Quiz — Devoir-de-contrôle-n°3-3ème-Mathématiques-Mr-Faleh-05-05-8.pdf

Question 1 sur 10 20:00

[{"id":18359,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = -2","option_d":"x = 1\/2 ou x = 2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La solution s'obtient en utilisant la formule des racines du second degré : x = [5 ± √(25 - 16)] \/ 4 = [5 ± 3]\/4. Les solutions sont donc x = 2 et x = 1\/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\": \"x = 1 ou x = 2\", \"b\": \"x = 2 ou x = 1\/2\", \"c\": \"x = -1 ou x = -2\"","_debug_options_count":4},{"id":18360,"question":"Le théorème de Pythagore s'applique-t-il dans un triangle rectangle uniquement ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le théorème de Pythagore s'applique exclusivement aux triangles rectangles, où le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","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":18361,"question":"Soit f(x) = 3x + 2. Quelle est l'image de x = -1 par cette fonction ?","option_a":"f(-1) = -1","option_b":"f(-1) = 1","option_c":"f(-1) = -5","option_d":"f(-1) = 5","option_e":"","option_f":"","bonne_reponse":"c","explication":"En substituant x = -1 dans f(x) = 3x + 2, on obtient f(-1) = 3*(-1) + 2 = -3 + 2 = -1. Attention à ne pas confondre avec f(-1) = -5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"f(-1) = -1\", \"b\": \"f(-1) = 1\", \"c\": \"f(-1) = -5\", \"d\": \"f(-1) = 5","_debug_options_count":4},{"id":18362,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 12 cm et AC = 13 cm, alors le triangle est :","option_a":"Acute","option_b":"Obtus","option_c":"Rectangle","option_d":"Isocèle","option_e":"","option_f":"","bonne_reponse":"c","explication":"On vérifie si AB² + BC² = AC² : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"Acute\", \"b\": \"Obtus\", \"c\": \"Rectangle\", \"d\": \"Isocèle\"}}","_debug_options_count":4},{"id":18363,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution :","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, soit x \u003E 4. L'inéquation est donc vérifiée pour x \u003E 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\": \"x \u003E 4\", \"b\": \"x \u003C 4\", \"c\": \"x \u003E 1\", \"d\": \"x \u003C 1\"}}","_debug_options_count":4},{"id":18364,"question":"Le volume d'une sphère de rayon r est donné par la formule V = (4\/3)πr³. Vrai ou faux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du volume d'une sphère est bien V = (4\/3)πr³, où r est le rayon de la sphère.","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":18365,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + x - 5 ?","option_a":"f'(x) = 3x² - 4x + 1","option_b":"f'(x) = x² - 2x + 1","option_c":"f'(x) = 3x² - 2x + 1","option_d":"f'(x) = 3x² - 4x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de f(x) = x³ - 2x² + x - 5 est f'(x) = 3x² - 4x + 1, obtenue en appliquant les règles de dérivation 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\": \"f'(x) = 3x² - 4x + 1\", \"b\": \"f'(x) = x² - 2x + 1\", \"c\": \"f'(x) ","_debug_options_count":4},{"id":18366,"question":"Un parallélogramme a des diagonales de même longueur. Alors c'est un :","option_a":"Losange","option_b":"Rectangle","option_c":"Carré","option_d":"Trapèze","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans un parallélogramme, si les diagonales sont de même longueur, alors c'est un rectangle (propriété caractéristique).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Losange\", \"b\": \"Rectangle\", \"c\": \"Carré\", \"d\": \"Trapèze\"}}","_debug_options_count":4},{"id":18367,"question":"La fonction f(x) = x² est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est positive pour tout x réel, car un carré est toujours positif ou nul. La réponse 'Vrai' est donc correcte.","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":18368,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 5 ?","option_a":"5","option_b":"-2","option_c":"2","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"b","explication":"Dans l'équation réduite y = mx + p, m représente le coefficient directeur. Ici, m = -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\": \"5\", \"b\": \"-2\", \"c\": \"2\", \"d\": \"-5\"}}","_debug_options_count":4}]