Quiz — Devoir de Synthèse N°1 Lycée pilote - Math - 3ème Math (2015-2016) Mr Lâamaimi.Mohieddine.pdf

Question 1 sur 10 20:00

[{"id":128560,"question":"Quelle est la dérivée de la fonction f(x) = x³ + 2x² - 5 ?","option_a":"3x² + 4x","option_b":"x² + 2x","option_c":"3x² + 4x - 5","option_d":"x³ + 2x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme en utilisant la règle : dérivée de x^n = n*x^(n-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\": \"3x² + 4x\", \"b\": \"x² + 2x\", \"c\": \"3x² + 4x - 5\", \"d\": \"x³ + 2x","_debug_options_count":4},{"id":128561,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x=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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":128562,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour les fonctions rationnelles, la limite à l'infini est égale au rapport des coefficients dominants (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\": \"0\", \"c\": \"1\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":128563,"question":"La fonction f(x) = sin(x) est périodique de période π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction sin(x) a une période de 2π, pas π.","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":128564,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"En simplifiant, on obtient x ≤ 12.","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 ≤ 12\", \"b\": \"x ≥ 12\", \"c\": \"x ≤ -12\", \"d\": \"x ≥ -12\"}}","_debug_options_count":4},{"id":128565,"question":"Le vecteur u(2, -3) et le vecteur v(-1, 4) sont orthogonaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Deux vecteurs sont orthogonaux si leur produit scalaire est nul : (2*-1) + (-3*4) = -2 -12 = -14 ≠ 0.","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":128566,"question":"Quelle est l'image de 2 par la fonction f(x) = e^(x-1) ?","option_a":"e","option_b":"1","option_c":"e²","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par 2, on obtient f(2) = e^(2-1) = e^1 = e.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"e\", \"b\": \"1\", \"c\": \"e²\", \"d\": \"0\"}}","_debug_options_count":4},{"id":128567,"question":"La fonction f(x) = ln(x) est définie pour tout x réel.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":128568,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 2","option_b":"x = 1","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En réécrivant 8 comme 2^3, on obtient 2^(x+1) = 2^3, donc x+1 = 3 et x = 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\": \"x = 2\", \"b\": \"x = 1\", \"c\": \"x = 3\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":128569,"question":"Le plan P d'équation x + 2y - z = 5 passe par le point A(1, 1, -2).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant les coordonnées de A dans l'équation, on obtient 1 + 2*1 - (-2) = 1 + 2 + 2 = 5, donc A appartient au plan P.","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}]