Mathématiques 4ème année secondaire : Évaluation des Compétences Clés

Question 1 sur 10 10:00

[{"id":48971,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48972,"question":"L'équation x² - 4x + 4 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation admet une solution double : x = 2 (car le discriminant est nul).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48973,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + 2x + C","option_c":"2x² + x + C","option_d":"x² + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale d'une fonction linéaire se calcule comme suit : ∫(2x + 1) dx = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48974,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore, valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48975,"question":"Quelle est la solution de l'équation 2^(x+1) = 8 ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = 3","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"B","explication":"2^(x+1) = 8 ⇒ 2^(x+1) = 2³ ⇒ x+1 = 3 ⇒ x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48976,"question":"La fonction f(x) = sin(x) est périodique de période π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction sin(x) est périodique de période 2π, pas π.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48977,"question":"Quel est le résultat de (3 + 2i)(1 - i) ?","option_a":"5 - i","option_b":"5 + i","option_c":"1 + i","option_d":"3 - 2i","option_e":"","option_f":"","bonne_reponse":"A","explication":"(3 + 2i)(1 - i) = 3 - 3i + 2i - 2i² = 3 - i + 2 = 5 - i (car i² = -1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48978,"question":"La suite définie par uₙ = 2n + 1 est arithmétique.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48979,"question":"Quelle est la valeur de la limite lim(x→∞) (3x² + 2x) \/ (x² + 1) ?","option_a":"0","option_b":"1","option_c":"3","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x², on obtient lim(x→∞) (3 + 2\/x) \/ (1 + 1\/x²) = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48980,"question":"Le vecteur u(2, -3) et le vecteur v(-4, 6) sont colinéaires.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les vecteurs sont colinéaires si l'un est un multiple de l'autre. Ici, v = -2u, donc ils sont colinéaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]