Quiz : Testez vos connaissances en mathématiques 4M !

Question 1 sur 10 10:00

[{"id":9073,"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. 5x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : la dérivée de 3x² est 6x, celle de 2x est 2, et celle de -5 est 0. Ainsi, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9074,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes : x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9075,"question":"Quelle est la solution de l'inéquation 2x - 7 ≤ 3x + 1 ?","option_a":"A. x ≥ -8","option_b":"B. x ≤ -8","option_c":"C. x ≥ 8","option_d":"D. x ≤ 8","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant l'inéquation : 2x - 7 ≤ 3x + 1 → -7 - 1 ≤ 3x - 2x → -8 ≤ x → x ≥ -8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9076,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est de :","option_a":"A. 1\/6","option_b":"B. 1\/2","option_c":"C. 1\/3","option_d":"D. 2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un dé équilibré a 6 faces : 1, 2, 3, 4, 5, 6. Les nombres pairs sont 2, 4, 6 → 3 cas favorables sur 6 possibles → P = 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9077,"question":"Le centre de symétrie d'un cercle est toujours situé sur sa circonférence.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le centre de symétrie d'un cercle est son centre, qui est à l'intérieur du cercle, et non sur sa circonférence.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9078,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 7 ?","option_a":"A. (x - 2)² + 3","option_b":"B. (x + 2)² + 3","option_c":"C. (x - 2)² - 3","option_d":"D. (x + 2)² - 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient par complétion du carré : f(x) = (x² - 4x + 4) + 3 = (x - 2)² + 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9079,"question":"Si deux droites sont parallèles, alors leurs coefficients directeurs sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont le même coefficient directeur, car elles ne se coupent jamais et gardent la même inclinaison.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9080,"question":"Calculez la valeur de l'expression E = (3 + 2)² - (3² + 2²).","option_a":"A. 12","option_b":"B. 0","option_c":"C. 25","option_d":"D. -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"E = (5)² - (9 + 4) = 25 - 13 = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9081,"question":"La fonction f(x) = 1\/x est définie pour 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, car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9082,"question":"Quelle est la solution de l'équation 3(x - 2) = 2x + 5 ?","option_a":"A. x = 11","option_b":"B. x = -11","option_c":"C. x = 1","option_d":"D. x = -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant : 3x - 6 = 2x + 5 → 3x - 2x = 5 + 6 → x = 11.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]