Quiz Mathématiques : Équations, Fonctions et Géométrie pour la Seconde

Question 1 sur 10 10:00

[{"id":18588,"question":"Quelle est la solution de l'équation 3x - 5 = 16 ?","option_a":"x = 7","option_b":"x = 11","option_c":"x = 5","option_d":"x = 21\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 3x - 5 = 16, on ajoute 5 des deux côtés : 3x = 21, puis on divise par 3 : x = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18589,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution est x \u003E 2. L'inéquation 2x + 3 \u003E 7 se résout en soustrayant 3 : 2x \u003E 4, puis en divisant par 2 : x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18590,"question":"Quelle est l'équation de la droite passant par les points A(1; 2) et B(3; 6) ?","option_a":"y = 2x","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = 3x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (6-2)\/(3-1) = 2. L'équation est donc y = 2x. Vérifiez avec A(1;2) : 2 = 2*1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18591,"question":"La fonction f(x) = -2x + 5 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 -2 (négatif), donc la fonction est décroissante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18592,"question":"Résolvez le système d'équations : { 2x + y = 5 ; x - y = 1 }","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En additionnant les deux équations : 3x = 6 ⇒ x = 2. En remplaçant dans la 2ème équation : 2 - y = 1 ⇒ y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18593,"question":"Le point C(4; 9) appartient-il à la droite d'équation y = 3x - 3 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x = 4, y = 3*4 - 3 = 9. Le point C(4;9) vérifie donc l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18594,"question":"Quelle est la distance entre les points D(2; 5) et E(-1; 1) ?","option_a":"5","option_b":"√25","option_c":"√13","option_d":"√17","option_e":"","option_f":"","bonne_reponse":"D","explication":"La distance est √[(2 - (-1))² + (5 - 1)²] = √(9 + 16) = √25 = 5. La réponse √17 est incorrecte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18595,"question":"La fonction g(x) = x² - 4x + 3 admet-elle un minimum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une fonction du second degré avec un coefficient directeur positif (a=1), donc elle admet un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18596,"question":"Résolvez l'inéquation : -3x + 7 ≤ 1","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x ≥ -2","option_d":"x ≤ -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"On soustrait 7 : -3x ≤ -6, puis on divise par -3 (inversion du sens) : x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":18597,"question":"Quelle est l'image de -3 par la fonction h(x) = 4x + 1 ?","option_a":"-11","option_b":"-12","option_c":"13","option_d":"11","option_e":"","option_f":"","bonne_reponse":"A","explication":"h(-3) = 4*(-3) + 1 = -12 + 1 = -11.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]