Quiz Maths : Algèbre, Analyse et Géométrie pour la 4ème année secondaire

Question 1 sur 10 10:00

[{"id":72622,"question":"Quelle est la solution de l'équation 2x² - 5x - 3 = 0 ?","option_a":"x = -1 ou x = 3\/2","option_b":"x = 1 ou x = -3\/2","option_c":"x = -1\/2 ou x = 3","option_d":"x = 1 ou x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la formule des racines du second degré : Δ = b² - 4ac = 25 + 24 = 49. Les solutions sont x = (5 ± 7)\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72623,"question":"La dérivée de la fonction f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 2 est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72624,"question":"Quel est le produit scalaire de deux vecteurs u(2; -1) et v(-3; 4) ?","option_a":"-10","option_b":"5","option_c":"-5","option_d":"10","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le produit scalaire est calculé par u·v = (2)(-3) + (-1)(4) = -6 -4 = -10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72625,"question":"La fonction exponentielle f(x) = e^x est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, e^x \u003E 0. La fonction exponentielle est strictement positive sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72626,"question":"Résoudre l'inéquation 3x - 7 ≤ 2x + 5.","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ 2","option_d":"x ≥ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"On soustrait 2x des deux côtés : x - 7 ≤ 5, puis on ajoute 7 : x ≤ 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72627,"question":"Le vecteur AB a pour coordonnées (4; -2). Quelle est la norme de AB ?","option_a":"√20","option_b":"√10","option_c":"2√5","option_d":"√5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La norme est calculée par √(4² + (-2)²) = √(16 + 4) = √20 = 2√5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72628,"question":"La fonction f(x) = x³ - 3x est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Sa dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante sur [-1; 1].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72629,"question":"Quel est le résultat de ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"2x² + x + C","option_c":"x² + 2x + C","option_d":"2x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale de 2x est x² et celle de 1 est x. La constante C est ajoutée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72630,"question":"Les vecteurs u(1; 2; -1) et v(2; -1; 3) sont-ils orthogonaux ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le produit scalaire u·v = (1)(2) + (2)(-1) + (-1)(3) = 2 - 2 - 3 = -3 ≠ 0. Ils ne sont pas orthogonaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":72631,"question":"Quelle est l'équation de la tangente à la courbe y = x² au point d'abscisse x = 1 ?","option_a":"y = 2x - 1","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x donne f'(1) = 2. L'équation est y = f(1) + f'(1)(x - 1) = 1 + 2(x - 1) = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]