Quiz : Maîtrisez les bases du 1er trimestre en maths !

Question 1 sur 10 10:00

[{"id":45116,"question":"Quelle est la solution de l'équation 2x - 5 = 3x + 1 ?","option_a":"x = -6","option_b":"x = -4","option_c":"x = 4","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"A","explication":"En isolant x, on obtient 2x - 3x = 1 + 5 → -x = 6 → x = -6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45117,"question":"L'inéquation 3(x - 2) ≤ 5x + 1 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"3x - 6 ≤ 5x + 1 → -6 - 1 ≤ 2x → -7 ≤ 2x → x ≥ -3.5. La solution n'est donc pas x ≤ -3.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45118,"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 différence de carrés : x² - 9 = (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45119,"question":"La fonction f(x) = 3x + 2 est :","option_a":"Affine","option_b":"Constante","option_c":"Quadratic","option_d":"Exponentielle","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction de la forme f(x) = ax + b est une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45120,"question":"Le point A(2; -1) appartient-il à la droite d'équation y = 2x - 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 2 dans l'équation : y = 2(2) - 5 = -1. Le point A appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45121,"question":"Quelle est la distance entre les points A(1; 2) et B(4; 6) ?","option_a":"5","option_b":"√13","option_c":"√25","option_d":"√5","option_e":"","option_f":"","bonne_reponse":"C","explication":"La distance est calculée par √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45122,"question":"La suite définie par uₙ = 2n + 1 est :","option_a":"Arithmétique de raison 2","option_b":"Géométrique de raison 2","option_c":"Arithmétique de raison 1","option_d":"Constante","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante : uₙ₊₁ - uₙ = 2. C'est une suite arithmétique de raison 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45123,"question":"L'équation x² + 4x + 4 = 0 admet :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 16 - 16 = 0. L'équation admet donc une solution double : x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45124,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + x ?","option_a":"3x² - 4x + 1","option_b":"3x² - 4x","option_c":"x² - 4x + 1","option_d":"3x² - 2x + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En appliquant les règles de dérivation : f'(x) = 3x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":45125,"question":"La fonction f(x) = 1\/x est définie pour :","option_a":"x ≠ 0","option_b":"x \u003E 0","option_c":"x ∈ ℝ","option_d":"x ≤ 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction inverse est définie pour tout x réel sauf x = 0, car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]