Quiz Maths Bac : Testez vos connaissances en 4ème année secondaire !

Question 1 sur 10 10:00

[{"id":78792,"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 x² - 5x + 6 = 0 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":78793,"question":"La fonction f(x) = x³ - 3x est-elle croissante sur l'intervalle ]-∞, -1[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 est négative sur ]-∞, -1[, donc la fonction est décroissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78794,"question":"Quel est le module du nombre complexe z = 3 + 4i ?","option_a":"5","option_b":"7","option_c":"12","option_d":"25","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est √(a² + b²) = √(3² + 4²) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78795,"question":"Dans un triangle rectangle, si l'angle A mesure 30°, alors sin(A) = ?","option_a":"1\/2","option_b":"√3\/2","option_c":"√2\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle, sin(30°) = côté opposé \/ hypoténuse = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78796,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les nombres pairs sur un dé sont 2, 4 et 6, soit 3 issues favorables sur 6 possibles. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78797,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) lorsque x tend vers +∞ ?","option_a":"2","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 1\/x²), donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78798,"question":"Un sac contient 5 boules rouges et 3 boules bleues. On tire une boule au hasard. Quelle est la probabilité de tirer une boule rouge ?","option_a":"5\/8","option_b":"3\/8","option_c":"5\/3","option_d":"8\/5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 5 boules rouges sur un total de 8 boules. La probabilité est donc 5\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78799,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78800,"question":"Quel est le développement de (x + 2)³ ?","option_a":"x³ + 6x² + 12x + 8","option_b":"x³ + 3x² + 3x + 8","option_c":"x³ + 8","option_d":"x³ + 6x + 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la formule (a + b)³ = a³ + 3a²b + 3ab² + b³, on obtient (x + 2)³ = x³ + 6x² + 12x + 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":78801,"question":"Dans un repère orthonormé, l'équation x² + y² - 4x + 6y - 3 = 0 représente-t-elle un cercle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En complétant le carré, on obtient (x-2)² + (y+3)² = 16, qui est l'équation d'un cercle de centre (2, -3) et de rayon 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]