Quiz — 6339b419f3df8_Exercice 8 type devoir.pdf

Question 1 sur 10 20:00

[{"id":15639,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A : x = 2 ou x = 3","option_b":"B : x = -2 ou x = -3","option_c":"C : x = 1 ou x = 6","option_d":"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\": \"A : x = 2 ou x = 3\", \"b\": \"B : x = -2 ou x = -3\", \"c\": \"C : x = 1","_debug_options_count":4},{"id":15640,"question":"La fonction f(x) = 2x + 3 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient directeur de la fonction affine f(x) = 2x + 3 est positif (2 \u003E 0), donc la fonction est croissante sur 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":15641,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"A : 0","option_b":"B : 1","option_c":"C : -1","option_d":"D : Impossible à déterminer","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0, car cos(90°) = 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\": \"A : 0\", \"b\": \"B : 1\", \"c\": \"C : -1\", \"d\": \"D : Impossible à dét","_debug_options_count":4},{"id":15642,"question":"Résolvez l'inéquation 3x - 7 ≤ 2x + 5.","option_a":"A : x ≤ 12","option_b":"B : x ≥ 12","option_c":"C : x ≤ -12","option_d":"D : x ≥ -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"3x - 7 ≤ 2x + 5 ⇒ 3x - 2x ≤ 5 + 7 ⇒ x ≤ 12. La solution est donc 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\": \"A : x ≤ 12\", \"b\": \"B : x ≥ 12\", \"c\": \"C : x ≤ -12\", \"d\": \"D","_debug_options_count":4},{"id":15643,"question":"La probabilité d'un événement impossible est-elle égale à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 1.","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":15644,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 5x - 2 ?","option_a":"A : 3x² - 8x + 5","option_b":"B : 3x² - 4x + 5","option_c":"C : x² - 8x + 5","option_d":"D : 3x² - 8x - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = x³ - 4x² + 5x - 2 est f'(x) = 3x² - 8x + 5 (dérivée terme à terme).","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 : 3x² - 8x + 5\", \"b\": \"B : 3x² - 4x + 5\", \"c\": \"C : x² - 8x ","_debug_options_count":4},{"id":15645,"question":"Un triangle rectangle a pour côtés 3 cm et 4 cm. Quelle est la longueur de l'hypoténuse ?","option_a":"A : 5 cm","option_b":"B : 7 cm","option_c":"C : 6 cm","option_d":"D : 4 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, l'hypoténuse c vérifie c² = 3² + 4² = 9 + 16 = 25 ⇒ c = 5 cm.","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 : 5 cm\", \"b\": \"B : 7 cm\", \"c\": \"C : 6 cm\", \"d\": \"D : 4 cm\"}}","_debug_options_count":4},{"id":15646,"question":"La moyenne de 5 notes : 10, 12, 14, 16, 18 est-elle égale à 14 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La moyenne est (10 + 12 + 14 + 16 + 18) \/ 5 = 70 \/ 5 = 14. L'affirmation est donc vraie.","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":15647,"question":"Quel est le résultat de ∫(2x + 1) dx ?","option_a":"A : x² + x + C","option_b":"B : x² + 2x + C","option_c":"C : 2x² + x + C","option_d":"D : x² - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x + 1 est x² + x + C (primitive de 2x est x², et celle de 1 est x).","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 : x² + x + C\", \"b\": \"B : x² + 2x + C\", \"c\": \"C : 2x² + x + C","_debug_options_count":4},{"id":15648,"question":"Un sac contient 3 boules rouges et 2 boules bleues. Quelle est la probabilité de tirer une boule rouge ?","option_a":"A : 3\/5","option_b":"B : 2\/5","option_c":"C : 1\/5","option_d":"D : 1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 3 boules rouges sur un total de 5 boules. La probabilité est donc 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\": \"A : 3\/5\", \"b\": \"B : 2\/5\", \"c\": \"C : 1\/5\", \"d\": \"D : 1\/2\"}}","_debug_options_count":4}]