Maîtrisez les exercices de mathématiques en Terminale

Question 1 sur 10 10:00

[{"id":12448,"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 + 2x","option_d":"D. 9x² + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la formule (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12449,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une suite est arithmétique si la différence entre deux termes consécutifs est constante. Ici, uₙ₊₁ - uₙ = 2, donc elle est arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12450,"question":"Résolvez l'équation : 2x - 3 = 5x + 6","option_a":"A. x = -3","option_b":"B. x = 3","option_c":"C. x = -1","option_d":"D. x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x : 2x - 5x = 6 + 3 → -3x = 9 → x = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12451,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ f(x), donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12452,"question":"Quelle est la limite de (3x² + 2x) \/ (x² - 1) quand x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 3","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x) \/ (1 - 1\/x²) → 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12453,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"A. b² - 4ac","option_b":"B. b² + 4ac","option_c":"C. 4ac - b²","option_d":"D. (b² - 4ac)\/2a","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac détermine le nombre de solutions réelles de l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12454,"question":"Une probabilité peut-elle être supérieure à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une probabilité est toujours comprise entre 0 et 1 inclus. Une valeur \u003E 1 est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12455,"question":"Quelle est la primitive de f(x) = 4x³ ?","option_a":"A. x⁴ + C","option_b":"B. 12x² + C","option_c":"C. x³ + C","option_d":"D. 4x⁴ + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de xⁿ est x^(n+1)\/(n+1). Ici, ∫4x³ dx = 4*(x⁴\/4) + C = x⁴ + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12456,"question":"La fonction exponentielle est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout x réel, eˣ \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12457,"question":"Résolvez l'inéquation : 5 - 2x \u003E 3x + 1","option_a":"A. x \u003C 4\/5","option_b":"B. x \u003E 4\/5","option_c":"C. x \u003C 0","option_d":"D. x \u003E 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x : 5 - 1 \u003E 3x + 2x → 4 \u003E 5x → x \u003C 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]