import{E as ne,ag as se,bE as $e,r as W,h as M,F as r,cj as z,T as ae,w as f,q as k,aA as oe,u as ce,P as re,_ as fe,c as b,a as p,o as H,a0 as B,s as d,j as U,l as le}from"./index-ajJ0B2-K.js";import{r as he}from"./reperes-w_D-727i.js";const me="Linear functions",xe="mathLive",pe=!0,de=!0,ye="AMCHybride",ge="13/04/2023",Ae="3F20",Se="aeb5a";function Fe(){ne.call(this),this.comment="The exercise offers different types of questions on linear functions:<br>image calculation, antecedent calculation or determination of the coefficient.<br>This coefficient can be either relative integer or relative rational.<br>Certain questions image calculations require the calculation of the coefficient beforehand.<br>The choice was made of a positive integer primary antecedent, the coefficient being negative with a probability of 50%.<br>",this.sup=1,this.nbQuestions=8,this.sup2="9",this.besoinFormulaireNumerique=["Coefficient : ",3,`1: Integer coefficient
2: Rational coefficient
3: Mixture`],this.besoinFormulaire2Texte=["Types of questions",`Numbers separated by hyphens:
1: Image by expression
2: Image by values
3: Image by graph
4: Antecedent by expression
5: Antecedent by values
6: Antecedent by graph
7: Expression by values
8 : Expression by graph
9: Mixture`],this.nouvelleVersion=function(){this.listeQuestions=[],this.listeCorrections=[],this.autoCorrection=[];const K=["imageByExpression","imageByValues","imageByGraphic","antecedentByExpression","historyByValues","historyByGraph","expressionByValues","expressionByGraph"],Z=se({saisie:this.sup2,min:1,max:8,defaut:9,nbQuestions:this.nbQuestions,listeOfCase:K,melange:9}),G=[];for(let o=0,x,m,X=0;o<this.nbQuestions&&X<50;){const y={},e=String.fromCharCode(102+o);this.sup=$e(1,3,this.sup,1);let $="",i="";const t=2*W(2,10)+1;let n,h;switch(this.sup){case 1:n=W(2,10)*M([-1,1]);break;case 2:n=new r(z(t,G)*M([-1,1]),t);break;case 3:Math.random()<.5?n=W(2,10)*M([-1,1]):n=new r(z(t,G)*M([-1,1]),t);break}let l,C;const a=M(ae(-10,10,[t,0,1,-1,2*t])),s=n instanceof r?n.num:n*t;n instanceof r?(h=n.multiplieEntier(a),l=h.texFSD,C="fractionEqual"):(h=n*a,l=f(h,0),C="calculation"),G.push(a,t);const u=n instanceof r?n.simplifie().texFSD:n.toString();let F,v,w,D,E,L;const g=[[5,1,1],[10,.5,2],[20,.25,4],[50,.1,10],[100,.05,20]],A=[[5,1,1],[10,.5,2],[20,.25,4],[50,.1,10],[100,.05,20],[200,.025,40],[500,.01,100]];F=g[0][1],w=g[0][2],E=-g[0][0]-w;for(let c=1;Math.abs(t)>g[c-1][0];c++)F=g[c][1],w=g[c][2],E=-g[c][0]-w;v=A[0][1],D=A[0][2],L=-A[0][0]-D;for(let c=1;Math.abs(s)>A[c-1][0];c++)v=A[c][1],D=A[c][2],L=-A[c][0]-D;const Y=E,J=-E+w,O=L,_=-L,I=Y*F,P=O*v,Q=J*F+.5,q=_*v+.5,V=he({xUnite:F,yUnite:v,xMin:Y,yMin:O,xMax:J,yMax:_,xThickDistance:w,yThickDistance:D,yLabelEcart:.8,grille:!1}),ee=k(0,0),S=k(t*F,s*v),N=oe(ee,S),j=ce(S),te=k(S.x,0),ie=k(0,S.y),T=re([ie,S,te],"red");T.pointilles=2,T.epaisseur=1;const R=fe(`(${t};${s})`,k(S.x+.2,S.y),"RIGHT");switch(Z[o]){case"imageByExpression":$+=`Let $${e}(x)=${n instanceof r?n.texFSD:f(n)}x$.<br>`,$+=`Calculate the image of $${a}$ by $${e}$.`+p(this,o,"width15 inline"),i+=`$${e}(${f(a,0)})=${n instanceof r?n.texFSD:f(n,0)} \\times ${U(a)}`,i+=`=${n instanceof r?h.texFSD:f(h,0)}$`,b.isAmc?(x=`image of $${a}$ by $${e}$`,m=h):d(this,o,h,{formatInteractif:C});break;case"imageByValues":if($+=`Let $${e}$ be the linear function such that $${e}(${t})=${f(s,0)}$.<br>`,$+=`Calculate the image of $${a}$ by $${e}$.`+p(this,o,"width15 inline"),i+=`As $${e}(${t})=${f(s,0)}$, the coefficient $a$ such that $${e}(x)=ax$ satisfies $a\\times ${t} = ${s}$.<br>`,i+=`We deduce $a=\\dfrac{${f(s,0)}}{${t}}`,B(s,t)!==1){const c=new r(s,t).simplifie().texFSD;i+=`=${c}`}i+=`$ and consequently $${e}(x)=${u}x$.<br>`,i+=`So $${e}(${f(a,0)})=${n instanceof r?n.texFSD:f(n,0)} \\times ${U(a)}`,i+=`=${n instanceof r?h.texFSD:f(h,0)}$.`,b.isAmc?(x=`image of $${a}$ by $${e}$`,m=h):d(this,o,h,{formatInteractif:C});break;case"imageByGraphic":$+=`The line representing the linear function $${e}$ passes through the coordinate point $(${t};${s})$.<br>`,$+=`Calculate the image of $${a}$ by $${e}$.`+p(this,o,"width15 inline"),$+="<br>",$+=H({scale:.6,xmin:I,ymin:P,xmax:Q,ymax:q},V,N,j,R,T),i+=`As $${e}(${t})=${s}$ and $${e}(x)=ax$ we deduce $a\\times ${t} = ${s}$ or $a=\\dfrac{${s}}{${t}}${n instanceof r?"":"="+u}$.<br>`,i+=`So $${e}(${a})=${u}\\times ${U(a)} = ${l}$.`,b.isAmc?(x=`image of $${a}$ by $${e}$`,m=h):d(this,o,h,{formatInteractif:C});break;case"antecedentByExpression":$+=`Let $${e}(x)=${n instanceof r?n.texFSD:f(n)}x$.<br>`,$+=`Calculate the antecedent of $${l}$ by $${e}$.`+p(this,o,"width15 inline"),i+=`Let $b$ be the antecedent of $${l}$, then $${e}(b)=${u}\\times b=${l}$.<br>`,n instanceof r?(i+=`So $b=\\dfrac{${h.texFSD}}{${u}}=`,i+=`${h.texFSD}\\times ${n.inverse().texFSP}=`):i+=`So $b=\\dfrac{${f(h,0)}}{${u}}=`,i+=`${a}$.`,b.isAmc?(x=`antecedent of $${l}$ by $${e}$`,m=a):d(this,o,a,{formatInteractif:"calculation"});break;case"historyByValues":if($+=`Let $${e}$ be the linear function such that $${e}(${t})=${f(s,0)}$.<br>`,$+=`Calculate the antecedent of $${l}$.`+p(this,o,"width15 inline"),i+=`As $${e}(${t})=${f(s,0)}$, the coefficient $a$ such that $${e}(x)=ax$ satisfies $a\\times ${t} = ${s}$.<br>`,i+=`$a=\\dfrac{${f(s,0)}}{${t}}`,B(s,t)!==1){const c=new r(s,t).simplifie().texFSD;i+=`=${c}`}i+=`$.<br>Let $b$ be the antecedent of $${l}$, then $${e}(b)=${u} \\times b=${l}$.<br>`,i+=`We deduce that $b=\\dfrac{${l}}{${u}}=`,n instanceof r&&(i+=`${l}\\times ${n.inverse().texFSP}=`),i+=`${a}$.`,b.isAmc?(x=`antecedent of $${l}$ by $${e}$`,m=a):d(this,o,a,{formatInteractif:"calculation"});break;case"historyByGraph":if($+=`The line representing the linear function $${e}$ passes through the coordinate point $(${t};${s})$.<br>`,$+=`Calculate the antecedent of $${l}$ by $${e}$.`+p(this,o,"width15 inline"),$+="<br>",$+=H({scale:.6,xmin:I,ymin:P,xmax:Q,ymax:q},V,N,j,R,T),i+=`As $${e}(${t})=${s}$ then $${e}(x)=\\dfrac{${s}}{${t}}x`,B(s,t)!==1){const c=new r(s,t).simplifie().texFSD;i+=`=${c}x`}i+=`$<br>Let $b$ be the antecedent of $${l}$, then $${e}(b)=${u}\\times b=${l}$.<br>`,i+=`We deduce that $b=\\dfrac{${l}}{${u}}=`,n instanceof r&&(i+=`${l}\\times ${n.inverse().texFSP}=`),i+=`${a}$.`,b.isAmc?(x=`antecedent of $${l}$ by $${e}$`,m=a):d(this,o,a,{formatInteractif:"calculation"});break;case"expressionByValues":if($+=`Let $${e}$ be the linear function such that $${e}(${t})=${f(s,0)}$.<br>`,b.isAmc?$+=`Give the coefficient of $${e}$.`:$+=`Give the expression for $${e}(x)$.`+p(this,o,"width15 inline"),i+=`As $${e}(${t})=${f(s,0)}$, the coefficient $a$ such that $${e}(x)=ax$ satisfies $a\\times ${t} = ${s}$.<br>`,i+=`Let $a=\\dfrac{${f(s,0)}}{${t}}`,B(s,t)!==1){const c=new r(s,t).simplifie().texFSD;i+=`=${c}`}i+=`$.<br>So $${e}(x)=${u}x$.`,b.isAmc?(x=`coefficient of $${e}$: value of $a$ in $${e}(x)=ax$`,m=n):d(this,o,[`${e}(x)=${u}x`,`${u}x`],{formatInteractif:"calculation"});break;case"expressionByGraph":if($+=`The line representing the linear function $${e}$ passes through the coordinate point $(${t};${s})$.<br>`,b.isAmc?$+=`Give the coefficient of $${e}$.`:$+=`Give the expression for $${e}(x)$.`+p(this,o,"width15 inline"),$+="<br>",$+=H({scale:.6,xmin:I,ymin:P,xmax:Q,ymax:q},V,N,j,R,T),i+=`As $${e}(${t})=${f(s,0)}$, the coefficient $a$ such that $${e}(x)=ax$ is:<br>`,i+=`$a=\\dfrac{${f(s,0)}}{${t}}`,B(s,t)!==1){const c=new r(s,t).simplifie().texFSD;i+=`=${c}`}i+=`$.<br>So $${e}(x)=${u}x$.`,b.isAmc?(x=`Coefficient of $${e}$: value of $a$ in $${e}(x)=ax$`,m=n):d(this,o,[`${e}(x)=${u}x`,`${u}x`],{formatInteractif:"calculation"});break}this.questionJamaisPosee(o,n,t,s)&&(b.isAmc&&(y.propositions=[{type:"AMCNum",propositions:[{reponse:{texte:"",valeur:m,param:{signe:!0,digits:2}}}]}],y.enonce=$+(m instanceof r?" We will give the answer in the form of an irreducible fraction.":"")+"\\\\",y.enonceAvant=!1,y.enonceApresNumQuestion=!0,y.propositions[0].propositions[0].texte=i,y.options={multicolsAll:!0},this.autoCorrection[o]=y),this.listeQuestions.push($),this.listeCorrections.push(i),o++),X++}le(this)}}export{de as amcReady,ye as amcType,ge as dateDePublication,Fe as default,pe as interactifReady,xe as interactifType,Ae as ref,me as titre,Se as uuid};
//# sourceMappingURL=3F20-Hy0MGva6.js.map