Quiz — 5 مواضيع نموذجية.pdf

Question 1 sur 10 20:00

[{"id":86913,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x et (2x)' = 2, donc f'(x) = 6x + 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\": \"6x + 2\", \"b\": \"3x + 2\", \"c\": \"6x² + 2x\", \"d\": \"3x² + 2\"}}","_debug_options_count":4},{"id":86914,"question":"La suite (Un) définie par Un = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, Un+1 - Un = 2, donc elle est arithmétique.","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":86915,"question":"Quelle est l'intégrale de f(x) = 4x³ entre 0 et 2 ?","option_a":"16","option_b":"8","option_c":"32","option_d":"4","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 4x³ est x⁴. Entre 0 et 2, cela donne 2⁴ - 0⁴ = 16.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"16\", \"b\": \"8\", \"c\": \"32\", \"d\": \"4\"}}","_debug_options_count":4},{"id":86916,"question":"Soit une expérience aléatoire avec 3 issues possibles. Si P(A) = 0.2 et P(B) = 0.3, quelle est la probabilité de l'issue C ?","option_a":"0.5","option_b":"0.4","option_c":"0.6","option_d":"0.7","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des probabilités est 1. Donc P(C) = 1 - (0.2 + 0.3) = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"0.5\", \"b\": \"0.4\", \"c\": \"0.6\", \"d\": \"0.7\"}}","_debug_options_count":4},{"id":86917,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle, notée exp(x) ou eˣ, est définie pour tout x réel et prend des valeurs strictement positives.","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":86918,"question":"Quelle est la limite de (2x² + 3x - 1)\/(x² - 4) lorsque x tend vers l'infini ?","option_a":"2","option_b":"3","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour x → ∞, on divise numérateur et dénominateur par x² : limite = 2x²\/x² = 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\": \"2\", \"b\": \"3\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":86919,"question":"Un dé équilibré est lancé deux fois. Quelle est la probabilité d'obtenir deux fois le même nombre ?","option_a":"1\/6","option_b":"1\/36","option_c":"1\/3","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 6 résultats possibles pour le premier lancer et 1 seul résultat identique pour le second. Probabilité = 6*(1\/6)*(1\/6) = 1\/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\": \"1\/6\", \"b\": \"1\/36\", \"c\": \"1\/3\", \"d\": \"1\/2\"}}","_debug_options_count":4},{"id":86920,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle [-2, 0] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-2, 0] (ex: f'(-1) = 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\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":86921,"question":"Quelle est la solution de l'équation ln(x) = 2 ?","option_a":"e²","option_b":"2e","option_c":"ln(2)","option_d":"e","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, ln(x) = 2 ⇒ x = e².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"e²\", \"b\": \"2e\", \"c\": \"ln(2)\", \"d\": \"e\"}}","_debug_options_count":4},{"id":86922,"question":"Soit un triangle ABC avec AB = 5, BC = 4 et AC = 3. Le triangle est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vérification du théorème de Pythagore : 3² + 4² = 5² ⇒ 9 + 16 = 25, donc le triangle est rectangle en 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]