Quiz Mathématiques : 4ème année secondaire — Algèbre & Analyse

Question 1 sur 10 10:00

[{"id":15128,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 4\/3","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 7 → 3x = 12 → x = 4. Il faut isoler x en ajoutant 5 puis en divisant par 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15129,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. Par exemple, f(1) = 1 - 4 + 3 = 0 et f(0) = 3, mais f(2) = 4 - 8 + 3 = -1. La fonction n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15130,"question":"Quel est le discriminant de l'équation x² - 5x + 6 = 0 ?","option_a":"Δ = 1","option_b":"Δ = 25 - 24 = 1","option_c":"Δ = 11","option_d":"Δ = -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour ax² + bx + c = 0, Δ = b² - 4ac. Ici, Δ = (-5)² - 4(1)(6) = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15131,"question":"La dérivée de f(x) = 3x³ - 2x² + x est f'(x) = 9x² - 4x + 1. Cette affirmation est-elle correcte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. La dérivée de 3x³ est 9x², celle de -2x² est -4x, et celle de x est 1. Donc f'(x) = 9x² - 4x + 1 est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15132,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E 5","option_c":"x \u003E -2","option_d":"x \u003E 10","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 → 2x \u003E 4 → x \u003E 2. On soustrait 3 puis on divise par 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15133,"question":"La fonction f(x) = 1\/x est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15134,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + x","option_c":"2x² + x + C","option_d":"x² + 2x + 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 d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15135,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. La différence entre deux termes consécutifs est constante : uₙ₊₁ - uₙ = 2(n+1) + 1 - (2n + 1) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15136,"question":"Quelle est la valeur de la limite lim (x→2) (x² - 4)\/(x - 2) ?","option_a":"0","option_b":"2","option_c":"4","option_d":"La limite n'existe pas","option_e":"","option_f":"","bonne_reponse":"B","explication":"On factorise : (x² - 4)\/(x - 2) = (x-2)(x+2)\/(x-2) = x+2 pour x ≠ 2. Donc lim (x→2) = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":15137,"question":"La fonction f(x) = |x| est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La fonction valeur absolue n'est pas dérivable en x = 0 car elle présente un point anguleux à cet endroit.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]