Quiz Mathématiques : Fonctions, Équations et Géométrie — 2ème Année Secondaire

Question 1 sur 10 10:00

[{"id":65132,"question":"Quelle est la représentation graphique d'une fonction affine f(x) = 2x + 3 ?","option_a":"Une droite parallèle à l'axe des abscisses","option_b":"Une droite de pente 2 et d'ordonnée à l'origine 3","option_c":"Une parabole","option_d":"Un cercle","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine f(x) = ax + b a pour représentation graphique une droite de pente a et d'ordonnée à l'origine b.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65133,"question":"L'équation 3x - 5 = 2x + 1 a pour solution :","option_a":"x = 4","option_b":"x = 6","option_c":"x = -4","option_d":"x = -6","option_e":"","option_f":"","bonne_reponse":"B","explication":"3x - 5 = 2x + 1 → 3x - 2x = 1 + 5 → x = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65134,"question":"Vrai ou Faux : Une fonction linéaire est toujours croissante.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction linéaire f(x) = ax est croissante si a \u003E 0 et décroissante si a \u003C 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65135,"question":"Quel est le discriminant de l'équation x² - 4x + 3 = 0 ?","option_a":"Δ = 4","option_b":"Δ = -4","option_c":"Δ = 0","option_d":"Δ = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = b² - 4ac = (-4)² - 4(1)(3) = 16 - 12 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65136,"question":"Vrai ou Faux : Deux droites parallèles ont le même coefficient directeur.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont des coefficients directeurs égaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65137,"question":"Résolvez le système : { 2x + y = 5 ; x - y = 1 }. La solution est :","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = -1, y = 7","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations : 3x = 6 → x = 2. En remplaçant : 2(2) + y = 5 → y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65138,"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 : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65139,"question":"Vrai ou Faux : Une inéquation du type 2x + 3 \u003E 7 a pour solution x \u003E 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 → 2x \u003E 4 → x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65140,"question":"Quel est le point d'intersection des droites d'équations y = 2x + 1 et y = -x + 4 ?","option_a":"(1, 3)","option_b":"(2, 5)","option_c":"(0, 1)","option_d":"(-1, -1)","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x + 1 = -x + 4 → 3x = 3 → x = 1. y = 2(1) + 1 = 3. Point (1, 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":65141,"question":"Vrai ou Faux : La fonction f(x) = x² est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = (-x)² = x² = f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]