Maths Seconde : Testez vos connaissances en algèbre et fonctions

Question 1 sur 10 10:00

[{"id":48791,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons l'équation : 3x - 5 = 7 → 3x = 12 → x = 4. La solution est donc x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48792,"question":"La fonction f(x) = 2x + 3 est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = 2x + 3 a un coefficient directeur positif (2 \u003E 0), donc elle est croissante sur ℝ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48793,"question":"Quelle est l'image de -2 par la fonction f(x) = x² - 4x + 1 ?","option_a":"f(-2) = 17","option_b":"f(-2) = 3","option_c":"f(-2) = -15","option_d":"f(-2) = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons f(-2) = (-2)² - 4*(-2) + 1 = 4 + 8 + 1 = 13. Aucune option n'est correcte, mais la méthode est à maîtriser.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48794,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution :","option_a":"x \u003E 4","option_b":"x \u003E 1","option_c":"x \u003C 4","option_d":"x \u003E 8","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons l'inéquation : 2x - 3 \u003E 5 → 2x \u003E 8 → x \u003E 4. La solution est x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48795,"question":"Le point A(3 ; 5) appartient-il à la droite d'équation y = 2x - 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Vérifions : si x = 3, y = 2*3 - 1 = 5. Le point A(3 ; 5) appartient bien à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48796,"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":48797,"question":"La fonction g(x) = -x² + 4x - 3 admet-elle un maximum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction g(x) = -x² + 4x - 3 est une parabole tournée vers le bas (coefficient de x² négatif), donc elle admet un maximum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48798,"question":"Résolvez l'inéquation : -3x + 2 ≤ 8","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Résolvons : -3x + 2 ≤ 8 → -3x ≤ 6 → x ≥ -2 (en divisant par un nombre négatif, on change le sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48799,"question":"La droite d'équation y = -2x + 5 est-elle parallèle à la droite y = -2x - 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites sont parallèles si elles ont le même coefficient directeur. Ici, les deux droites ont un coefficient directeur de -2, donc elles sont parallèles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":48800,"question":"Quelle est la solution du système : { 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":"Résolvons le système : de la 2ème équation, x = y + 1. En remplaçant dans la 1ère : 2(y + 1) + y = 5 → 3y + 2 = 5 → y = 1. Donc x = 2. La solution est (2 ; 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]