Quiz Maths : Testez vos connaissances en algèbre et analyse — 4ème année secondaire

Question 1 sur 10 10:00

[{"id":59207,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 2x + 7 ⇒ 3x - 2x = 7 + 5 ⇒ x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59208,"question":"La fonction f(x) = x² - 4x + 3 est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est positive uniquement pour x ≤ 1 ou x ≥ 3 (racines en x=1 et x=3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59209,"question":"Quel est le résultat de (2x + 3)(x - 4) ?","option_a":"2x² - 5x - 12","option_b":"2x² + 5x - 12","option_c":"2x² - 11x - 12","option_d":"2x² - 5x + 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Développement : 2x * x + 2x * (-4) + 3 * x + 3 * (-4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59210,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore est valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59211,"question":"Résoudre l'inéquation 2x + 1 \u003E 5.","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 1 \u003E 5 ⇒ 2x \u003E 4 ⇒ x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59212,"question":"La dérivée de f(x) = 3x³ - 2x² + x est f'(x) = 9x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dérivée correcte : f'(x) = 9x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59213,"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 = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Factorisation : (x - 2)(x - 3) = 0 ⇒ x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59214,"question":"La fonction exponentielle f(x) = eˣ est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction exponentielle est strictement croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59215,"question":"Calculer la limite de (3x² - 2x + 1)\/(x² + 1) quand x tend vers +∞.","option_a":"3","option_b":"1","option_c":"0","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"En divisant par x², on obtient (3 - 2\/x + 1\/x²)\/(1 + 1\/x²) → 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":59216,"question":"Le centre de symétrie d'une parabole d'équation y = ax² + bx + c est en x = -b\/(2a).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le centre de symétrie (sommet) d'une parabole est bien en x = -b\/(2a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]