Quiz : Les incontournables du 3ème trimestre en mathématiques (3ème année secondaire)

Question 1 sur 10 10:00

[{"id":74182,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_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},{"id":74183,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction n'est donc pas croissante sur tout ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74184,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers +∞ ?","option_a":"0","option_b":"2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). La limite est donc 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74185,"question":"Un dé cubique est truqué : la probabilité d'obtenir 6 est de 0,3. Quelle est la probabilité d'obtenir un nombre pair ?","option_a":"0,35","option_b":"0,4","option_c":"0,5","option_d":"0,6","option_e":"","option_f":"","bonne_reponse":"D","explication":"Les nombres pairs sont 2, 4 et 6. P(2) = P(4) = (1-0,3)\/2 = 0,35. P(6) = 0,3. La probabilité totale est 0,35 + 0,35 + 0,3 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74186,"question":"La section d'un cube par un plan parallèle à une face est toujours un carré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si le plan est parallèle à une face, la section est effectivement un carré de même taille que la face.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74187,"question":"Quelle est la dérivée de la fonction f(x) = (x² + 1)\/(x - 1) ?","option_a":"f'(x) = (2x)\/(x - 1)","option_b":"f'(x) = (x² - 2x - 1)\/(x - 1)²","option_c":"f'(x) = (2x² - 2x + 2)\/(x - 1)²","option_d":"f'(x) = (x² + 2x - 1)\/(x - 1)²","option_e":"","option_f":"","bonne_reponse":"B","explication":"En utilisant la formule de dérivation d'un quotient, f'(x) = [(2x)(x-1) - (x²+1)(1)]\/(x-1)² = (x² - 2x - 1)\/(x - 1)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74188,"question":"Soit une suite arithmétique de premier terme u₀ = 5 et de raison r = -2. Quel est le 10ème terme ?","option_a":"u₁₀ = -13","option_b":"u₁₀ = -15","option_c":"u₁₀ = 5","option_d":"u₁₀ = 25","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule du terme général d'une suite arithmétique est uₙ = u₀ + n*r. Donc u₁₀ = 5 + 10*(-2) = -15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74189,"question":"La fonction f(x) = √(x² + 1) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = √((-x)² + 1) = √(x² + 1) = f(x). Donc f est paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74190,"question":"Quelle est l'aire d'un triangle de côtés 5 cm, 6 cm et 7 cm ?","option_a":"14,7 cm²","option_b":"15 cm²","option_c":"16,5 cm²","option_d":"18 cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule de Héron : s = (5+6+7)\/2 = 9. Aire = √[s(s-a)(s-b)(s-c)] = √[9*4*3*2] = √216 ≈ 14,7 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74191,"question":"La fonction exponentielle est-elle toujours positive sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle eˣ est définie pour tout x ∈ ℝ et eˣ \u003E 0 pour tout x ∈ ℝ. Donc elle est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]