Quiz Mathématiques : 4ème année secondaire — Série 24

Question 1 sur 10 10:00

[{"id":26258,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2x","option_d":"3x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : (3x²)' = 6x, (2x)' = 2 et (-5)' = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26259,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions 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":26260,"question":"Quelle est la formule de l'aire d'un triangle de base b et de hauteur h ?","option_a":"A = b × h","option_b":"A = (b × h)\/2","option_c":"A = 2 × (b + h)","option_d":"A = b² + h²","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire d'un triangle se calcule avec la formule A = (base × hauteur) \/ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26261,"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":26262,"question":"Quelle est la solution de l'équation 2(x - 3) = 4x + 1 ?","option_a":"x = -7\/2","option_b":"x = 7\/2","option_c":"x = -3","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant : 2x - 6 = 4x + 1 → -6 - 1 = 4x - 2x → -7 = 2x → x = -7\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26263,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26264,"question":"Quelle est la probabilité d'obtenir un 6 en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"1\/4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé équilibré a 6 faces, donc la probabilité d'obtenir un 6 est de 1\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26265,"question":"La fonction f(x) = x³ est-elle paire ou impaire ?","option_a":"Paire","option_b":"Impaire","option_c":"Ni l'une ni l'autre","option_d":"Les deux","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ = -x³ = -f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26266,"question":"Quelle est la médiane d'un ensemble de nombres : 3, 5, 7, 9, 11 ?","option_a":"5","option_b":"7","option_c":"9","option_d":"11","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour trouver la médiane, on ordonne les nombres et on prend la valeur centrale : 3, 5, 7, 9, 11 → médiane = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26267,"question":"L'équation x² + 1 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0 - 4 = -4 \u003C 0, donc l'équation n'a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]