Quiz : Maîtrisez les calculs mathématiques en Terminale FMM

Question 1 sur 10 10:00

[{"id":46781,"question":"Quelle est la solution de l'équation 3x + 5 = 2x + 10 ?","option_a":"x = 5","option_b":"x = -5","option_c":"x = 15","option_d":"x = -15","option_e":"","option_f":"","bonne_reponse":"A","explication":"Soustraire 2x des deux côtés donne x + 5 = 10, puis soustraire 5 pour obtenir x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46782,"question":"L'inéquation 2x - 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résoudre l'inéquation : 2x \u003E 10 → x \u003E 5. La solution est donc x \u003E 5, pas x \u003E 10.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46783,"question":"Quelle est la dérivée de la fonction f(x) = 4x² + 3x - 2 ?","option_a":"f'(x) = 8x + 3","option_b":"f'(x) = 4x + 3","option_c":"f'(x) = 8x - 2","option_d":"f'(x) = 4x² + 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de 4x² est 8x, celle de 3x est 3, et celle de -2 est 0. Donc f'(x) = 8x + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46784,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = a² - 4bc","option_d":"Δ = c² - 4ab","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est calculé par la formule Δ = b² - 4ac, essentielle pour déterminer le nombre de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46785,"question":"La fonction f(x) = x³ est toujours croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 3x² est toujours positive ou nulle, donc la fonction est toujours croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46786,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) lorsque x tend vers l'infini ?","option_a":"2","option_b":"0","option_c":"1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant le numérateur et le dénominateur par x², on obtient (2 + 3\/x) \/ (1 - 1\/x²), dont la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46787,"question":"Le développement de (x + 2)² est :","option_a":"x² + 4x + 4","option_b":"x² + 2x + 4","option_c":"x² + 4x + 2","option_d":"x² + 2x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le développement de (x + 2)² est x² + 2*x*2 + 2² = x² + 4x + 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46788,"question":"La fonction exponentielle f(x) = e^x est 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 strictement positive pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46789,"question":"Quelle est la solution de l'inéquation x² - 5x + 6 \u003C 0 ?","option_a":"x ∈ ]2, 3[","option_b":"x ∈ ]-∞, 2[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, 2[","option_d":"x ∈ ]3, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines de x² - 5x + 6 = 0 sont x = 2 et x = 3. Le polynôme est négatif entre ces deux racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46790,"question":"La primitive de f(x) = 6x est F(x) = 3x² + C, où C est une constante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive de 6x est bien 3x² + C, car la dérivée de 3x² est 6x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]