Algèbre 3ème année secondaire : Équations, Inéquations et Fonctions

Question 1 sur 10 10:00

[{"id":26948,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 5","option_c":"x = -2","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés et en ajoutant 5, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26949,"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":"A","explication":"En soustrayant 3 et en divisant par 2, on obtient x \u003E 2, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26950,"question":"Quelle est la forme réduite de l'expression (2x + 3)(x - 4) ?","option_a":"2x² - 5x - 12","option_b":"2x² - 8x + 3x - 12","option_c":"2x² - 5x + 12","option_d":"2x² + 5x - 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant, on obtient 2x² - 8x + 3x - 12 = 2x² - 5x - 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26951,"question":"La fonction f(x) = 3x + 2 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, donc f(x) = 3x + 2 est bien affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26952,"question":"Résoudre le 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":"En additionnant les deux équations, on obtient 3x = 6, donc x = 2. En remplaçant, y = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26953,"question":"L'équation x² - 4x + 4 = 0 a pour solution :","option_a":"x = 2 (double)","option_b":"x = -2","option_c":"x = 4","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est nul (Δ = 0), donc l'équation a une solution double x = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26954,"question":"La représentation graphique d'une fonction affine est toujours une droite.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, car une fonction affine s'écrit f(x) = ax + b, dont la courbe est une droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26955,"question":"Quelle est la solution de l'inéquation -2x + 5 ≤ 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":"En soustrayant 5 et en divisant par -2 (attention au changement de sens), on obtient x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26956,"question":"Si f(x) = 4x - 1, alors f(3) = ?","option_a":"11","option_b":"12","option_c":"13","option_d":"14","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 3, on obtient f(3) = 4*3 - 1 = 11.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":26957,"question":"L'équation 5x² + 3x - 2 = 0 a deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est Δ = 9 + 40 = 49 \u003E 0, donc deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]