Maths 1ère année : Devoir de Contrôle N°1 — Quiz de Révision

Question 1 sur 10 10:00

[{"id":14988,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 1 ?","option_a":"x = 4","option_b":"x = 6","option_c":"x = -4","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"C","explication":"Pour résoudre 3x - 5 = 2x + 1, on soustrait 2x des deux côtés : x - 5 = 1, puis on ajoute 5 : x = 6. La solution est donc x = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14989,"question":"L'inéquation 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":"Pour résoudre 2x + 3 \u003E 7, on soustrait 3 : 2x \u003E 4, puis on divise par 2 : x \u003E 2. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14990,"question":"Factorisez l'expression 4x² - 9.","option_a":"(2x - 3)(2x + 3)","option_b":"(4x - 3)(x + 3)","option_c":"(2x - 9)(2x + 1)","option_d":"(x - 3)(4x + 3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x² - 9 est une différence de carrés : (2x)² - 3² = (2x - 3)(2x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14991,"question":"La droite d'équation y = 2x + 1 passe par le point (0, 1).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour vérifier si la droite passe par (0, 1), on remplace x par 0 : y = 2*0 + 1 = 1. Le point (0, 1) appartient bien à la droite. L'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14992,"question":"Résolvez l'équation x² - 5x + 6 = 0.","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On factorise : (x - 2)(x - 3) = 0. Les solutions sont donc x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14993,"question":"L'expression 3(x + 2) - 2(x - 1) est égale à x + 8.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En développant : 3x + 6 - 2x + 2 = x + 8. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14994,"question":"Quelle est la solution de l'inéquation -2x + 4 ≤ 0 ?","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre -2x + 4 ≤ 0, on soustrait 4 : -2x ≤ -4, puis on divise par -2 (en inversant le sens) : x ≥ 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14995,"question":"Le point d'intersection des droites y = 3x + 1 et y = -x + 5 est (1, 4).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour trouver l'intersection, on résout 3x + 1 = -x + 5 : 4x = 4 → x = 1. En remplaçant, y = 4. Le point (1, 4) est donc correct.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14996,"question":"Factorisez l'expression x² - 4x + 4.","option_a":"(x - 2)²","option_b":"(x - 4)(x + 1)","option_c":"(x - 1)(x - 3)","option_d":"(x + 2)(x - 6)","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 4x + 4 est un carré parfait : (x - 2)².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":14997,"question":"L'équation 2x² - 8 = 0 a pour solutions x = 2 et x = -2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x² - 8 = 0 : 2x² = 8 → x² = 4 → x = 2 ou x = -2. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]