Quiz : Maîtrisez les bases des fonctions en Terminale Maths

Question 1 sur 10 10:00

[{"id":64242,"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. 6x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et la dérivée de -5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64243,"question":"L'équation x² - 4x + 3 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-4)² - 4*1*3 = 16 - 12 = 4 \u003E 0, donc l'équation admet deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64244,"question":"Quelle est la limite de la fonction f(x) = (2x + 1)\/(x - 3) lorsque x tend vers l'infini ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. +∞","option_d":"D. -∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant numérateur et dénominateur par x, on obtient f(x) = (2 + 1\/x)\/(1 - 3\/x). Lorsque x tend vers l'infini, 1\/x et 3\/x tendent vers 0, donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64245,"question":"La fonction f(x) = x³ - 3x est croissante sur l'intervalle [-2, 2].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3. Sur [-2, 2], f'(x) est négative pour x ∈ [-1, 1], donc la fonction n'est pas croissante sur tout l'intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64246,"question":"Quelle est la solution de l'inéquation 2x - 5 \u003E 3x + 1 ?","option_a":"A. x \u003C -6","option_b":"B. x \u003E -6","option_c":"C. x \u003C 6","option_d":"D. x \u003E 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 5 \u003E 3x + 1, on obtient -x \u003E 6, soit x \u003C -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64247,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel, car e^x \u003E 0 pour tout x ∈ ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64248,"question":"Quelle est l'équation de la tangente à la courbe de f(x) = x² + 1 au point d'abscisse x = 1 ?","option_a":"A. y = 2x + 1","option_b":"B. y = 2x","option_c":"C. y = x + 1","option_d":"D. y = 2x - 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 2x. En x = 1, f'(1) = 2 et f(1) = 2. L'équation de la tangente est y = f'(1)(x - 1) + f(1) = 2(x - 1) + 2 = 2x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64249,"question":"Le nombre complexe z = 3 + 4i a pour module |z| = 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le module de z = a + bi est |z| = √(a² + b²). Ici, |z| = √(3² + 4²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64250,"question":"Quelle est la primitive de la fonction f(x) = 4x³ qui s'annule en x = 0 ?","option_a":"A. x⁴ + C","option_b":"B. x⁴","option_c":"C. 12x²","option_d":"D. 4x⁴","option_e":"","option_f":"","bonne_reponse":"B","explication":"La primitive de 4x³ est x⁴ + C. Pour que F(0) = 0, on choisit C = 0, donc F(x) = x⁴.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":64251,"question":"La fonction f(x) = sin(x) est périodique de période π.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction sin(x) est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]