Quiz — P-PB20-40-FM.pdf

Question 1 sur 10 20:00

[{"id":48937,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 4","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'équation, on obtient : 2x - 5 = 3x + 1 → -x = 6 → 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 = -4\", \"c\": \"x = 4\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":48938,"question":"La fonction f(x) = x² est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[.","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":48939,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x + 1 ?","option_a":"f'(x) = 9x² - 2","option_b":"f'(x) = 3x² - 2","option_c":"f'(x) = 9x² + 1","option_d":"f'(x) = 6x² - 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En dérivant terme à terme, on obtient f'(x) = 9x² - 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\": \"f'(x) = 9x² - 2\", \"b\": \"f'(x) = 3x² - 2\", \"c\": \"f'(x) = 9x² + ","_debug_options_count":4},{"id":48940,"question":"Un triangle rectangle a un angle de 30°. Quelle est la valeur du troisième angle ?","option_a":"30°","option_b":"60°","option_c":"90°","option_d":"120°","option_e":"","option_f":"","bonne_reponse":"b","explication":"La somme des angles d'un triangle est 180°. Si deux angles sont 90° et 30°, le troisième est 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"30°\", \"b\": \"60°\", \"c\": \"90°\", \"d\": \"120°\"}}","_debug_options_count":4},{"id":48941,"question":"L'intégrale de f(x) = 2x entre 0 et 2 est égale à 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 2x entre 0 et 2 est [x²]₀² = 4 - 0 = 4. L'affirmation 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":48942,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","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 - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":48943,"question":"Un vecteur u a pour coordonnées (2, -3). Quelle est la norme de u ?","option_a":"√13","option_b":"5","option_c":"√5","option_d":"√10","option_e":"","option_f":"","bonne_reponse":"a","explication":"La norme de u est √(2² + (-3)²) = √(4 + 9) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"√13\", \"b\": \"5\", \"c\": \"√5\", \"d\": \"√10\"}}","_debug_options_count":4},{"id":48944,"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 eˣ est toujours positive pour tout x réel.","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":48945,"question":"Quelle est la solution de l'inéquation 3x + 2 ≤ 11 ?","option_a":"x ≤ 3","option_b":"x ≤ -3","option_c":"x ≥ 3","option_d":"x ≥ -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"En résolvant l'inéquation, on obtient : 3x ≤ 9 → x ≤ 3.","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 ≤ 3\", \"b\": \"x ≤ -3\", \"c\": \"x ≥ 3\", \"d\": \"x ≥ -3\"}}","_debug_options_count":4},{"id":48946,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est nul.","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}]