Quiz — m04p22ca.pdf

Question 1 sur 10 20:00

[{"id":90371,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 7","option_c":"x = -2","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 2x des deux côtés, on obtient x - 5 = 7, puis en ajoutant 5, x = 12.","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 = 12\", \"b\": \"x = 7\", \"c\": \"x = -2\", \"d\": \"x = 2\"}}","_debug_options_count":4},{"id":90372,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum en x = 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le sommet de la parabole a pour abscisse x = -b\/(2a) = 4\/2 = 2, et la fonction admet bien un minimum en ce point.","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":90373,"question":"Quel est le résultat de (2x + 3)² - (x - 1)² ?","option_a":"3x² + 14x + 8","option_b":"3x² + 10x + 8","option_c":"x² + 14x + 8","option_d":"3x² + 14x + 10","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant : (4x² + 12x + 9) - (x² - 2x + 1) = 3x² + 14x + 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"3x² + 14x + 8\", \"b\": \"3x² + 10x + 8\", \"c\": \"x² + 14x + 8\", \"d\"","_debug_options_count":4},{"id":90374,"question":"Dans un triangle rectangle, si le cosinus d'un angle est égal à 0,5, alors cet angle mesure :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"a","explication":"cos(60°) = 0,5, donc l'angle mesure 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"30°\", \"b\": \"45°\", \"c\": \"60°\", \"d\": \"90°\"}}","_debug_options_count":4},{"id":90375,"question":"La dérivée de la fonction f(x) = 3x³ - 2x² + x est f'(x) = 9x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x³ est 9x², celle de -2x² est -4x, et celle de x est 1. La formule est donc correcte.","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":90376,"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 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},{"id":90377,"question":"Si une série statistique a pour moyenne 15 et pour écart-type 3, alors environ 95% des valeurs sont comprises entre :","option_a":"12 et 18","option_b":"9 et 21","option_c":"6 et 24","option_d":"15 et 21","option_e":"","option_f":"","bonne_reponse":"b","explication":"D'après la règle des 2 écarts-types, 95% des valeurs sont dans l'intervalle [moyenne - 2σ, moyenne + 2σ] soit [9, 21].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"12 et 18\", \"b\": \"9 et 21\", \"c\": \"6 et 24\", \"d\": \"15 et 21\"}}","_debug_options_count":4},{"id":90378,"question":"La probabilité d'un événement certain est toujours égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement certain est égale à 1. Un événement impossible a une probabilité de 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":90379,"question":"Quel est le résultat de ∫(4x³ - 2x) dx ?","option_a":"x⁴ - x² + C","option_b":"x⁴ - x²","option_c":"4x⁴ - 2x² + C","option_d":"x⁴ - x + C","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'intégrale de 4x³ est x⁴, celle de -2x est -x², et on ajoute la constante d'intégration 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\": \"x⁴ - x² + C\", \"b\": \"x⁴ - x²\", \"c\": \"4x⁴ - 2x² + C\", \"d\":","_debug_options_count":4},{"id":90380,"question":"Dans un repère orthonormé, la distance entre les points A(2, 3) et B(-1, 5) est :","option_a":"√13","option_b":"√17","option_c":"5","option_d":"√29","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance est calculée par √[(xB - xA)² + (yB - yA)²] = √[(-3)² + (2)²] = √(9 + 4) = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"√13\", \"b\": \"√17\", \"c\": \"5\", \"d\": \"√29\"}}","_debug_options_count":4}]