Quiz Maths : Évalue tes connaissances en algèbre et géométrie

Question 1 sur 10 10:00

[{"id":59767,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = 1 ou x = 6","option_c":"x = -2 ou x = -3","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":59768,"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 correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59769,"question":"Quel est le volume d'un cube d'arête 4 cm ?","option_a":"16 cm³","option_b":"32 cm³","option_c":"64 cm³","option_d":"128 cm³","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le volume d'un cube est donné par V = arête³. Ici, V = 4³ = 64 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59770,"question":"L'équation sin(x) = 0,5 admet une solution dans l'intervalle [0, π] égale à π\/6.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/6) = 0,5, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59771,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x-3)(x+3)","option_b":"(x-9)(x+1)","option_c":"(x-3)²","option_d":"(x+3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés, donc factorisable en (x-3)(x+3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59772,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x=0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59773,"question":"Résoudre le système : { 2x + y = 5 ; x - y = 1 }","option_a":"x=2, y=1","option_b":"x=1, y=3","option_c":"x=3, y=-1","option_d":"x=0, y=5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations, on obtient 3x = 6, donc x=2. En remplaçant dans la 2ème équation, y=1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59774,"question":"L'aire d'un triangle de base 6 cm et de hauteur 4 cm est de 12 cm².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un triangle est (base × hauteur)\/2. Ici, (6×4)\/2 = 12 cm², donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59775,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² - 1) quand x tend vers l'infini ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x², on obtient (2 + 3\/x - 1\/x²)\/(1 - 1\/x²), donc la limite est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59776,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore stipule que dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Il ne s'applique donc qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]