Quiz : Les incontournables des maths en 3ème année secondaire

Question 1 sur 10 10:00

[{"id":61767,"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":"On factorise l'équation : (x-2)(x-3)=0. Les solutions sont donc x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61768,"question":"La fonction f(x) = x³ - 3x² + 2x est-elle dérivable en x=1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Toute fonction polynôme est dérivable sur ℝ. La dérivée f'(x)=3x²-6x+2 existe donc en x=1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61769,"question":"Quel est le terme général d'une suite géométrique de premier terme u₀=2 et de raison q=3 ?","option_a":"uₙ = 2 × 3ⁿ","option_b":"uₙ = 3 × 2ⁿ","option_c":"uₙ = 2 + 3n","option_d":"uₙ = 3 + 2n","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une suite géométrique, uₙ = u₀ × qⁿ. Ici, uₙ = 2 × 3ⁿ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61770,"question":"La limite de (x² + 1)\/(x - 1) quand x tend vers 1 par valeurs supérieures est-elle +∞ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Quand x→1⁺, le dénominateur tend vers 0⁺ et le numérateur vers 2. La limite est donc +∞.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61771,"question":"Quelle est la dérivée de la fonction f(x) = (2x + 1)\/(x - 3) ?","option_a":"f'(x) = 2\/(x-3)²","option_b":"f'(x) = (2x-7)\/(x-3)²","option_c":"f'(x) = (x-3)\/(2x+1)","option_d":"f'(x) = -2\/(x-3)²","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise la formule de dérivation d'un quotient : f'(x) = [2(x-3) - (2x+1)(1)]\/(x-3)² = (2x-6-2x-1)\/(x-3)² = -7\/(x-3)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61772,"question":"Une suite croissante est-elle toujours convergente ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une suite croissante peut diverger vers +∞ (exemple : uₙ = n). Elle n'est convergente que si elle est majorée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61773,"question":"Quel est le reste de la division euclidienne de P(x) = x³ - 2x² + 3x - 4 par (x - 1) ?","option_a":"R = 0","option_b":"R = -2","option_c":"R = 2","option_d":"R = -4","option_e":"","option_f":"","bonne_reponse":"D","explication":"D'après le théorème du reste, R = P(1) = 1 - 2 + 3 - 4 = -2. Le reste est donc -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61774,"question":"La fonction f(x) = |x| est-elle dérivable en x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction valeur absolue n'est pas dérivable en x=0 car sa dérivée à gauche (-1) ≠ dérivée à droite (+1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61775,"question":"Quelle est la somme des 5 premiers termes d'une suite arithmétique de premier terme u₀=3 et de raison r=2 ?","option_a":"S₅ = 35","option_b":"S₅ = 40","option_c":"S₅ = 25","option_d":"S₅ = 50","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des n premiers termes d'une suite arithmétique est Sₙ = n\/2 × (2u₀ + (n-1)r). Ici, S₅ = 5\/2 × (6 + 8) = 35.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":61776,"question":"La fonction f(x) = √(x² + 1) est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction est paire si f(-x) = f(x). Ici, f(-x) = √((-x)² + 1) = √(x² + 1) = f(x). La fonction est donc paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]