Quiz — 1576612598_62577_exercice-4.pdf

Question 1 sur 10 20:00

[{"id":36370,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = 6","option_c":"x = -4","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'équation : 2x - 5 = 3x + 1 → -5 - 1 = 3x - 2x → -6 = x. La solution est x = -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\": \"x = -6\", \"b\": \"x = 6\", \"c\": \"x = -4\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":36371,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [-∞, 2] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² - 4x + 3 est une parabole tournée vers le haut. Son sommet est en x = 2, donc elle est décroissante sur [-∞, 2] et croissante sur [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":36372,"question":"Quel est le résultat de ∫(3x² + 2x) dx ?","option_a":"x³ + x² + C","option_b":"x³ + x + C","option_c":"3x³ + x² + C","option_d":"x³ + 2x² + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 3x² est x³ et celle de 2x est x². La constante d'intégration est notée C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x³ + x² + C\", \"b\": \"x³ + x + C\", \"c\": \"3x³ + x² + C\", \"d\": \"","_debug_options_count":4},{"id":36373,"question":"Dans un triangle rectangle, si cos(θ) = 3\/5, quelle est la valeur de sin(θ) ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"2\/5","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, sin²(θ) + cos²(θ) = 1 → sin²(θ) = 1 - (3\/5)² = 16\/25 → sin(θ) = 4\/5 (car θ est un angle aigu).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"4\/5\", \"b\": \"3\/4\", \"c\": \"5\/3\", \"d\": \"2\/5\"}}","_debug_options_count":4},{"id":36374,"question":"La moyenne d'une série de 5 notes est 12. Si on ajoute une 6ème note de 15, la nouvelle moyenne devient-elle 12,5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des 5 notes est 5 × 12 = 60. Avec la 6ème note, la somme devient 60 + 15 = 75. La nouvelle moyenne est 75 \/ 6 = 12,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":36375,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)³ ?","option_a":"6(2x + 1)²","option_b":"3(2x + 1)²","option_c":"2(2x + 1)²","option_d":"(2x + 1)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"En utilisant la formule de dérivation des fonctions composées : f'(x) = 3(2x + 1)² × 2 = 6(2x + 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\": \"6(2x + 1)²\", \"b\": \"3(2x + 1)²\", \"c\": \"2(2x + 1)²\", \"d\": \"(2x +","_debug_options_count":4},{"id":36376,"question":"Dans un cercle de rayon 5 cm, quelle est la longueur d'un arc correspondant à un angle de 60° ?","option_a":"5π\/3 cm","option_b":"10π\/3 cm","option_c":"5π cm","option_d":"π cm","option_e":"","option_f":"","bonne_reponse":"b","explication":"La longueur d'un arc est donnée par L = (θ\/360) × 2πr. Ici, L = (60\/360) × 2π × 5 = (1\/6) × 10π = 10π\/3 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"5π\/3 cm\", \"b\": \"10π\/3 cm\", \"c\": \"5π cm\", \"d\": \"π cm\"}}","_debug_options_count":4},{"id":36377,"question":"La probabilité d'un événement A est P(A) = 0,4. Quelle est la probabilité de l'événement contraire A̅ ?","option_a":"0,4","option_b":"0,6","option_c":"0,8","option_d":"0,2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité de l'événement contraire est P(A̅) = 1 - P(A) = 1 - 0,4 = 0,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0,4\", \"b\": \"0,6\", \"c\": \"0,8\", \"d\": \"0,2\"}}","_debug_options_count":4},{"id":36378,"question":"Le vecteur u(3, -2) et le vecteur v(-1, 4) sont-ils orthogonaux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Deux vecteurs sont orthogonaux si leur produit scalaire est nul. u·v = (3 × -1) + (-2 × 4) = -3 - 8 = -11 ≠ 0. Ils ne sont pas orthogonaux.","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":36379,"question":"Quelle est la solution de l'inéquation 2x² - 5x - 3 \u003E 0 ?","option_a":"x ∈ ]-∞, -1\/2[ ∪ ]3, +∞[","option_b":"x ∈ ]-1\/2, 3[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]-1\/2, +∞[","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les racines de l'équation 2x² - 5x - 3 = 0 sont x = -1\/2 et x = 3. Le coefficient de x² est positif, donc l'inéquation est vérifiée en dehors des racines.","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 ∈ ]-∞, -1\/2[ ∪ ]3, +∞[\", \"b\": \"x ∈ ]-1\/2, 3[\", \"c\": \"","_debug_options_count":4}]