Quiz Mathématiques : Équations, Fonctions et Suites — 4ème Secondaire

Question 1 sur 10 10:00

[{"id":24528,"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":24529,"question":"La fonction f(x) = 3x + 2 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, a = 3 et b = 2, donc f est bien affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24530,"question":"Quelle est la limite de la suite uₙ = (2n + 1)\/(n + 3) quand n tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n, on obtient uₙ = (2 + 1\/n)\/(1 + 3\/n). Quand n tend vers l'infini, 1\/n tend vers 0, donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24531,"question":"L'inéquation 2x - 5 \u003E 3x + 1 a pour solution :","option_a":"x \u003C -6","option_b":"x \u003E -6","option_c":"x \u003C 6","option_d":"x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -6 \u003E x, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24532,"question":"La dérivée de f(x) = x³ - 2x² + x est f'(x) = 3x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant terme à terme, f'(x) = 3x² - 4x + 1 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24533,"question":"Quelle est l'image de 2 par la fonction f(x) = x² - 4x + 5 ?","option_a":"5","option_b":"1","option_c":"0","option_d":"9","option_e":"","option_f":"","bonne_reponse":"B","explication":"f(2) = 2² - 4*2 + 5 = 4 - 8 + 5 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24534,"question":"Une suite géométrique de raison q = 2 et de premier terme u₀ = 3 a pour terme général :","option_a":"uₙ = 3 * 2ⁿ","option_b":"uₙ = 3 + 2n","option_c":"uₙ = 3 * n²","option_d":"uₙ = 2 * 3ⁿ","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le terme général d'une suite géométrique est uₙ = u₀ * qⁿ. Ici, uₙ = 3 * 2ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24535,"question":"L'intégrale ∫(2x + 1)dx est égale à :","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x² et celle de 1 est x. On ajoute la constante C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24536,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les nombres pairs sur un dé sont 2, 4 et 6, soit 3 cas favorables sur 6 possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":24537,"question":"Quelle est la solution de l'inéquation (x - 1)(x + 3) ≤ 0 ?","option_a":"x ∈ [-3, 1]","option_b":"x ∈ ]-∞, -3] ∪ [1, +∞[","option_c":"x ∈ ]-3, 1[","option_d":"x ∈ ]-∞, -1] ∪ [3, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit (x - 1)(x + 3) est négatif ou nul entre les racines -3 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]