Quiz Mathématiques Bac : Algèbre, Analyse et Géométrie

Question 1 sur 10 10:00

[{"id":19578,"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":19579,"question":"La fonction f(x) = x³ est-elle strictement croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x)=3x² est toujours positive (sauf en x=0 où elle est nulle), donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19580,"question":"Quel est le domaine de définition de la fonction f(x) = 1\/(x-2) ?","option_a":"ℝ","option_b":"ℝ \\ {2}","option_c":"ℝ \\ {-2}","option_d":"[2; +∞[","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est définie pour tout x sauf x=2, car le dénominateur ne peut pas être nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19581,"question":"Le théorème de Pythagore s'applique-t-il dans un triangle quelconque ?","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 que dans un triangle rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19582,"question":"Quelle est la dérivée de la fonction f(x) = 2x⁴ - 3x² + 5 ?","option_a":"f'(x) = 8x³ - 6x","option_b":"f'(x) = 6x³ - 4x","option_c":"f'(x) = 8x³ - 6x + 5","option_d":"f'(x) = 8x² - 6x","option_e":"","option_f":"","bonne_reponse":"A","explication":"En dérivant terme à terme, on obtient f'(x) = 8x³ - 6x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19583,"question":"L'équation 2x + 3 = 0 admet-elle une solution entière ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution est x = -1.5, qui n'est pas un entier.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19584,"question":"Quel est le volume d'un cube d'arête 3 cm ?","option_a":"9 cm³","option_b":"12 cm³","option_c":"27 cm³","option_d":"36 cm³","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le volume d'un cube est donné par V = arête³, donc V = 3³ = 27 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19585,"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 la dérivée à gauche et à droite ne sont pas égales.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19586,"question":"Quelle est la solution de l'inéquation 3x - 5 \u003E 1 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 1","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'inéquation, on obtient 3x \u003E 6, soit x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19587,"question":"Les droites d'équations y = 2x + 1 et y = -0.5x + 3 sont-elles perpendiculaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit des coefficients directeurs est 2 × (-0.5) = -1, donc les droites sont perpendiculaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]