Quiz — serie 20 p3.pdf

Question 1 sur 10 20:00

[{"id":16859,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 15\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution est obtenue en isolant x : 3x = 15 → x = 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\": \"x = 5\", \"b\": \"x = 3\", \"c\": \"x = 15\/3\", \"d\": \"x = 15\"}}","_debug_options_count":4},{"id":16860,"question":"La dérivée de la fonction f(x) = x² est-elle f'(x) = 2x ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de x² est bien 2x, selon la règle de dérivation des fonctions puissances.","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":16861,"question":"Quelle est l'image de -2 par la fonction f(x) = -3x + 4 ?","option_a":"f(-2) = 10","option_b":"f(-2) = -2","option_c":"f(-2) = -10","option_d":"f(-2) = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En remplaçant x par -2 : f(-2) = -3*(-2) + 4 = 6 + 4 = 10.","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(-2) = 10\", \"b\": \"f(-2) = -2\", \"c\": \"f(-2) = -10\", \"d\": \"f(-2) =","_debug_options_count":4},{"id":16862,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = 2b - 4ac","option_d":"Δ = b - 4a","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est calculé par la formule Δ = b² - 4ac, déterminant le nombre de solutions.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Δ = b² - 4ac\", \"b\": \"Δ = b² + 4ac\", \"c\": \"Δ = 2b - 4ac\", \"d\"","_debug_options_count":4},{"id":16863,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","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":16864,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers l'infini ?","option_a":"2","option_b":"1\/3","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant numérateur et dénominateur par x, on obtient 2\/(1 - 3\/x) → 2 quand 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\": \"2\", \"b\": \"1\/3\", \"c\": \"0\", \"d\": \"∞\"}}","_debug_options_count":4},{"id":16865,"question":"Un parallélogramme a-t-il des diagonales de même longueur ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Seuls les rectangles (cas particulier de parallélogramme) ont des diagonales de même longueur.","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":16866,"question":"Quelle est la dérivée de la fonction f(x) = sin(x) ?","option_a":"f'(x) = cos(x)","option_b":"f'(x) = -cos(x)","option_c":"f'(x) = sin(x)","option_d":"f'(x) = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de sin(x) est cos(x), selon les règles de dérivation des fonctions trigonométriques.","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) = cos(x)\", \"b\": \"f'(x) = -cos(x)\", \"c\": \"f'(x) = sin(x)\", \"","_debug_options_count":4},{"id":16867,"question":"L'équation x² + 4x + 5 = 0 admet-elle des solutions réelles ?","option_a":"Oui, deux solutions","option_b":"Non, pas de solutions réelles","option_c":"Oui, une solution double","option_d":"Oui, une solution réelle","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant Δ = 16 - 20 = -4 \u003C 0, donc pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Oui, deux solutions\", \"b\": \"Non, pas de solutions réelles\", \"c\":","_debug_options_count":4},{"id":16868,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","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}]