Maths 4ème : Devoir de Synthèse — Quiz d'Évaluation

Question 1 sur 10 10:00

[{"id":47241,"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":"On factorise l'équation : (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":47242,"question":"La dérivée de la fonction f(x) = 3x² + 2x - 1 est f'(x) = 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de -1 est 0. Donc f'(x) = 6x + 2 est correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47243,"question":"Quel est le volume d'un cône de rayon 3 cm et de hauteur 5 cm ?","option_a":"15π cm³","option_b":"45π cm³","option_c":"30π cm³","option_d":"9π cm³","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule du volume d'un cône est V = (1\/3)πr²h. Avec r=3 et h=5, on obtient V = (1\/3)π×9×5 = 15π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47244,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x=±1. Sur [-2, -1] et [1, 2], f est croissante, mais pas sur tout l'intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47245,"question":"Quelle est la solution de l'inéquation 2x - 7 \u003E 3x + 1 ?","option_a":"x \u003C -8","option_b":"x \u003E -8","option_c":"x \u003C 8","option_d":"x \u003E 8","option_e":"","option_f":"","bonne_reponse":"A","explication":"En simplifiant, on obtient -x \u003E 8, donc x \u003C -8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47246,"question":"Le théorème de Thalès s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Thalès s'applique à tous les triangles, pas seulement aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47247,"question":"Quelle est l'équation de la tangente à la courbe y = x² en x = 1 ?","option_a":"y = 2x - 1","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente a pour équation y = f'(1)(x-1) + f(1). Avec f(x)=x², f'(x)=2x, donc f'(1)=2 et f(1)=1. D'où y=2(x-1)+1=2x-1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47248,"question":"La probabilité d'obtenir un nombre pair en lançant un dé est 1\/2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé a 6 faces : 3 nombres pairs (2,4,6) et 3 nombres impairs. La probabilité est donc 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47249,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ x quand x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"∞","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x, on obtient f(x) = 2x + 3. Quand x tend vers l'infini, la limite est ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":47250,"question":"Le centre de gravité d'un triangle est l'intersection de ses médianes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le centre de gravité d'un triangle est bien l'intersection de ses médianes, un point qui divise chaque médiane dans un rapport 2:1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]