Maths 3ème : Devoir de Synthèse — Testez vos connaissances !

Question 1 sur 10 10:00

[{"id":73102,"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 = -1 ou x = -6","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":73103,"question":"La dérivée de f(x) = x³ est f'(x) = 3x².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est bien 3x², selon la règle de dérivation des puissances.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73104,"question":"Quel est le domaine de définition de la fonction f(x) = 1\/(x-2) ?","option_a":"A) ℝ","option_b":"B) ℝ \\ {2}","option_c":"C) ℝ \\ {0}","option_d":"D) [0, +∞[","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction n'est pas définie lorsque le dénominateur est nul, soit x = 2. Le domaine est donc ℝ privé de 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73105,"question":"Si sin(θ) = 0.5, alors θ = 30° + k*360° (k ∈ ℤ).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les solutions de sin(θ) = 0.5 sont θ = 30° + k*360° ou θ = 150° + k*360° (k ∈ ℤ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73106,"question":"Quelle est la limite de f(x) = (x² - 1)\/(x - 1) lorsque x tend vers 1 ?","option_a":"A) 0","option_b":"B) 1","option_c":"C) 2","option_d":"D) +∞","option_e":"","option_f":"","bonne_reponse":"C","explication":"En factorisant, f(x) = (x-1)(x+1)\/(x-1) = x+1 pour x ≠ 1. La limite est donc 1+1 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73107,"question":"Le produit scalaire de deux vecteurs orthogonaux est toujours nul.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, le produit scalaire de deux vecteurs orthogonaux est nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73108,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"A) x \u003E 1","option_b":"B) x \u003E 4","option_c":"C) x \u003C 4","option_d":"D) x \u003E 8","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73109,"question":"La fonction f(x) = x² est convexe sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée seconde de f(x) = x² est f''(x) = 2 \u003E 0, donc la fonction est convexe sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73110,"question":"Quelle est la valeur de cos(60°) ?","option_a":"A) 0","option_b":"B) 0.5","option_c":"C) √2\/2","option_d":"D) 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"cos(60°) = 0.5, valeur standard à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73111,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est bien défini par Δ = b² - 4ac pour une équation du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]