Variables et fonctions en Terminale Math : Testez vos connaissances !

Question 1 sur 10 10:00

[{"id":22738,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 4","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'équation : 2x - 5 = 3x + 1 → -5 - 1 = 3x - 2x → -6 = x. La solution est donc x = -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22739,"question":"La fonction f(x) = x² est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = x² est dérivable en tout point, y compris en x = 0, car sa dérivée f'(x) = 2x existe pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22740,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + 5x - 1 ?","option_a":"f'(x) = 9x² - 4x + 5","option_b":"f'(x) = 3x² - 2x + 5","option_c":"f'(x) = 9x² - 4x + 1","option_d":"f'(x) = 6x² - 4x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant la règle de dérivation : f'(x) = 9x² - 4x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22741,"question":"L'inéquation 2x + 3 \u003E 5x - 4 a pour solution :","option_a":"x \u003C 7\/3","option_b":"x \u003E 7\/3","option_c":"x \u003C -7\/3","option_d":"x \u003E -7\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant l'inéquation : 2x + 3 \u003E 5x - 4 → 3 + 4 \u003E 5x - 2x → 7 \u003E 3x → x \u003C 7\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22742,"question":"La fonction f(x) = 1\/x est-elle continue en 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, donc elle n'est pas continue en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22743,"question":"Quelle est la solution de l'équation |2x - 3| = 5 ?","option_a":"x = -1 ou x = 4","option_b":"x = 1 ou x = -4","option_c":"x = -1 ou x = -4","option_d":"x = 1 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation |2x - 3| = 5 donne deux cas : 2x - 3 = 5 → x = 4, ou 2x - 3 = -5 → x = -1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22744,"question":"La fonction f(x) = √(x) est-elle dérivable en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = √(x) n'est pas dérivable en x = 0 car sa dérivée f'(x) = 1\/(2√x) n'est pas définie en ce point.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22745,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003E 0 ?","option_a":"x ∈ ]-∞; 1[ ∪ ]3; +∞[","option_b":"x ∈ ]1; 3[","option_c":"x ∈ ]-∞; 3[","option_d":"x ∈ ]-∞; 1[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le polynôme x² - 4x + 3 a pour racines x = 1 et x = 3. Le coefficient de x² est positif, donc l'inéquation est vérifiée en dehors de l'intervalle [1; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22746,"question":"La fonction f(x) = e^x est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle e^x est toujours positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22747,"question":"Quelle est la dérivée de la fonction f(x) = ln(x) ?","option_a":"f'(x) = 1\/x","option_b":"f'(x) = x","option_c":"f'(x) = e^x","option_d":"f'(x) = -1\/x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]