Quiz Maths Seconde : Algèbre et Équations

Question 1 sur 10 10:00

[{"id":5715,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -12","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés et en ajoutant 7, on obtient x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5716,"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":"La solution est x \u003E 2, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5717,"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":"Il s'agit d'une identité remarquable : a² - b² = (a - b)(a + b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5718,"question":"La fonction f(x) = 2x + 1 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 c'est vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5719,"question":"Résoudre le système : { 2x + y = 5 ; x - y = 1 }. Quelle est la solution ?","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":5720,"question":"L'équation x² + 4x + 4 = 0 a pour solution :","option_a":"x = -2 (double)","option_b":"x = 2","option_c":"x = 0","option_d":"x = -4","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une identité remarquable : (x + 2)² = 0, donc x = -2 (solution double).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5721,"question":"La fonction f(x) = x² est-elle croissante sur ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction est décroissante sur ]-∞, 0] et croissante sur [0, +∞[, donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5722,"question":"Quelle est la solution de l'inéquation -3x + 5 ≤ 2 ?","option_a":"x ≥ 1","option_b":"x ≤ 1","option_c":"x ≥ -1","option_d":"x ≤ -1","option_e":"","option_f":"","bonne_reponse":"B","explication":"En soustrayant 5 et en divisant par -3 (qui inverse le sens de l'inégalité), on obtient x ≥ 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5723,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b - 4ac","option_c":"Δ = a² - 4bc","option_d":"Δ = b² + 4ac","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule du discriminant est bien Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5724,"question":"La fonction f(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 même valeur pour tout x, donc c'est vrai.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]