Quiz — cor S3 mr ammar ex 1+2.pdf

Question 1 sur 10 20:00

[{"id":70582,"question":"Quelle est l'équation d'une fonction affine dont la représentation graphique passe par les points A(1; 3) et B(2; 5) ?","option_a":"A. y = 2x + 1","option_b":"B. y = x + 2","option_c":"C. y = 3x - 2","option_d":"D. y = -x + 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La pente m = (5-3)\/(2-1) = 2. En utilisant la formule y = mx + b et le point A(1;3), on trouve 3 = 2*1 + b =\u003E b = 1. Donc l'équation est y = 2x + 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\": \"A. y = 2x + 1\", \"b\": \"B. y = x + 2\", \"c\": \"C. y = 3x - 2\", \"d\": \"","_debug_options_count":4},{"id":70583,"question":"La fonction f(x) = -3x + 7 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine f(x) = ax + b est décroissante si a \u003C 0. Ici, a = -3 \u003C 0, donc la fonction est décroissante.","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":70584,"question":"Quel est l'antécédent de 10 par la fonction f(x) = 2x - 4 ?","option_a":"A. 3","option_b":"B. 5","option_c":"C. 7","option_d":"D. 9","option_e":"","option_f":"","bonne_reponse":"d","explication":"On résout l'équation 2x - 4 = 10 =\u003E 2x = 14 =\u003E x = 7. L'antécédent de 10 est donc 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"A. 3\", \"b\": \"B. 5\", \"c\": \"C. 7\", \"d\": \"D. 9\"}}","_debug_options_count":4},{"id":70585,"question":"La section plane d'un cube par un plan parallèle à une face est toujours un carré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si le plan est parallèle à une face du cube, la section est un carré de même taille que la face. La propriété 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":70586,"question":"Quel est le volume d'un cylindre de rayon 3 cm et de hauteur 5 cm ? (π ≈ 3,14)","option_a":"A. 47,1 cm³","option_b":"B. 141,3 cm³","option_c":"C. 94,2 cm³","option_d":"D. 282,6 cm³","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le volume d'un cylindre est V = πr²h = 3,14 * 3² * 5 = 3,14 * 9 * 5 = 141,3 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. 47,1 cm³\", \"b\": \"B. 141,3 cm³\", \"c\": \"C. 94,2 cm³\", \"d\": \"D","_debug_options_count":4},{"id":70587,"question":"La fonction f(x) = x² + 4x + 4 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x² + 4x + 4 = (x+2)² est une parabole tournée vers le haut, donc elle admet un minimum en 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":70588,"question":"Quel est le coefficient directeur de la droite d'équation y = -5x + 2 ?","option_a":"A. -5","option_b":"B. 2","option_c":"C. 5","option_d":"D. -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans l'équation d'une droite y = ax + b, a représente le coefficient directeur. Ici, a = -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. -5\", \"b\": \"B. 2\", \"c\": \"C. 5\", \"d\": \"D. -2\"}}","_debug_options_count":4},{"id":70589,"question":"Un cône de révolution a un rayon de base de 4 cm et une hauteur de 9 cm. Quel est son volume ? (π ≈ 3,14)","option_a":"A. 150,72 cm³","option_b":"B. 75,36 cm³","option_c":"C. 301,44 cm³","option_d":"D. 452,16 cm³","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le volume d'un cône est V = (1\/3)πr²h = (1\/3)*3,14*4²*9 = (1\/3)*3,14*16*9 = 150,72 cm³.","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. 150,72 cm³\", \"b\": \"B. 75,36 cm³\", \"c\": \"C. 301,44 cm³\", \"d\"","_debug_options_count":4},{"id":70590,"question":"La fonction f(x) = 3x² - 6x + 2 admet-elle un maximum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = 3x² - 6x + 2 est une parabole tournée vers le haut (coefficient de x² \u003E 0), donc elle n'admet pas de maximum.","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":70591,"question":"Quel est le résultat de f(2) pour la fonction f(x) = 4x - 7 ?","option_a":"A. 1","option_b":"B. 3","option_c":"C. 5","option_d":"D. 7","option_e":"","option_f":"","bonne_reponse":"b","explication":"On remplace x par 2 dans l'équation : f(2) = 4*2 - 7 = 8 - 7 = 1. Le résultat est donc 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\": \"A. 1\", \"b\": \"B. 3\", \"c\": \"C. 5\", \"d\": \"D. 7\"}}","_debug_options_count":4}]