Quiz interactif : Mathématiques avancées — 4ème année secondaire

Question 1 sur 10 10:00

[{"id":43406,"question":"Quelle est la solution de l'équation du second degré x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions s'obtiennent en factorisant : (x-2)(x-3)=0. Donc x=2 ou x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43407,"question":"La fonction f(x) = (2x + 1)\/(x - 3) est-elle une fonction rationnelle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction rationnelle est le quotient de deux polynômes. Ici, 2x+1 et x-3 sont des polynômes, donc c'est une fonction rationnelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43408,"question":"Quelle est la limite de la suite u_n = (3n² + 2n - 1)\/(n² + 5) quand n tend vers l'infini ?","option_a":"3","option_b":"2\/5","option_c":"1","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n², on obtient (3 + 2\/n - 1\/n²)\/(1 + 5\/n²) → 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43409,"question":"Le point A(2; -3) appartient-il à la droite d'équation y = 2x - 7 ?","option_a":"Oui","option_b":"Non","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x=2 dans l'équation, on obtient y=2*2-7=-3. Donc A appartient à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43410,"question":"La suite géométrique de premier terme 5 et de raison 2 est-elle croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite géométrique de raison r\u003E1 et de premier terme positif est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43411,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 5x - 2 ?","option_a":"f'(x) = 3x² - 8x + 5","option_b":"f'(x) = 3x² - 4x + 5","option_c":"f'(x) = x² - 8x + 5","option_d":"f'(x) = 3x² - 8x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée se calcule terme à terme : 3x² - 8x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43412,"question":"Un sac contient 4 boules rouges et 6 boules bleues. Quelle est la probabilité de tirer une boule rouge ?","option_a":"0.4","option_b":"0.6","option_c":"0.25","option_d":"0.75","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 4 boules rouges sur un total de 10 boules. La probabilité est donc 4\/10 = 0.4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43413,"question":"La fonction f(x) = |x| est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x=0 car sa dérivée à gauche (-1) diffère de sa dérivée à droite (1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43414,"question":"Quelle est la solution de l'inéquation 2x² - 3x - 5 ≤ 0 ?","option_a":"x ∈ [-1; 2.5]","option_b":"x ∈ ]-∞; -1] ∪ [2.5; +∞[","option_c":"x ∈ [1; 2.5]","option_d":"x ∈ [-2.5; 1]","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x=-1 et x=2.5. Le polynôme est négatif entre les racines car le coefficient de x² est positif.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":43415,"question":"Le centre de gravité d'un triangle est-il toujours situé à l'intérieur du triangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le centre de gravité est toujours situé à l'intérieur du triangle, car il est l'intersection des médianes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]