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

Question 1 sur 10 10:00

[{"id":50851,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x : 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50852,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est un polynôme du second degré avec un discriminant positif (Δ = 4 \u003E 0), donc elle change de signe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50853,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 1 ?","option_a":"f'(x) = 6x + 2","option_b":"f'(x) = 3x + 2","option_c":"f'(x) = 6x² + 2","option_d":"f'(x) = 3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'un polynôme est obtenue en multipliant chaque terme par son exposant : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50854,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est le théorème de Pythagore, une propriété fondamentale en géométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50855,"question":"Quelle est la valeur de log₂(8) ?","option_a":"2","option_b":"3","option_c":"8","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"log₂(8) = log₂(2³) = 3 car 2³ = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50856,"question":"La fonction exponentielle f(x) = eˣ est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de eˣ est eˣ, qui est toujours positive, donc la fonction est strictement croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50857,"question":"Résoudre l'inéquation 2x + 3 ≥ 7.","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x ≥ -2","option_d":"x ≤ -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x ≥ 4 → x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50858,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est la formule standard pour calculer le discriminant d'une équation du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50859,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"On factorise : f(x) = (x - 1)(x + 1)\/(x - 1) = x + 1 pour x ≠ 1. Donc lim(x→1) f(x) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50860,"question":"La probabilité d'un événement certain est égale à 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement certain est égale à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]