tableau de signes

\text{     ?     }

\text{    }+\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{     ?     }

\text{     ?     }

\text{     ?     }

\text{   }

\text{ }0\text{ }

\text{   }

\text{   }

\text{ }0\text{ }

\text{ }0\text{ }

\text{     ?     }

\text{    }+\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{     ?     }

\text{     ?     }

\text{     ?     }

\text{   }

\text{ }0\text{ }

\text{   }

\text{   }

\text{ }0\text{ }

\text{ }0\text{ }

\text{     ?     }

\text{    }+\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{     ?     }

\text{     ?     }

\text{     ?     }

\text{   }

\text{ }0\text{ }

\text{   }

\text{   }

\text{ }0\text{ }

\text{ }0\text{ }

\text{     ?     }

\text{    }+\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }-\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{    }+\text{    }

\text{     ?     }

\text{     ?     }

\text{     ?     }

\text{   }

\text{ }0\text{ }

\text{   }

\text{   }

\text{ }0\text{ }

\text{ }0\text{ }

RAZ

\text{  }

\text{  }

\text{  }

-\infty

+\infty

1

3

4

i

m

s

Juste

Juste

Juste

Juste

Juste

Faux

Faux

Faux

Faux

Faux

Valider ce tableau de signes

\ovalbox{]}

\ovalbox{[}

\ovalbox{\text{;}}

\ovalbox{-\infty}

\ovalbox{+\infty}

\ovalbox{\ \cup\ }

\geqslant 0

-x+5

-2x+7

-3x+2

Nouvel énoncé

Commencer la série d'exercices

Clavier virtuel

Mathématiques à Valin

Valider cet ensemble de solutions

Juste

Faux

Voir la bonne réponse

Faux

Faux

Faux

\text{Ceci est le dernier exercice. Une fois terminé,}\
\text{cliquez sur }\ovalbox{\text{Envoyer et terminer}}

hh(x) = (3 * x) + 1
L = Intersect(hh, xAxis)
gg(x) = 2 - (7 * x)
M = Intersect(gg, xAxis)
ff(x) = (3 * x) - 9
kk(x) = ff(x) / ((gg(x) * hh(x)))
K = Intersect(ff, xAxis)
smax = Max({x(K), x(L), x(M)})
kkmax: (-1000000  <  kk(smax)) ∧ (kk(smax)  <  1000000)
smin = Min({x(K), x(L), x(M)})
Lmoy = Remove({x(K), x(L), x(M)}, {smax, smin})
smoy = Element(Lmoy, 1)
kkmoy: (-1000000  <  kk(smoy)) ∧ (kk(smoy)  <  1000000)
kkmin: (-1000000  <  kk(smin)) ∧ (kk(smin)  <  10000000)
A1 = 0
A2 = 0
A3 = 0
A4 = 0
A5 = 0
A6 = 0
B1 = 0
B2 = 0
B3 = 0
B4 = 0
B5 = 0
B6 = 0
C1 = 0
C2 = 0
C3 = 0
C4 = 0
C5 = 0
C6 = 0
A7 = 0
B7 = 0
C7 = 0
D1 = 0
D2 = 0
D3 = 0
D4 = 0
D5 = 0
D6 = 0
D7 = 0
A = (1.46, 5.88)
a: y = y(A)
B = Point(a)
b: x = x(A)
C = Point(b)
c: y = y(C)
D: (x(B), y(C))
d = Segment(A, B)
e = Segment(B, D)
f = Segment(D, C)
g = Segment(A, C)
E = Point(d)
F = Point(d)
G = Point(d)
E': (x(E), y(C))
F': (x(F), y(C))
G': (x(G), y(C))
h = Segment(E, E')
i = Segment(F, F')
j = Segment(G, G')
H = Point(g)
I = Point(g)
J = Point(g)
H': (x(B), y(H))
I': (x(B), y(I))
J': (x(B), y(J))
k = Segment(H, H')
l = Segment(I, I')
m = Segment(J, J')
A11 = If(ff(-100)  <  0, 2, 1)
A13 = If(ff((smin + smoy) / 2)  <  0, 2, 1)
A12 = If(ff(smin) ≟ 0, 1, 0)
A14 = If(ff(smoy) ≟ 0, 1, 0)
A16 = If(ff(smax) ≟ 0, 1, 0)
A15 = If(ff((smax + smoy) / 2)  <  0, 2, 1)
A17 = If(ff(50)  <  0, 2, 1)
B11 = If(gg(-100)  <  0, 2, 1)
B12 = If(gg(smin) ≟ 0, 1, 0)
B13 = If(gg((smin + smoy) / 2)  <  0, 2, 1)
B14 = If(gg(smoy) ≟ 0, 1, 0)
B15 = If(gg((smax + smoy) / 2)  <  0, 2, 1)
B16 = If(gg(smax) ≟ 0, 1, 0)
B17 = If(gg(50)  <  0, 2, 1)
C17 = If(hh(50)  <  0, 2, 1)
C11 = If(hh(-100)  <  0, 2, 1)
C12 = If(hh(smin) ≟ 0, 1, 0)
C13 = If(hh((smin + smoy) / 2)  <  0, 2, 1)
C14 = If(hh(smoy) ≟ 0, 1, 0)
C15 = If(hh((smax + smoy) / 2)  <  0, 2, 1)
C16 = If(hh(smax) ≟ 0, 1, 0)
D11 = If(kk(-100)  <  0, 2, 1)
D13 = If(kk((smin + smoy) / 2)  <  0, 2, 1)
D15 = If(kk((smax + smoy) / 2)  <  0, 2, 1)
D17 = If(kk(50)  <  0, 2, 1)
A21: A1 ≟ A11
A22: A2 ≟ A12
A23: A3 ≟ A13
A24: A4 ≟ A14
A25: A5 ≟ A15
A26: A6 ≟ A16
A27: A7 ≟ A17
B21: B1 ≟ B11
B22: B2 ≟ B12
B23: B3 ≟ B13
B24: B4 ≟ B14
B25: B5 ≟ B15
B26: B6 ≟ B16
B27: B7 ≟ B17
C21: C1 ≟ C11
C22: C2 ≟ C12
C23: C3 ≟ C13
C24: C4 ≟ C14
C25: C5 ≟ C15
C26: C6 ≟ C16
C27: C7 ≟ C17
D21: D1 ≟ D11
D12 = If(kkmin, 1, 2)
D22: D2 ≟ D12
D23: D3 ≟ D13
D14 = If(kkmoy, 1, 2)
D24: D4 ≟ D14
D25: D5 ≟ D15
D16 = If(kkmax, 1, 2)
D26: D6 ≟ D16
D27: D7 ≟ D17
A28: A21 ∧ A22 ∧ A23 ∧ A24 ∧ A25 ∧ A26 ∧ A27
B28: B21 ∧ B22 ∧ B23 ∧ B24 ∧ B25 ∧ B26 ∧ B27
C28: C21 ∧ C22 ∧ C23 ∧ C24 ∧ C25 ∧ C26 ∧ C27
D28: D21 ∧ D22 ∧ D23 ∧ D24 ∧ D25 ∧ D26 ∧ D27
texte6: "" + (LaTeX[ff]) + ""
texte7: "" + (LaTeX[gg]) + ""
texte8: "" + (LaTeX[hh]) + ""
texte9: "" + (LaTeX[kk]) + ""
aa: kk(smin)
N = Intersect(h, m)
O = Intersect(i, m)
P = Intersect(j, m)
bar11 = Segment(N - (0.05, 0), E' - (0.05, 0))
bar12 = Segment(N + (0.05, 0), E' + (0.05, 0))
bar21 = Segment(O - (0.05, 0), F' - (0.05, 0))
bar22 = Segment(O + (0.05, 0), F' + (0.05, 0))
p = Segment(O, F')
bar31 = Segment(P - (0.05, 0), G' - (0.05, 0))
bar32 = Segment(P + (0.05, 0), G' + (0.05, 0))
n = Segment(N, E')
q = Segment(P, G')
Q = Point(a)
Q': (x(Q), y(C))
H0: (x(Q), y(H))
I0: (x(Q), y(I))
J0: (x(Q), y(J))
a_1 = Segment(Q, Q')
b_1 = Segment(Q', C)
c_1 = Segment(J0, J)
d_1 = Segment(I0, I)
e_1 = Segment(H0, H)
R = Intersect(d, g)
f_1 = Segment(Q, R)
M1: (x(A), y(A) + 1)
E1: (x(E), y(E) + 0.1)
r = Segment(E1, N)
F1: (x(F), y(F) + 0.1)
s = Segment(F1, O)
G1: (x(G), y(G) + 0.1)
t = Segment(G1, P)
N1: (x(B), y(M1))
S = Intersect(d, g)
g_1 = Segment(M1, S)
h_1 = Segment(M1, N1)
i_1 = Segment(N1, B)
ChampTexte1 = Textfield(repinf)
ChampTexte2 = Textfield(repmoy)
ChampTexte3 = Textfield(repmax)
vch1 = false
vch2 = false
vch3 = false
nrep1: 1
nrep2: 3
nrep3: 4
texte12 = SurdText(nrep1)
texte13 = SurdText(nrep2)
texte14 = SurdText(nrep3)
ligne1juste: nrep1 ≟ smin ∧ nrep2 ≟ smoy ∧ nrep3 ≟ smax
ligne2juste: A21 ∧ A22 ∧ A23 ∧ A24 ∧ A25 ∧ A26 ∧ A27
ligne3juste: B21 ∧ B22 ∧ B23 ∧ B24 ∧ B25 ∧ B26 ∧ B27
ligne4juste: C21 ∧ C22 ∧ C23 ∧ C24 ∧ C25 ∧ C26 ∧ C27
ligne5juste: D21 ∧ D22 ∧ D23 ∧ D24 ∧ D25 ∧ D26 ∧ D27
test = false
texte21: "\ovalbox{" + (LaTeX[texte12]) + "}"
texte22: "\ovalbox{" + (LaTeX[texte13]) + "}"
texte23: "\ovalbox{" + (LaTeX[texte14]) + "}"
T = (7.86, -0.08)
U = (8.6, -0.08)
texte25: "\text{L'ensemble des solutions est : } " + (LaTeX[textesolution]) + ""
texte26: "\text{Résoudre l'inéquation }" + (LaTeX[texte9]) + "" + (LaTeX[signe]) + ""
ex1: {"-x+5", "-2x+7", "-3x+2", "ff(x)/((gg(x))(hh(x)))", "\geqslant 0", "]-\infty\text{ ; } \frac{ 2 }{ 3 } [\ \ \cup\ \  ] \frac{ 7 }{ 2 } \text{ ; }5]"}
enon = 18
texteattendu = Element(ex1, 6)
solutionjuste: texteattendu ≟ textesolution
listeprincipale: {"3x-9", "2-7x", "3x+1", "((ff(x)*gg(x)))/hh(x)", "\geqslant 0", "]-\infty\text{ ; }- \frac{ 1 }{ 3 } [\ \ \cup\ \  [\frac{2}{7}\text{ ; }3]"}
ex2: {"2x-5", "3-x", "3x+4", "ff(x)/((gg(x))(hh(x)))", "\leqslant 0", "]- \frac{ 4 }{ 3 } \text{ ; } \frac{ 5 }{ 2 } ]\ \ \cup\ \  ]3\text{ ; }+\infty["}
ex3: {"3x+1", "3-2x", "-3x+5", "ff(x)/((gg(x))(hh(x)))", "\leqslant 0", "]-\infty\text{ ; }- \frac{ 1 }{ 3 } ]\ \ \cup\ \  ] \frac{ 3 }{ 2 } \text{ ; } \frac{ 5 }{ 3 } ["}
ex4: {"3x+5", "-3x", "2-3x", "ff(x)/(gg(x)(hh(x)))", "\geqslant 0", "[- \frac{ 5 }{ 3 } \text{ ; }0[\ \ \cup\ \  ] \frac{ 2 }{ 3 } \text{ ; }+\infty["}
ex5: {"7x", "7x+3", "3x+8", "ff(x)/((gg(x))(hh(x)))", "\leqslant 0", "]-\infty\text{ ; }- \frac{ 8 }{ 3 } [\ \ \cup\ \  ]-\frac{3}{7}\text{ ; }0]"}
ex6: {"x-1", "5x-3", "3x-4", "ff(x)/((gg(x))(hh(x)))", "\geqslant 0", "]\frac{3}{5}\text{ ; }1]\ \ \cup\ \  ] \frac{ 4 }{ 3 } \text{ ; }+\infty["}
ex7: {"4x", "2x-9", "3-4x", "((ff(x)*gg(x)))/hh(x)", "\geqslant 0", "]-\infty\text{ ; }0]\ \ \cup\ \  ] \frac{ 3 }{ 4 } \text{ ; } \frac{ 9 }{ 2 } ]"}
ex8: {"5x+1", "3x-1", "7-5x", "((ff(x)*gg(x)))/hh(x)", "\leqslant 0", "[- \frac{ 1 }{ 5 } \text{ ; } \frac{ 1 }{ 3 } ]\ \ \cup\ \  ]\frac{7}{5}\text{ ; }+\infty["}
ex9: {"2x+9", "3-4x", "7x", "((ff(x)*gg(x)))/hh(x)", "\leqslant 0", "[- \frac{ 9 }{ 2 } \text{ ; }0[\ \ \cup\ \  [ \frac{ 3 }{ 4 } \text{ ; }+\infty["}
ex10: {"-3x+7", "5-4x", "3x-1", "((ff(x)*gg(x)))/hh(x)", "\geqslant 0", "] \frac{ 1 }{ 3 } \text{ ; } \frac{ 5 }{ 4 } ]\ \ \cup\ \  [ \frac{ 7 }{ 3 } \text{ ; }+\infty["}
ex11: {"5-x", "4x+3", "6x+5", "((ff(x)*gg(x)))/hh(x)", "\geqslant 0", "]-\infty\text{ ; }- \frac{ 5 }{ 6 } [\ \ \cup\ \  [- \frac{ 3 }{ 4 } \text{ ; }5]"}
ex12: {"-4x", "3-2x", "3x+5", "ff(x)*gg(x)*hh(x)", "< 0", "]-\infty\text{ ; }- \frac{ 5 }{ 3 } [\ \ \cup\ \  ]0\text{ ; } \frac{ 3 }{ 2 } ["}
ex13: {"5+7x", "2x-3", "6x+5", "ff(x)*gg(x)*hh(x)", "\leqslant 0", "]-\infty\text{ ; }- \frac{ 5 }{ 6 } ]\ \ \cup\ \  [-\frac{5}{7}\text{ ; } \frac{ 3 }{ 2 } ]"}
ex14: {"3x^2", "2x+5", "-3x+2", "ff(x)/((gg(x))(hh(x)))", "\geqslant 0", "]- \frac{ 5 }{ 2 } \text{ ; } \frac{ 2 }{ 3 } ["}
ex15: {"3x+2", "-2x^2", "2x+9", "ff(x)/(gg(x) *(hh(x)))", "<0", "]-\infty\text{ ; }- \frac{ 9 }{ 2 } [\ \ \cup\ \  ]- \frac{ 2 }{ 3 } \text{ ; }0[\ \ \cup\ \  ]0\text{ ; }+\infty["}
ex16: {"5x+2", "2x-9", "3x+1", "ff(x)/(gg(x) *(hh(x)))", "\leqslant0", "]-\infty\text{ ; }-\frac{2}{5}]\ \ \cup\ \  ]- \frac{ 1 }{ 3 } \text{ ; } \frac{ 9 }{ 2 } ["}
ex17: {"x-4", "5-x", "2x-5", "ff(x)/((gg(x))(hh(x)))", "\leqslant 0", "] \frac{ 5 }{ 2 } \text{ ; }4]\ \ \cup\ \  ]5\text{ ; }+\infty["}
ex18: {"3x-9", "2-7x", "3x+1", "((ff(x)*gg(x)))/hh(x)", "\geqslant 0", "]-\infty\text{ ; }- \frac{ 1 }{ 3 } [\ \ \cup\ \  [\frac{2}{7}\text{ ; }3]"}
ex19: {"2+x", "5-6x", "3x-5", "ff(x)*gg(x)*hh(x)", "\geqslant 0", "]-\infty\text{ ; }-2]\ \ \cup\ \  [ \frac{ 5 }{ 6 } \text{ ; } \frac{ 5 }{ 3 } ]"}
V = (7.66, 0.9)
V': V + (3.5, 0)
V_1: V + (0, -2.9)
V_2: (x(V'), y(V_1))
poly1, v, v', v_2, v_1 = Polygon(V, V', V_2, V_1)
debut = false
decale = 6
tableauvalide = false
lignes5juste: ligne1juste ∧ ligne2juste ∧ ligne3juste ∧ ligne4juste ∧ ligne5juste
test2 = false
score = 0
gain = 1
numexo = 1
texte31: "Exercices réussis sans faute : " + score + " / " + numexo + ""
essai2 = 1
donnereponse2 = false
signe2 = If(signe ≟ "\leqslant 0" ∨ signe ≟ "< 0" ∨ signe ≟ "<0", "-", "+")
texte32: "\text{Cette réponse a été donnée par le programme.}\\
\text{Faites le lien entre l'inégalité qui figure dans l'inéquation } (" + (LaTeX[signe]) + ")\\
\text{et les signes }" + (LaTeX[signe2]) + "\text{ qui figurent sur la dernière ligne du tableau.}\\
"
val2 = If(D14 ≟ 2, texte13 + "\text{    }", "")
val3 = If(D16 ≟ 2, texte14 + "\text{    }", "")
val1 = If(D12 ≟ 2, texte12 + "\text{    }", "")
zerointerdite: (D16 ≠ 2) ∧ (D14 ≠ 2) ∧ (D12 ≠ 2)
texte33: "\text{Attentions aux valeurs interdites ici : }" + (LaTeX[val1]) + "" + (LaTeX[val2]) + "" + (LaTeX[val3]) + ""
poly2, j_1, n_1, e', c_2 = Polygon(J, N, E', C)
poly3, n_2, o, f', e'_1 = Polygon(N, O, F', E')
poly4, o_1, p_1, g', f'_1 = Polygon(O, P, G', F')
W = Intersect(o_1, p_1)
Z = Intersect(p_1, g')
poly5, w, j', d_2, z_1 = Polygon(W, J', D, Z)
R_11: S + (0, 0.1)
k_1 = Segment(E1, R_11)
l_1 = Segment(E1, F1)
m_1 = Segment(F1, G1)
BB_1: B + (0, 0.1)
q_1 = Segment(G1, BB_1)
vert1: (signe2 ≟ "+" ∧ D1 ≟ 1 ∧ D21 ∨ signe2 ≟ "-" ∧ D1 ≟ 2 ∧ D21) ∧ solutionjuste ∧ tableauvalide ∧ test2
vert2: (signe2 ≟ "+" ∧ D3 ≟ 1 ∧ D23 ∨ signe2 ≟ "-" ∧ D3 ≟ 2 ∧ D23) ∧ solutionjuste ∧ tableauvalide ∧ test2
vert3: (signe2 ≟ "+" ∧ D5 ≟ 1 ∧ D25 ∨ signe2 ≟ "-" ∧ D5 ≟ 2 ∧ D25) ∧ solutionjuste ∧ tableauvalide ∧ test2
vert4: (signe2 ≟ "+" ∧ D7 ≟ 1 ∧ D27 ∨ signe2 ≟ "-" ∧ D7 ≟ 2 ∧ D27) ∧ solutionjuste ∧ tableauvalide ∧ test2
egal0: signe ≟ "\leqslant 0" ∨ signe ≟ "\geqslant 0"
voirpoint1: egal0 ∧ D12 ≟ 1 ∧ solutionjuste ∧ tableauvalide ∧ test2
voirpoint2: egal0 ∧ D14 ≟ 1 ∧ solutionjuste ∧ tableauvalide ∧ test2
voirpoint3: egal0 ∧ D16 ≟ 1 ∧ solutionjuste ∧ tableauvalide ∧ test2
grade: score