Maths Terminale : Testez vos connaissances avec ce quiz interactif !

Question 1 sur 10 10:00

[{"id":65612,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"A) 6x + 2","option_b":"B) 3x + 2","option_c":"C) 6x² + 2","option_d":"D) 6x - 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65613,"question":"La suite (un) définie par un = n² est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite arithmétique a une différence constante entre deux termes consécutifs. Ici, un+1 - un = (n+1)² - n² = 2n + 1, qui n'est pas constant.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65614,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) quand x tend vers +∞ ?","option_a":"A) 0","option_b":"B) 2","option_c":"C) +∞","option_d":"D) -∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En divisant numérateur et dénominateur par x, on obtient f(x) = (2 + 1\/x)\/(1 - 3\/x), dont la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65615,"question":"L’équation x² + 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 16 = 0, donc l’équation admet une solution double (x = -2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65616,"question":"Quelle est la primitive de la fonction f(x) = 5x⁴ ?","option_a":"A) x⁵ + C","option_b":"B) 20x³ + C","option_c":"C) 5x⁵ + C","option_d":"D) x⁴ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de xⁿ est x^(n+1)\/(n+1), donc ∫5x⁴ dx = 5x⁵\/5 + C = x⁵ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65617,"question":"Le vecteur u(2; -3) et le vecteur v(-4; 6) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les vecteurs sont colinéaires si leurs coordonnées sont proportionnelles : -4\/2 = -2 et 6\/-3 = -2, donc oui.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65618,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"A) 0","option_b":"B) 1\/2","option_c":"C) √2\/2","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(π\/6) = 1\/2, valeur à connaître par cœur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65619,"question":"La fonction f(x) = ln(x) est-elle définie pour x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction ln(x) est définie uniquement pour x \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65620,"question":"Quelle est la solution de l’inéquation 3x - 7 \u003E 2x + 1 ?","option_a":"A) x \u003E 8","option_b":"B) x \u003E 6","option_c":"C) x \u003C 8","option_d":"D) x \u003C 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 7 \u003E 2x + 1 ⇒ x \u003E 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65621,"question":"Le produit scalaire de deux vecteurs orthogonaux est-il toujours nul ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]