Quiz — Série1.doc

Question 1 sur 10 20:00

[{"id":54447,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A) x = 2 ou x = 3","option_b":"B) x = -2 ou x = -3","option_c":"C) x = 1 ou x = 6","option_d":"D) x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et 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\": \"A) x = 2 ou x = 3\", \"b\": \"B) x = -2 ou x = -3\", \"c\": \"C) x = 1 ou","_debug_options_count":4},{"id":54448,"question":"La fonction f(x) = x³ - 3x est-elle impaire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ - 3(-x) = -x³ + 3x = -(x³ - 3x) = -f(x). Donc la fonction est impaire.","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":54449,"question":"Quel est le terme général d'une suite géométrique de premier terme u₀ = 2 et de raison q = 3 ?","option_a":"A) uₙ = 2 × 3ⁿ","option_b":"B) uₙ = 3 × 2ⁿ","option_c":"C) uₙ = 2 + 3n","option_d":"D) uₙ = 3ⁿ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une suite géométrique, le terme général est uₙ = u₀ × qⁿ. Ici, u₀ = 2 et q = 3, donc uₙ = 2 × 3ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) uₙ = 2 × 3ⁿ\", \"b\": \"B) uₙ = 3 × 2ⁿ\", \"c\": \"C) uₙ =","_debug_options_count":4},{"id":54450,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Cette affirmation est-elle vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore, qui s'applique uniquement aux triangles rectangles.","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":54451,"question":"Quelle est la dérivée de la fonction f(x) = 2x² + 3x - 5 ?","option_a":"A) f'(x) = 4x + 3","option_b":"B) f'(x) = 2x + 3","option_c":"C) f'(x) = 4x² + 3x","option_d":"D) f'(x) = 2x² + 3","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 2x² est 4x, celle de 3x est 3, et celle de -5 est 0. Donc f'(x) = 4x + 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\": \"A) f'(x) = 4x + 3\", \"b\": \"B) f'(x) = 2x + 3\", \"c\": \"C) f'(x) = 4x","_debug_options_count":4},{"id":54452,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La probabilité d'un événement impossible est égale à 0, tandis que celle d'un événement certain est égale à 1.","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":54453,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"A) 5","option_b":"B) 7","option_c":"C) 25","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le module d'un nombre complexe z = a + bi est donné par √(a² + b²). Ici, √(3² + 4²) = √(9 + 16) = √25 = 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\": \"A) 5\", \"b\": \"B) 7\", \"c\": \"C) 25\", \"d\": \"D) 1\"}}","_debug_options_count":4},{"id":54454,"question":"La médiane d'un triangle est une droite qui passe par un sommet et le milieu du côté opposé.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition exacte d'une médiane dans un triangle.","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":54455,"question":"Résoudre l'inéquation 2x - 3 \u003E 5.","option_a":"A) x \u003E 4","option_b":"B) x \u003C 4","option_c":"C) x \u003E 1","option_d":"D) x \u003C 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. Donc la solution est 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\": \"A) x \u003E 4\", \"b\": \"B) x \u003C 4\", \"c\": \"C) x \u003E 1\", \"d\": \"D) x \u003C 1\"}}","_debug_options_count":4},{"id":54456,"question":"Quel est le centre de symétrie de la fonction f(x) = x³ - 2x ?","option_a":"A) Le point (0, 0)","option_b":"B) Le point (1, -1)","option_c":"C) Le point (0, -2)","option_d":"D) Le point (2, 0)","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction f(x) = x³ - 2x est impaire, donc son centre de symétrie est l'origine (0, 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A) Le point (0, 0)\", \"b\": \"B) Le point (1, -1)\", \"c\": \"C) Le poin","_debug_options_count":4}]