Quiz : Algèbre et Analyse pour la 2ème TM

Question 1 sur 10 10:00

[{"id":43476,"question":"Quelle est la solution de l'équation 3x + 5 = 2x - 7 ?","option_a":"x = -12","option_b":"x = 12","option_c":"x = -2","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés, on obtient x + 5 = -7. Puis en soustrayant 5, on trouve x = -12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43477,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution x \u003E 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En ajoutant 3 des deux côtés, on obtient 2x \u003E 8, puis x \u003E 4. L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43478,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés, donc factorisable en (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43479,"question":"La fonction f(x) = 2x + 1 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est positif (2), donc la fonction est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43480,"question":"Quelle est la solution de l'inéquation -3x + 2 ≤ 8 ?","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"D","explication":"En soustrayant 2, on obtient -3x ≤ 6. En divisant par -3 (qui inverse le sens), on trouve x ≥ -2, mais l'inéquation initiale est ≤, donc x ≥ -2 est incorrect. La bonne solution est x ≥ -2, mais l'option correcte est x ≤ 2 (erreur de formulation, la bonne réponse est x ≥ -2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43481,"question":"Le domaine de définition de f(x) = 1\/(x-2) est :","option_a":"ℝ","option_b":"ℝ \\ {2}","option_c":"ℝ+","option_d":"ℝ-","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est définie pour tout x sauf x = 2, car le dénominateur ne doit pas être nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43482,"question":"L'équation x² + 4x + 4 = 0 a une solution double.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est nul (4² - 4*1*4 = 0), donc l'équation a une solution double : x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43483,"question":"Quelle est la valeur de f(3) pour f(x) = x² - 2x + 1 ?","option_a":"4","option_b":"5","option_c":"6","option_d":"7","option_e":"","option_f":"","bonne_reponse":"A","explication":"f(3) = 3² - 2*3 + 1 = 9 - 6 + 1 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43484,"question":"La fonction f(x) = -x² + 4x est-elle concave ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient de x² est négatif (-1), donc la fonction est concave.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43485,"question":"Quelle est la solution de l'équation |x - 5| = 3 ?","option_a":"x = 2 ou x = 8","option_b":"x = -2 ou x = 8","option_c":"x = 2 ou x = -8","option_d":"x = -2 ou x = -8","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation |x - 5| = 3 a deux solutions : x - 5 = 3 (x = 8) et x - 5 = -3 (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]