Quiz Maths : Testez vos connaissances en 4ème année secondaire

Question 1 sur 10 10:00

[{"id":28508,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"6x² + 2","option_c":"3x + 2","option_d":"5x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28509,"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 l'énoncé du théorème de Pythagore, une propriété fondamentale en géométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28510,"question":"Résolvez l'équation : 2(x - 3) = 4x + 1.","option_a":"x = -7\/2","option_b":"x = -1","option_c":"x = 7\/2","option_d":"x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant : 2x - 6 = 4x + 1 → -6 - 1 = 4x - 2x → -7 = 2x → x = -7\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28511,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré à 6 faces ?","option_a":"1\/2","option_b":"1\/3","option_c":"2\/3","option_d":"1\/6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28512,"question":"La fonction f(x) = x³ est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Sa dérivée f'(x) = 3x² est toujours positive (sauf en x=0 où elle est nulle), donc la fonction est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28513,"question":"Quel est le développement de (x + 2)(x - 3) ?","option_a":"x² - x - 6","option_b":"x² + x - 6","option_c":"x² - 5x - 6","option_d":"x² + 5x - 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En utilisant la distributivité : x*x + x*(-3) + 2*x + 2*(-3) = x² - 3x + 2x - 6 = x² - x - 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28514,"question":"Dans un cercle de rayon r, l'aire est donnée par la formule :","option_a":"πr","option_b":"2πr","option_c":"πr²","option_d":"4πr²","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'aire d'un cercle est π multiplié par le carré du rayon, soit πr².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28515,"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":28516,"question":"Résolvez l'inéquation : -2x + 5 \u003E 1.","option_a":"x \u003C 2","option_b":"x \u003E 2","option_c":"x \u003C -2","option_d":"x \u003E -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x : -2x \u003E -4 → x \u003C 2 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":28517,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x - 1)\/(x² + 1) lorsque x tend vers l'infini ?","option_a":"0","option_b":"2","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x² : (2 + 3\/x - 1\/x²)\/(1 + 1\/x²) → 2\/1 = 2 lorsque x → ∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]