Maths 4M : Testez vos connaissances du 2ème trimestre !

Question 1 sur 10 10:00

[{"id":69442,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 2 ou x = 1\/2","option_c":"x = -1 ou x = 2","option_d":"x = 1\/2 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise la formule des racines d'une équation du second degré : Δ = b² - 4ac. Ici, Δ = 25 - 16 = 9, donc x = (5 ± 3)\/4 → x = 2 ou x = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69443,"question":"La fonction f(x) = (2x + 1)\/(x - 3) admet-elle une asymptote verticale ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une asymptote verticale existe si le dénominateur s'annule pour une valeur réelle de x. Ici, x - 3 = 0 → x = 3, donc oui, il y a une asymptote verticale en x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69444,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 3x² - 4x + 5","option_b":"f'(x) = 3x² - 2x + 5","option_c":"f'(x) = x² - 4x + 5","option_d":"f'(x) = 3x² - 4x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme se calcule terme par terme : (x³)' = 3x², (-2x²)' = -4x, (5x)' = 5, et (-1)' = 0. Donc f'(x) = 3x² - 4x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69445,"question":"Dans un triangle rectangle, si un angle mesure 30°, alors l'autre angle non droit mesure :","option_a":"30°","option_b":"60°","option_c":"45°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"B","explication":"La somme des angles d'un triangle est 180°. Dans un triangle rectangle, un angle est 90°, donc les deux autres angles mesurent ensemble 90°. Si l'un mesure 30°, l'autre mesure 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69446,"question":"La limite de la fonction f(x) = (x² - 4)\/(x - 2) quand x tend vers 2 est :","option_a":"0","option_b":"2","option_c":"4","option_d":"indéterminée","option_e":"","option_f":"","bonne_reponse":"B","explication":"On factorise le numérateur : (x² - 4) = (x - 2)(x + 2). Donc f(x) = (x - 2)(x + 2)\/(x - 2) = x + 2 pour x ≠ 2. Ainsi, lim(x→2) f(x) = 2 + 2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69447,"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. Pour les autres triangles, on utilise d'autres théorèmes comme la loi des cosinus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69448,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x : 3x - 2x ≤ 5 + 7 → x ≤ 12. La solution est donc x ≤ 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69449,"question":"La fonction f(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une fonction du second degré avec un coefficient positif (1) devant x², donc elle admet un minimum en son sommet. Le minimum est f(2) = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69450,"question":"Dans une expérience aléatoire, si la probabilité d'un événement A est 0,25, alors la probabilité de son contraire est :","option_a":"0,25","option_b":"0,5","option_c":"0,75","option_d":"1","option_e":"","option_f":"","bonne_reponse":"C","explication":"La probabilité de l'événement contraire est 1 - P(A) = 1 - 0,25 = 0,75.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69451,"question":"Quelle est l'aire d'un cercle de rayon r = 5 cm ?","option_a":"10π cm²","option_b":"25π cm²","option_c":"50π cm²","option_d":"100π cm²","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire d'un cercle est donnée par la formule A = πr². Ici, A = π × 5² = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]