Quiz — devoir-de-synthèse-n°2--2016-2017(mr-moutia-mabrouk).pdf

Question 1 sur 10 20:00

[{"id":4956,"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. Les solutions sont donc 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":4957,"question":"Une fonction f est définie par f(x) = 3x + 2. Cette fonction est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine f(x) = ax + b est croissante si a \u003E 0. Ici, a = 3 \u003E 0, donc la fonction est croissante.","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":4958,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) -1","option_d":"D) Impossible à déterminer","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0, car le cosinus de l'angle entre eux 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\": \"A) 0\", \"b\": \"B) 1\", \"c\": \"C) -1\", \"d\": \"D) Impossible à détermi","_debug_options_count":4},{"id":4959,"question":"La médiane d'une série statistique est toujours égale à la moyenne ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont deux indicateurs différents. La médiane est la valeur centrale, tandis que la moyenne est la somme des valeurs divisée par leur nombre. Elles ne sont égales que dans des cas particuliers.","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":4960,"question":"Quelle est la forme canonique de l'expression x² - 6x + 5 ?","option_a":"A) (x-3)² - 4","option_b":"B) (x-2)² - 1","option_c":"C) (x-5)² - 1","option_d":"D) (x-1)² - 4","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique s'obtient en complétant le carré : x² - 6x + 5 = (x² - 6x + 9) - 4 = (x-3)² - 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-3)² - 4\", \"b\": \"B) (x-2)² - 1\", \"c\": \"C) (x-5)² - 1\", \"d","_debug_options_count":4},{"id":4961,"question":"Dans un repère orthonormé, la distance entre les points A(1,2) et B(4,6) est :","option_a":"A) 5","option_b":"B) √7","option_c":"C) √13","option_d":"D) 7","option_e":"","option_f":"","bonne_reponse":"c","explication":"La distance entre A et B est calculée par la formule √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5. L'option C est incorrecte car √13 ≈ 3,6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 5\", \"b\": \"B) √7\", \"c\": \"C) √13\", \"d\": \"D) 7\"}}","_debug_options_count":4},{"id":4962,"question":"Soit une fonction f définie par f(x) = x² - 4x + 3. Quel est le sommet de sa parabole ?","option_a":"A) (2, -1)","option_b":"B) (1, 0)","option_c":"C) (3, 0)","option_d":"D) (-1, 8)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le sommet d'une parabole y = ax² + bx + c a pour abscisse x = -b\/(2a). Ici, x = 4\/2 = 2. L'ordonnée est f(2) = 4 - 8 + 3 = -1. Le sommet est donc (2, -1).","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) (2, -1)\", \"b\": \"B) (1, 0)\", \"c\": \"C) (3, 0)\", \"d\": \"D) (-1, 8)","_debug_options_count":4},{"id":4963,"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. La probabilité 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":4964,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) lorsque x tend vers l'infini ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) 2","option_d":"D) ∞","option_e":"","option_f":"","bonne_reponse":"c","explication":"Pour x tendant vers l'infini, on divise le numérateur et le dénominateur par x² : f(x) ≈ (2 + 3\/x - 1\/x²)\/(1 - 1\/x²) → 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A) 0\", \"b\": \"B) 1\", \"c\": \"C) 2\", \"d\": \"D) ∞\"}}","_debug_options_count":4},{"id":4965,"question":"Une suite géométrique de raison q = -2 et de premier terme u₀ = 3 a pour terme général :","option_a":"A) uₙ = 3 * (-2)ⁿ","option_b":"B) uₙ = 3 * 2ⁿ","option_c":"C) uₙ = -3 * (-2)ⁿ","option_d":"D) uₙ = 3 * (-2)ⁿ⁺¹","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ. Ici, u₀ = 3 et q = -2, donc uₙ = 3 * (-2)ⁿ.","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 = 3 * (-2)ⁿ\", \"b\": \"B) uₙ = 3 * 2ⁿ\", \"c\": \"C) uₙ ","_debug_options_count":4}]