Quiz — syn24m2007-2008.pdf

Question 1 sur 10 20:00

[{"id":22099,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A. 6x + 2","option_b":"B. 3x + 2","option_c":"C. 6x² + 2x","option_d":"D. 6x - 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : 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. 3x + 2\", \"c\": \"C. 6x² + 2x\", \"d\": \"D. 6x - ","_debug_options_count":4},{"id":22100,"question":"L'équation sin(x) = √2\/2 admet-elle des solutions dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans [0, π], sin(x) = √2\/2 admet deux solutions : x = π\/4 et x = 3π\/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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":22101,"question":"Soit f(x) = x³ - 3x² + 2. Quel est le coefficient directeur de la tangente à la courbe au point d'abscisse x = 1 ?","option_a":"A. -3","option_b":"B. 0","option_c":"C. 3","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur de la tangente est f'(1). f'(x) = 3x² - 6x, donc f'(1) = 3 - 6 = -3. Attention, la question demande le coefficient directeur, mais l'option B correspond à f(1) = 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\": \"A. -3\", \"b\": \"B. 0\", \"c\": \"C. 3\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":22102,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, alors cos(θ) est égal à :","option_a":"A. 4\/5","option_b":"B. 3\/4","option_c":"C. 5\/3","option_d":"D. 2\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, cos(θ) = √(1 - sin²(θ)) = √(1 - 9\/25) = 4\/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\": \"A. 4\/5\", \"b\": \"B. 3\/4\", \"c\": \"C. 5\/3\", \"d\": \"D. 2\/5\"}}","_debug_options_count":4},{"id":22103,"question":"La dérivée de la fonction f(x) = cos(2x) est f'(x) = -2sin(2x).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la règle de dérivation des fonctions composées, f'(x) = -sin(2x) * 2 = -2sin(2x).","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":22104,"question":"Quelle est la valeur de tan(π\/3) ?","option_a":"A. 1","option_b":"B. √3","option_c":"C. 1\/√3","option_d":"D. 0","option_e":"","option_f":"","bonne_reponse":"b","explication":"tan(π\/3) = sin(π\/3)\/cos(π\/3) = (√3\/2)\/(1\/2) = √3.","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. √3\", \"c\": \"C. 1\/√3\", \"d\": \"D. 0\"}}","_debug_options_count":4},{"id":22105,"question":"Soit un cube d'arête 4 cm. Quel est son volume ?","option_a":"A. 16 cm³","option_b":"B. 64 cm³","option_c":"C. 32 cm³","option_d":"D. 12 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'un cube est donné par V = arête³ = 4³ = 64 cm³.","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. 16 cm³\", \"b\": \"B. 64 cm³\", \"c\": \"C. 32 cm³\", \"d\": \"D. 12 cm","_debug_options_count":4},{"id":22106,"question":"La fonction f(x) = x² + 1 est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 2x est négative pour x \u003C 0, donc la fonction est décroissante sur ]-∞, 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":22107,"question":"Quelle est la dérivée de la fonction f(x) = e^(3x) ?","option_a":"A. 3e^(3x)","option_b":"B. e^(3x)","option_c":"C. 3x e^(3x)","option_d":"D. e^(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"En appliquant la règle de dérivation des fonctions exponentielles, f'(x) = 3e^(3x).","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. 3e^(3x)\", \"b\": \"B. e^(3x)\", \"c\": \"C. 3x e^(3x)\", \"d\": \"D. e^(x","_debug_options_count":4},{"id":22108,"question":"Dans un repère orthonormé, la distance entre les points A(1, 2) et B(4, 6) est :","option_a":"A. 5","option_b":"B. 7","option_c":"C. √7","option_d":"D. √29","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance AB = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. L'option B correspond à la somme des coordonnées.","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. 5\", \"b\": \"B. 7\", \"c\": \"C. √7\", \"d\": \"D. √29\"}}","_debug_options_count":4}]