Une initiation au calcul littéral

L'exercice demande à l'élève de calculer une expression à partir de quelques valeurs de x.

Dans un deuxième temps il doit trouver, par essais successifs, la valeur de x pour laquelle la même expression est égale à une autre valeur y.

\title{Utiliser la lettre x pour calculer}
\language{fr}
\range{-5..5}
\author{Bénassy Odile}
\email{obenassy@free.fr}
\license{GNU GPL}
\computeanswer{no}
\format{html}
\precision{10000}
 
 
\integer{fignum=random(1..5)}
\real{t=random(2,2.5,3,3.5,4,4.5,5,5.5,10,12,15,20,30,50,100,120)}
\text{exprs=2x+\t,3x+\t,5x,\t-x,\t+x,x/4}
\text{expr=item(\fignum,\exprs)}
\function{expr=\expr}
 
\integer{xval=random(1..20)}
\if{\fignum=4}{\real{xval=random(1,1.5,\t*0.2,\t*0.5,\t*0.7,\t*0.8)}}
\real{yres=evalue(\expr,x=\xval)}
\integer{xres=random(1..20)}
\if{\fignum=4}{\real{xres=random(1.5,\t*0.2,\t*0.5,\t*0.7,\t*0.8)}}
\if{\xres=\xval}{\integer{\xres=\xval-1}}
\real{yval=evalue(\expr,x=\xres)}
 
\real{essai=evalue(\expr,x=\xval)}
 
 
\steps{reply 1,
reply 2,
reply 3
}

                                                                              
\statement{
<p><center>
\if{\fignum=1}{\draw{440,100}{
xrange -20,420
yrange -50,50
line 0,0,400,0,green
line 0,-5,0,5,green
line 400,-5,400,5,green
line 120,-5,120,5,green
line 240,-5,240,5,green
arrow 45,-20,0,-20,8,black
arrow 75,-20,120,-20,8,black
arrow 305,-20,240,-20,8,black
arrow 335,-20,400,-20,8,black
line 56,-3,64,3,red
line 176,-3,184,3,red
text green,-2,25,large,A
text green,118,25,large,B
text green,398,25,large,C
text black,60,-15,normal,x
text black,318,-15,normal,\t
}}
\if{\fignum=2}{\draw{440,100}{
xrange -20,420
yrange -50,50
line 0,0,400,0,purple
line 0,-5,0,5,purple
line 80,-5,80,5,purple
line 160,-5,160,5,purple
line 240,-5,240,5,purple
line 400,-5,400,5,purple
line 36,-3,44,3,red
line 116,-3,124,3,red
line 176,-3,184,3,red
arrow 25,-20,0,-20,8,black
arrow 55,-20,80,-20,8,black
arrow 305,-20,240,-20,8,black
arrow 335,-20,400,-20,8,black
text purple,-2,25,large, A
text purple,78,25,large, B
text purple,398,25,large, C
text black,38,-15,normal, x
text black,318,-15,normal,\t
}}
\if{\fignum=3}{\draw{440,100}{
xrange -20,420
yrange -50,50
line 0,0,400,0,blue
line 0,-5,0,5,blue
line 80,-5,80,5,blue
line 160,-5,160,5,blue
line 240,-5,240,5,blue
line 320,-5,320,5,blue
line 400,-5,400,5,blue
line 36,-3,44,3,red
line 116,-3,124,3,red
line 196,-3,204,3,red
line 276,-3,284,3,red
line 356,-3,364,3,red
arrow 25,-20,0,-20,8,black
arrow 55,-20,80,-20,8,black
text blue,-2,25,large, A
text blue,78,25,large, B
text blue,398,25,large, C
text black,38,-15,normal, x
}}
\if{\fignum=4}{\draw{440,100}{
xrange -20,420
yrange -50,50
line 0,0,400,0,orange
line 0,-5,0,5,orange
line 160,-5,160,5,orange
line 400,-5,400,5,orange
arrow 255,5,160,5,8,black
arrow 295,5,400,5,8,black
arrow 185,-20,0,-20,8,black
arrow 215,-20,400,-20,8,black
text orange,-2,25,large, C
text orange,158,25,large, A
text orange,398,25,large, B
text black,275,15,normal, x
text black,195,-15,normal, \t
}}
\if{\fignum=5}{\draw{440,100}{
xrange -20,420
yrange -50,50
line 0,0,400,0,orange
line 0,-5,0,5,orange
line 240,-5,240,5,orange
line 400,-5,400,5,orange
arrow 305,-20,240,-20,8,black
arrow 335,-20,400,-20,8,black
arrow 105,-20,0,-20,8,black
arrow 135,-20,240,-20,8,black
text orange,-2,25,large, C
text orange,238,25,large, B
text orange,398,25,large, A
text black,315,-15,normal, x
text black,115,-15,normal, \t
}}
\if{\fignum=6}{\draw{440,100}{
xrange -20,420
yrange -50,50
line 0,0,400,0,blue
line 0,-5,0,5,blue
line 100,-5,100,5,blue
line 200,-5,200,5,blue
line 300,-5,300,5,blue
line 400,-5,400,5,blue
line 46,-3,54,3,red
line 146,-3,154,3,red
line 246,-3,254,3,red
line 346,-3,354,3,red
arrow 185,-20,0,-20,8,black
arrow 215,-20,400,-20,8,black
text blue,-2,25,large, A
text blue,98,25,large, C
text blue,398,25,large, B
text black,195,-15,normal, x
}}
</center>
                                                                              
\if{\step<=1}{
<p>Si la longueur AB vaut x, combien vaut la longueur AC ?
<p>Ma formule : AC = \embed{reply 1, 15}
}
                                                                              
\if{\step=2}{
<p>Ma formule : AC = \reply1
<p>Calculer AC pour la valeur x = \xval
<p>Pour la valeur x = \xval,  la longueur AC vaut \embed{reply 2,5}
}
                                                                              
\if{\step=3}{
<p>Ma formule : AC = \reply1
<p>Comment faut-il choisir le nombre x pour que la longueur AC soit égale à \yval ?
<p>Pour obtenir le résultat \yval pour la longueur AC, il faut choisir x = \embed{reply 3,5}
}
                                                                              
}
                                                                              
\answer{}{\expr}{type=function}
\answer{}{\yres}{type=numeric}
\answer{}{\xres}{type=numeric}