Quiz — Manuel_scolaire_3_math_section_math_t2.pdf

Question 1 sur 5 10:00

[{"id":1254,"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":"L'équation x² - 5x + 6 = 0 se factorise en (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":1255,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2x","option_d":"f'(x) = 3x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-1)' = 0. D'où f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f'(x) = 6x + 2\", \"b\": \"f'(x) = 3x + 2\", \"c\": \"f'(x) = 6x² + 2x\",","_debug_options_count":4},{"id":1256,"question":"Dans un triangle rectangle, si cos(θ) = 4\/5, quelle est la valeur de sin(θ) ?","option_a":"3\/5","option_b":"4\/3","option_c":"5\/3","option_d":"1\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après l'identité trigonométrique sin²(θ) + cos²(θ) = 1, on a sin(θ) = √(1 - (4\/5)²) = √(1 - 16\/25) = √(9\/25) = 3\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3\/5\", \"b\": \"4\/3\", \"c\": \"5\/3\", \"d\": \"1\/5\"}}","_debug_options_count":4},{"id":1257,"question":"Quelle est l'aire d'un disque de rayon r = 3 cm ?","option_a":"9π cm²","option_b":"6π cm²","option_c":"3π cm²","option_d":"12π cm²","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un disque est donnée par la formule A = πr². Pour r = 3 cm, A = π × 3² = 9π 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\": \"9π cm²\", \"b\": \"6π cm²\", \"c\": \"3π cm²\", \"d\": \"12π cm²\"}}","_debug_options_count":4},{"id":1258,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) lorsque x tend vers l'infini ?","option_a":"2","option_b":"3","option_c":"1","option_d":"-1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les fonctions rationnelles, la limite à l'infini est égale au rapport des coefficients dominants. Ici, lim(x→∞) f(x) = 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"2\", \"b\": \"3\", \"c\": \"1\", \"d\": \"-1\"}}","_debug_options_count":4}]