Quiz : Maîtrisez les équations et fonctions pour le Bac

Question 1 sur 10 10:00

[{"id":19958,"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 = 4\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation en isolant x : 3x = 12 → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19959,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2, +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f’(x) = 2x - 4 est positive pour x \u003E 2, donc la fonction est croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19960,"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(x - 9)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Utilisez l'identité remarquable a² - b² = (a - b)(a + b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19961,"question":"L'inéquation 2x + 1 ≤ 5 a pour solution :","option_a":"x ≤ 2","option_b":"x ≥ 2","option_c":"x ≤ 1","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'inéquation : 2x ≤ 4 → x ≤ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19962,"question":"Le point A(2, 3) appartient-il à la droite d'équation y = 2x - 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour x = 2, y = 2*2 - 1 = 3, donc A appartient à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19963,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003E 0 ?","option_a":"x ∈ ]2, 3[","option_b":"x ∈ ]-∞, 2[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, 2[","option_d":"x ∈ ]3, +∞[","option_e":"","option_f":"","bonne_reponse":"B","explication":"Factorisez : (x - 2)(x - 3) \u003E 0. Les solutions sont les intervalles où le produit est positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19964,"question":"La fonction f(x) = -x² + 4x - 3 admet-elle un maximum ? Si oui, quelle est sa valeur ?","option_a":"Non, elle n'a pas de maximum","option_b":"Oui, maximum = 1","option_c":"Oui, maximum = -3","option_d":"Oui, maximum = 4","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est une parabole tournée vers le bas. Le sommet donne le maximum : f(2) = -4 + 8 - 3 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19965,"question":"L'équation |x - 1| = 3 a pour solutions :","option_a":"x = 4 ou x = -2","option_b":"x = 2 ou x = -4","option_c":"x = 1 ou x = 3","option_d":"x = 0 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez |x - 1| = 3 → x - 1 = 3 ou x - 1 = -3 → x = 4 ou x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19966,"question":"La droite d'équation y = 3x + 2 est-elle parallèle à la droite d'équation y = 3x - 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites sont parallèles si elles ont le même coefficient directeur (ici, 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19967,"question":"Quelle est la solution de l'équation (x + 1)² = 4 ?","option_a":"x = 1 ou x = -3","option_b":"x = 2 ou x = -2","option_c":"x = 0 ou x = -2","option_d":"x = 1 ou x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez (x + 1)² = 4 → x + 1 = 2 ou x + 1 = -2 → x = 1 ou x = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]