Quiz : Maîtrisez les fondamentaux des mathématiques de Terminale Scientifique

Question 1 sur 10 10:00

[{"id":50311,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"A. x = 2 ou x = 3","option_b":"B. x = -2 ou x = -3","option_c":"C. x = 1 ou x = 6","option_d":"D. x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3) = 0, donc les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50312,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = x³ - 3x² + 2x est bien f'(x) = 3x² - 6x + 2, car la dérivée de x³ est 3x², celle de -3x² est -6x, et celle de 2x est 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50313,"question":"Quelle est la probabilité d'obtenir deux fois pile en lançant deux fois une pièce équilibrée ?","option_a":"A. 1\/2","option_b":"B. 1\/4","option_c":"C. 1\/3","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'obtenir pile une fois est 1\/2. Pour deux lancers indépendants, la probabilité est (1\/2) × (1\/2) = 1\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50314,"question":"L'intégrale ∫(2x + 1) dx entre 0 et 1 est égale à :","option_a":"A. 1","option_b":"B. 2","option_c":"C. 1.5","option_d":"D. 3","option_e":"","option_f":"","bonne_reponse":"C","explication":"L'intégrale de 2x + 1 est x² + x. Évaluée entre 0 et 1, cela donne (1² + 1) - (0² + 0) = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50315,"question":"La fonction f(x) = 1\/x est définie pour tout x réel.","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 pour x = 0, car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50316,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"A. x \u003E 4","option_b":"B. x \u003C 4","option_c":"C. x \u003E 1","option_d":"D. x \u003C 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50317,"question":"Dans une loi binomiale de paramètres n = 10 et p = 0.3, l'espérance est égale à :","option_a":"A. 3","option_b":"B. 7","option_c":"C. 10","option_d":"D. 0.3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale est E = n × p = 10 × 0.3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50318,"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":50319,"question":"Quelle est la dérivée de la fonction f(x) = ln(x) ?","option_a":"A. 1\/x","option_b":"B. x","option_c":"C. e^x","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est 1\/x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50320,"question":"Un sac contient 4 boules rouges et 6 boules bleues. On tire une boule au hasard. Quelle est la probabilité de tirer une boule bleue ?","option_a":"A. 0.4","option_b":"B. 0.6","option_c":"C. 0.5","option_d":"D. 0.3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 6 boules bleues sur un total de 10 boules, donc la probabilité est 6\/10 = 0.6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]