Quiz : Mathématiques 2ème année secondaire — Devoir de Contrôle

Question 1 sur 10 10:00

[{"id":55301,"question":"Quelle est la solution de l'équation 3x - 5 = 16 ?","option_a":"x = 7","option_b":"x = 10","option_c":"x = 5","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"B","explication":"3x - 5 = 16 → 3x = 21 → x = 7. La solution est x = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55302,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine s'écrit f(x) = ax + b. Ici, f(x) est un polynôme du second degré (présence de x²), donc ce n'est pas une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55303,"question":"Quel est le discriminant de l'équation x² - 4x + 3 = 0 ?","option_a":"Δ = 4","option_b":"Δ = 16","option_c":"Δ = -4","option_d":"Δ = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour ax² + bx + c = 0, Δ = b² - 4ac. Ici, Δ = (-4)² - 4(1)(3) = 16 - 12 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55304,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles. Pour les autres triangles, on utilise d'autres propriétés géométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55305,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : a² - b² = (a - b)(a + b). Ici, a = x et b = 3, donc (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55306,"question":"La moyenne de 5, 7, 9 et 11 est-elle égale à 8 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Moyenne = (5 + 7 + 9 + 11) \/ 4 = 32 \/ 4 = 8. La moyenne est bien égale à 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55307,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 5 ?","option_a":"-2","option_b":"5","option_c":"2","option_d":"-5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation y = ax + b, a est le coefficient directeur. Ici, a = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55308,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérifions avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55309,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E 5","option_c":"x \u003C 2","option_d":"x \u003C 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 → 2x \u003E 4 → x \u003E 2. La solution est x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":55310,"question":"La fonction f(x) = 4x - 1 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine f(x) = ax + b est croissante si a \u003E 0. Ici, a = 4 \u003E 0, donc la fonction est croissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]