Quiz Maths : Fonctions, Équations et Géométrie — 3ème Année Secondaire

Question 1 sur 10 10:00

[{"id":21508,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x² + 2x","option_d":"6x + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : f'(x) = n*x^(n-1). Ici, 3x² devient 6x et 2x devient 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21509,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21510,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4. L'inéquation se résout en isolant x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21511,"question":"La fonction f(x) = x³ est-elle 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) = -x³ ≠ f(x), donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21512,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 7 ?","option_a":"7","option_b":"-2","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation réduite y = mx + p, m représente le coefficient directeur. Ici, m = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21513,"question":"La somme des angles d'un triangle vaut-elle toujours 180° ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle, la somme des angles est toujours égale à 180°, que ce soit en géométrie plane ou non euclidienne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21514,"question":"Quelle est la solution de l'équation 3(x - 2) = 2x + 1 ?","option_a":"x = 7","option_b":"x = 5","option_c":"x = 3","option_d":"x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 6 = 2x + 1 ⇒ 3x - 2x = 1 + 6 ⇒ x = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21515,"question":"La fonction f(x) = 1\/x est-elle définie en 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":21516,"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":"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 d'intégration C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":21517,"question":"Un parallélogramme a-t-il des diagonales de même longueur ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Seuls les rectangles (un type de parallélogramme) ont des diagonales de même longueur. Un parallélogramme général n'a pas cette propriété.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]