Quiz interactif : Maîtrisez l'algèbre en 10 questions

Question 1 sur 10 10:00

[{"id":40776,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résoudre l'équation : 3x - 5 = 7 → 3x = 12 → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40777,"question":"Le polynôme P(x) = x² - 5x + 6 admet-il deux racines réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc deux racines réelles distinctes : x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40778,"question":"Quelle est la factorisation correcte 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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40779,"question":"L'équation x² + 4 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0 - 16 = -16 \u003C 0, donc aucune solution réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40780,"question":"Quel est le résultat de (2x + 3)(x - 1) ?","option_a":"2x² + x - 3","option_b":"2x² + 5x - 3","option_c":"2x² - x + 3","option_d":"2x² + x + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Développer : 2x * x + 2x * (-1) + 3 * x + 3 * (-1) = 2x² - 2x + 3x - 3 = 2x² + x - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40781,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ x³, donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40782,"question":"Résoudre le système : { 2x + y = 5 ; x - y = 1 }","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolution : Additionner les deux équations → 3x = 6 → x = 2. Puis y = 5 - 4 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40783,"question":"Le nombre 15 est-il un nombre premier ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"15 est divisible par 3 et 5, donc ce n'est pas un nombre premier.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40784,"question":"Quelle est la valeur de x dans l'équation 4^(x+1) = 16 ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = 0","option_d":"x = -1","option_e":"","option_f":"","bonne_reponse":"C","explication":"4^(x+1) = 16 → 4^(x+1) = 4² → x + 1 = 2 → x = 1. (Note : correct = 0 pour x=1, mais ici la bonne réponse est x=1, donc correct=0. Correction : l'option correcte est x=1, donc correct=0.)","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":40785,"question":"L'ensemble {0, 1, 2} muni de l'addition modulo 3 est-il un groupe ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est un groupe car : 1) l'addition est associative, 2) 0 est l'élément neutre, 3) chaque élément a un inverse (0→0, 1→2, 2→1), 4) l'ensemble est stable.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]