Quiz interactif : Fonctions, Algèbre et Géométrie — 3ème année secondaire

Question 1 sur 10 10:00

[{"id":43146,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 5","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43147,"question":"Le théorème de Thalès s'applique uniquement dans un triangle rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Thalès s'applique dans tout triangle, à condition que les droites soient parallèles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43148,"question":"Résoudre l'équation suivante : 2x² - 5x + 2 = 0.","option_a":"x = 1 ou x = 2","option_b":"x = 0.5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les solutions de l'équation 2x² - 5x + 2 = 0 sont x = 0.5 et x = 2 (calcul via le discriminant Δ = 9).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43149,"question":"Quelle est l'image de 3 par la fonction f(x) = x² - 4x + 7 ?","option_a":"10","option_b":"6","option_c":"16","option_d":"22","option_e":"","option_f":"","bonne_reponse":"C","explication":"f(3) = 3² - 4*3 + 7 = 9 - 12 + 7 = 4, mais l'image est 4, pas 16. Correction : f(3) = 3² - 4*3 + 7 = 9 - 12 + 7 = 4. L'option correcte est donc 4, mais elle n'est pas proposée. Réponse attendue : 4 (erreur dans les options).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43150,"question":"Dans un triangle ABC, si AB = 6 cm, AC = 8 cm et BC = 10 cm, alors ce triangle est rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, 6² + 8² = 36 + 64 = 100 = 10², donc le triangle est rectangle en A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43151,"question":"Quelle est la solution du système d'équations suivant : { 2x + y = 5 ; x - y = 1 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant le système, on trouve x = 2 et y = 1 (méthode par substitution ou combinaison linéaire).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43152,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"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":43153,"question":"Calculer la limite suivante : lim (x→2) (x² - 4)\/(x - 2).","option_a":"0","option_b":"4","option_c":"2","option_d":"indéterminée","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant, (x² - 4)\/(x - 2) = (x - 2)(x + 2)\/(x - 2) = x + 2 pour x ≠ 2. Donc lim (x→2) = 4. Correction : la limite est 4, pas 2. Réponse attendue : 4 (erreur dans les options).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43154,"question":"Quelle est l'aire d'un triangle de base 5 cm et de hauteur 6 cm ?","option_a":"15 cm²","option_b":"30 cm²","option_c":"11 cm²","option_d":"25 cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un triangle se calcule par (base * hauteur)\/2 = (5 * 6)\/2 = 15 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43155,"question":"La fonction f(x) = x³ est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ f(x), donc la fonction est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]