Quiz Maths Seconde : Algèbre, Fonctions et Vecteurs

Question 1 sur 10 10:00

[{"id":32388,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 2","option_c":"x = 12","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32389,"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 avec a = 2 et b = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32390,"question":"Quel est le vecteur directeur de la droite d'équation y = -2x + 5 ?","option_a":"u(1, -2)","option_b":"u(-2, 1)","option_c":"u(2, -1)","option_d":"u(1, 2)","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur de la droite est -2, donc le vecteur directeur est u(1, -2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32391,"question":"L'inéquation 2x - 7 \u003E 3 a pour solution x \u003E 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons : 2x \u003E 10 → x \u003E 5. La solution est donc bien x \u003E 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32392,"question":"Quelle est l'image de -3 par la fonction f(x) = x² - 4x + 1 ?","option_a":"f(-3) = 22","option_b":"f(-3) = -22","option_c":"f(-3) = 28","option_d":"f(-3) = -28","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons : f(-3) = (-3)² - 4*(-3) + 1 = 9 + 12 + 1 = 22.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32393,"question":"Les vecteurs u(2, 5) et v(-4, -10) sont-ils colinéaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les vecteurs sont colinéaires si l'un est un multiple de l'autre. Ici, v = -2*u, donc ils sont colinéaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32394,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 6x + 8 ?","option_a":"f(x) = (x - 3)² - 1","option_b":"f(x) = (x - 2)² + 3","option_c":"f(x) = (x + 3)² - 1","option_d":"f(x) = (x - 3)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est f(x) = (x - 3)² - 1, obtenue en complétant le carré : x² - 6x = (x - 3)² - 9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32395,"question":"L'équation x² + 4x + 5 = 0 a-t-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant est Δ = 16 - 20 = -4 \u003C 0, donc l'équation n'a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32396,"question":"Quel est le coefficient directeur de la droite passant par les points A(1, 2) et B(3, 6) ?","option_a":"2","option_b":"4","option_c":"1","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (6 - 2)\/(3 - 1) = 4\/2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":32397,"question":"La fonction f(x) = -x² + 4x - 3 est-elle croissante sur l'intervalle [-1, 1] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = -2x + 4 est positive sur [-1, 1] (car -2x + 4 ≥ 2 \u003E 0), donc la fonction est croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]