Quiz — controle 3-4.pdf

Question 1 sur 10 20:00

[{"id":3631,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"Factorisez l'équation : (x-2)(x-3)=0. Les solutions sont donc x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 2 ou x = 3\", \"b\": \"x = -2 ou x = -3\", \"c\": \"x = 1 ou x = 6\", ","_debug_options_count":4},{"id":3632,"question":"La dérivée de f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 2 est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":3633,"question":"Quel est le volume d'un cylindre de rayon r = 3 cm et de hauteur h = 5 cm ?","option_a":"45π cm³","option_b":"15π cm³","option_c":"90π cm³","option_d":"30π cm³","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le volume d'un cylindre est V = πr²h = π × 3² × 5 = 45π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"45π cm³\", \"b\": \"15π cm³\", \"c\": \"90π cm³\", \"d\": \"30π cm³\"}","_debug_options_count":4},{"id":3634,"question":"La fonction f(x) = x³ - 3x² + 2x est croissante sur l'intervalle [-1, 0].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 6x + 2. En x=-1, f'(-1)=3+6+2=11\u003E0. En x=0, f'(0)=2\u003E0. La fonction est donc croissante sur [-1, 0]. Réponse : Vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":3635,"question":"Quelle est la solution du 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":"En additionnant les deux équations : 3x = 6 ⇒ x=2. Puis y=5-2×2=1. La solution est (2,1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 2, y = 1\", \"b\": \"x = 1, y = 3\", \"c\": \"x = 3, y = -1\", \"d\": \"x","_debug_options_count":4},{"id":3636,"question":"La moyenne d'une série statistique est toujours égale à la médiane.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La moyenne et la médiane sont égales uniquement si la distribution est symétrique. Sinon, elles diffèrent.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":3637,"question":"Quelle est la dérivée de f(x) = (2x + 1)³ ?","option_a":"f'(x) = 3(2x+1)²","option_b":"f'(x) = 6(2x+1)²","option_c":"f'(x) = 2(2x+1)²","option_d":"f'(x) = 6(2x+1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la formule de dérivation d'une fonction composée : f'(x) = 3(2x+1)² × 2 = 6(2x+1)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"f'(x) = 3(2x+1)²\", \"b\": \"f'(x) = 6(2x+1)²\", \"c\": \"f'(x) = 2(2x+","_debug_options_count":4},{"id":3638,"question":"Un triangle rectangle a des côtés de 3 cm, 4 cm et 5 cm. Quelle est son aire ?","option_a":"6 cm²","option_b":"12 cm²","option_c":"10 cm²","option_d":"8 cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un triangle rectangle est (base × hauteur)\/2 = (3×4)\/2 = 6 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6 cm²\", \"b\": \"12 cm²\", \"c\": \"10 cm²\", \"d\": \"8 cm²\"}}","_debug_options_count":4},{"id":3639,"question":"La fonction f(x) = ln(x) est définie pour x \u003E 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction logarithme népérien ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":3640,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003E 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4}]