Quiz : Équations et Fonctions — 3ème Mathématiques

Question 1 sur 10 10:00

[{"id":11988,"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 = -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons l'équation : 3x - 5 = 7 → 3x = 12 → x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11989,"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 f(x) = ax + b. Ici, a = 2 et b = 3, donc c'est bien une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11990,"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 : x² - 3² = (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11991,"question":"L'équation x² + 4x + 4 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 16 = 0, donc l'équation admet une solution double : x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11992,"question":"Quelle est l'image de 5 par la fonction f(x) = -2x + 1 ?","option_a":"f(5) = -9","option_b":"f(5) = 9","option_c":"f(5) = -11","option_d":"f(5) = 11","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons f(5) = -2*5 + 1 = -10 + 1 = -9.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11993,"question":"La fonction g(x) = 5 est-elle une fonction constante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction constante a la forme g(x) = k, où k est un nombre réel. Ici, g(x) = 5, donc c'est une fonction constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11994,"question":"Quelle est la solution de l'inéquation 2x + 1 \u003E 5 ?","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":"Résolvons l'inéquation : 2x + 1 \u003E 5 → 2x \u003E 4 → x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11995,"question":"La fonction h(x) = x² - 4x + 4 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction h(x) = (x - 2)² est toujours positive ou nulle, donc elle admet un minimum en x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11996,"question":"Quelle est la solution de l'équation (x + 1)(x - 3) = 0 ?","option_a":"x = -1 ou x = 3","option_b":"x = 1 ou x = -3","option_c":"x = 0","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un produit de facteurs est nul si l'un des facteurs est nul : x + 1 = 0 → x = -1 ou x - 3 = 0 → x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11997,"question":"La fonction k(x) = -3x + 7 est-elle décroissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est -3 (négatif), donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]