,4),c=r(-L,4),a=r(b,3),p=r(D,3),m=r(y,4),$=r(E,4),f=r(v,3),d=r(Q,3),u={1:{gauche:`(${n})^2`,droite:`(${c})^2`,signe:"<",justification:`La fonction carré est strictement décroissante sur $]-\\infty\\,;\\,0]$ et $${n} > ${c}$, donc $(${n})^2 < (${c})^2$.`},2:{gauche:`\\dfrac{1}{${a}}`,droite:`\\dfrac{1}{${p}}`,signe:">",justification:`La fonction inverse est strictement décroissante sur $]0\\,;\\,+\\infty[$ et $${a}<${p}$, donc $\\dfrac{1}{${a}} > \\dfrac{1}{${p}}$.`},3:{gauche:`${f}^2`,droite:`${d}^2`,signe:"<",justification:`La fonction carré est strictement croissante sur $[0\\,;\\,+\\infty[$ et $${f}<${d}$, donc $${f}^2<${d}^2$.`},4:{gauche:`\\left(\\dfrac{1}{${$}}\\right)^2`,droite:`\\left(\\dfrac{1}{${m}}\\right)^2`,signe:"<",justification:`La fonction carré est strictement croissante sur $[0\\,;\\,+\\infty[$ et $\\dfrac{1}{${$}} < \\dfrac{1}{${m}}$, donc $\\left(\\dfrac{1}{${$}}\\right)^2<\\left(\\dfrac{1}{${m}}\\right)^2$.`}};if(this.versionQcm){const e={1:`$(${n})^2>(${c})^2$`,2:`$\\dfrac{1}{${a}} < \\dfrac{1}{${p}}$`,3:`$${f}^2>${d}^2$`,4:`$\\left(\\dfrac{1}{${$}}\\right)^2>\\left(\\dfrac{1}{${m}}\\right)^2$`},s=[1,2,3,4].filter(o=>o!==l),i=u[l];this.consigne="",this.question="La seule inégalité vraie est : ",this.reponse=`$${i.gauche} ${i.signe} ${i.droite}$`,this.distracteurs=s.map(o=>e[o]),this.correction=`La seule inégalité vraie est : $${A(`${i.gauche} ${i.signe} ${i.droite}`)}$.<br>
16        En effet, ${i.justification}<br><br>
17        Concernant les autres propositions :<br>`+s.map(o=>`${e[o]} est fausse car ${u[o].justification}<br>`).join("")}else{const{gauche:e,droite:s,signe:i,justification:o}=u[l],[h,g]=C?[s,e]:[e,s],j=C?i==="<"?">":"<":i;this.consigne="Compléter avec le symbole $<$ ou $>$.",this.question=this.interactif?"":`$${h} \\,\\ldots\\, ${g}$`,this.optionsChampTexte={texteAvant:`$${h}$`,texteApres:`$${g}$`,dataKeys:["<",">"]},this.optionsDeComparaison={texteSansCasse:!0},this.reponse=j,this.correction=`${o}<br>
18      Ainsi, $${h} ${A(j)} ${g}$.`}}}export{oi as amcReady,ri as amcType,ni as dateDeModifImportante,si as dateDePublication,ci as default,ii as interactifReady,ti as refs,ei as titre,Zt as uuid};