Quiz : Les fondamentaux des mathématiques en Seconde

Question 1 sur 10 10:00

[{"id":51901,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution est obtenue en isolant x : 3x = 15 ⇒ x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51902,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51903,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 7 ?","option_a":"7","option_b":"-4","option_c":"4","option_d":"-7","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur est le nombre devant x, soit -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51904,"question":"L'inéquation 2x + 1 \u003E 5 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 3","option_d":"x \u003C 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x : 2x \u003E 4 ⇒ x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51905,"question":"Le point A(2, -3) appartient-il à la droite d'équation y = x - 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 2 dans l'équation : y = 2 - 5 = -3. Le point A appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51906,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x + 3)²","option_c":"(x - 3)²","option_d":"x(x - 9)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il s'agit d'une identité remarquable : a² - b² = (a - b)(a + b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51907,"question":"La fonction f(x) = x² est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est décroissante sur ]-∞, 0] et croissante sur [0, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51908,"question":"Quel est le centre du cercle d'équation (x - 1)² + (y + 2)² = 16 ?","option_a":"(1, -2)","option_b":"(1, 2)","option_c":"(-1, 2)","option_d":"(2, -1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation d'un cercle est (x - a)² + (y - b)² = r², donc le centre est (a, b) = (1, -2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51909,"question":"L'équation x² + 4x + 4 = 0 admet-elle une solution double ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 0, donc l'équation admet une solution double : x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":51910,"question":"Si f(x) = 3x² - 2x + 1, quelle est l'image de 2 par f ?","option_a":"9","option_b":"7","option_c":"11","option_d":"5","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 2 : f(2) = 3*(2)² - 2*2 + 1 = 12 - 4 + 1 = 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]