Mathématiques 3ème année secondaire : Évaluation des acquis

Question 1 sur 10 10:00

[{"id":55261,"question":"Quelle est la solution de l'équation 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":"L'équation se factorise en (x-2)(x-3)=0, donc les solutions sont x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55262,"question":"La fonction f(x) = x² - 4x + 3 est croissante sur l'intervalle [2, +∞[.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x)=2x-4 est positive pour x\u003E2, donc la fonction est bien croissante sur [2, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55263,"question":"Quel est le volume d'une sphère de rayon 3 cm ?","option_a":"36π cm³","option_b":"12π cm³","option_c":"18π cm³","option_d":"24π cm³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le volume d'une sphère est donné par V = (4\/3)πr³ = (4\/3)π(27) = 36π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55264,"question":"Si A et B sont deux événements incompatibles, alors P(A ∪ B) = P(A) + P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements incompatibles, la probabilité de leur union est bien la somme de leurs probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55265,"question":"Quelle est la forme canonique de la fonction f(x) = 2x² - 8x + 5 ?","option_a":"f(x) = 2(x-2)² - 3","option_b":"f(x) = 2(x-4)² + 5","option_c":"f(x) = 2(x-1)² + 3","option_d":"f(x) = 2(x+2)² - 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est obtenue par f(x) = 2(x² - 4x) + 5 = 2[(x-2)² - 4] + 5 = 2(x-2)² - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55266,"question":"Le volume d'un cône de rayon 3 cm et de hauteur 4 cm est de 12π cm³.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le volume d'un cône est V = (1\/3)πr²h = (1\/3)π(9)(4) = 12π cm³. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55267,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/2","option_b":"1\/3","option_c":"1\/6","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces, dont 3 paires (2,4,6), donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55268,"question":"La fonction f(x) = (x+1)\/(x-2) est définie pour x ≠ 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction est définie pour tout x sauf x=2, car le dénominateur s'annule en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55269,"question":"Quelle est la solution de l'inéquation x² - 3x - 4 ≤ 0 ?","option_a":"x ∈ [-1, 4]","option_b":"x ∈ ]-∞, -1] ∪ [4, +∞[","option_c":"x ∈ [1, 4]","option_d":"x ∈ ]-1, 4[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de l'équation x² - 3x - 4 = 0 sont x=-1 et x=4. Le trinôme est négatif entre ses racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55270,"question":"La section d'un cube par un plan parallèle à une face est toujours un carré.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si le plan est parallèle à une face, la section est un carré de même côté que le cube.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]