Quiz — Série d'exercices N°3 - Math - 2ème Sciences exp (2016-2017) Mr Zantour Hamdi.pdf

Question 1 sur 10 20:00

[{"id":24514,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A) 6x + 2","option_b":"B) 6x² + 2","option_c":"C) 3x + 2","option_d":"D) 6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme est obtenue en appliquant la règle de dérivation : 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\": \"A) 6x + 2\", \"b\": \"B) 6x² + 2\", \"c\": \"C) 3x + 2\", \"d\": \"D) 6x - 5","_debug_options_count":4},{"id":24515,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = b² - 4ac = 0, donc l'équation admet une solution réelle 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":24516,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ x quand x tend vers l'infini ?","option_a":"A) 0","option_b":"B) 2","option_c":"C) +∞","option_d":"D) -∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"La limite de (2x² + 3x)\/x quand x tend vers l'infini est 2x + 3, donc la limite est +∞. Aucune option n'est correcte, donc cette question doit être modifiée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 0\", \"b\": \"B) 2\", \"c\": \"C) +∞\", \"d\": \"D) -∞\"}}","_debug_options_count":4},{"id":24517,"question":"Soit un vecteur u(3, -2). Quelle est la norme de ce vecteur ?","option_a":"A) 1","option_b":"B) √13","option_c":"C) 5","option_d":"D) √5","option_e":"","option_f":"","bonne_reponse":"b","explication":"La norme d'un vecteur u(a, b) est √(a² + b²) = √(9 + 4) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A) 1\", \"b\": \"B) √13\", \"c\": \"C) 5\", \"d\": \"D) √5\"}}","_debug_options_count":4},{"id":24518,"question":"La fonction f(x) = x³ est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² ≥ 0 pour tout x ∈ ℝ, et f'(x) = 0 seulement en x = 0. La fonction est donc strictement croissante.","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":24519,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A) x \u003C -6","option_b":"B) x \u003E -6","option_c":"C) x \u003C 6","option_d":"D) x \u003E 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant, on obtient 2x - 5 \u003E 3x + 1 → -x \u003E 6 → x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) x \u003C -6\", \"b\": \"B) x \u003E -6\", \"c\": \"C) x \u003C 6\", \"d\": \"D) x \u003E 6\"}}","_debug_options_count":4},{"id":24520,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours égal à zéro ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, deux vecteurs orthogonaux ont un produit scalaire nul.","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":24521,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 10 ?","option_a":"A) (x - 3)² + 1","option_b":"B) (x - 3)² - 1","option_c":"C) (x + 3)² + 1","option_d":"D) (x - 6)² + 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique est f(x) = (x - 3)² + 1, obtenue par complétion du carré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) (x - 3)² + 1\", \"b\": \"B) (x - 3)² - 1\", \"c\": \"C) (x + 3)² + ","_debug_options_count":4},{"id":24522,"question":"La fonction exponentielle est-elle toujours positive sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle eˣ est strictement positive pour tout x ∈ ℝ.","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":24523,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"A) x = e²","option_b":"B) x = 2e","option_c":"C) x = 1\/2","option_d":"D) x = ln(2)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En exponentiant les deux côtés, on obtient x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) x = e²\", \"b\": \"B) x = 2e\", \"c\": \"C) x = 1\/2\", \"d\": \"D) x = ln","_debug_options_count":4}]