Quiz Maths : Testez vos connaissances en 4ème année secondaire

Question 1 sur 10 10:00

[{"id":9393,"question":"Quelle est la solution de l'équation x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = -1 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":9394,"question":"La fonction f(x) = 3x² - 2x + 1 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = (-2)² - 4*3*1 = 4 - 12 = -8 \u003C 0, et le coefficient de x² est positif, donc la fonction est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9395,"question":"Quelle est la limite de la suite uₙ = (2n² + 3n - 1)\/(n² + 5) quand n tend vers l'infini ?","option_a":"2","option_b":"3","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par n², on obtient uₙ = (2 + 3\/n - 1\/n²)\/(1 + 5\/n²), donc la limite est 2\/1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9396,"question":"Un triangle ABC est rectangle en A. Si AB = 3 cm et AC = 4 cm, quelle est la longueur de BC ?","option_a":"5 cm","option_b":"7 cm","option_c":"√7 cm","option_d":"√10 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9397,"question":"La probabilité d'obtenir un nombre pair en lançant un dé équilibré est-elle de 1\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un dé équilibré a 3 nombres pairs (2, 4, 6) sur 6 faces, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9398,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 5x - 2 ?","option_a":"f'(x) = 3x² - 8x + 5","option_b":"f'(x) = 3x² - 4x + 5","option_c":"f'(x) = x² - 8x + 5","option_d":"f'(x) = 3x² - 8x - 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est 3x², celle de -4x² est -8x, celle de 5x est 5, et celle de -2 est 0, donc f'(x) = 3x² - 8x + 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9399,"question":"Un carré a une aire de 16 cm². Quelle est la longueur de sa diagonale ?","option_a":"4√2 cm","option_b":"8 cm","option_c":"4 cm","option_d":"2√2 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le côté du carré est √16 = 4 cm. La diagonale d'un carré de côté c est c√2, donc 4√2 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9400,"question":"La fonction f(x) = 1\/x est-elle définie 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 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9401,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 1","option_d":"x \u003C -1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x - 3 \u003E 5, on obtient 2x \u003E 8, donc x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":9402,"question":"Un sac contient 5 boules rouges et 3 boules bleues. Quelle est la probabilité de tirer une boule bleue ?","option_a":"3\/8","option_b":"5\/8","option_c":"3\/5","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 3 boules bleues sur un total de 8 boules, donc la probabilité est 3\/8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]