Quiz : Nombres réels, fonctions et équations — 4ème Math

Question 1 sur 10 10:00

[{"id":58346,"question":"Quel est l'ensemble des solutions de l'inéquation 3x - 5 ≤ 7 ?","option_a":"x ≤ 4","option_b":"x ≥ 4","option_c":"x ≤ 12\/3","option_d":"x ∈ [4 ; +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvons l'inéquation : 3x - 5 ≤ 7 → 3x ≤ 12 → x ≤ 4. L'ensemble des solutions est donc x ≤ 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58347,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b. Ici, f(x) = 2x² - 3x + 1 est une fonction du second degré, donc non affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58348,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"5","option_b":"7","option_c":"√25","option_d":"10","option_e":"","option_f":"","bonne_reponse":"B","explication":"√(16) = 4 et √(9) = 3. Donc √(16) + √(9) = 4 + 3 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58349,"question":"L'équation x² - 5x + 6 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculons le discriminant : Δ = (-5)² - 4×1×6 = 25 - 24 = 1 \u003E 0. L'équation admet donc deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58350,"question":"Quelle est la valeur de f(2) pour la fonction f(x) = -3x + 7 ?","option_a":"1","option_b":"13","option_c":"-1","option_d":"10","option_e":"","option_f":"","bonne_reponse":"C","explication":"f(2) = -3×2 + 7 = -6 + 7 = 1. La bonne réponse est donc 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58351,"question":"L'ensemble des nombres réels est-il noté ℝ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, l'ensemble des nombres réels est traditionnellement noté ℝ (R majuscule).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58352,"question":"Résolvez l'équation 4x + 8 = 0. Quelle est la solution ?","option_a":"x = -2","option_b":"x = 2","option_c":"x = -8","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"4x + 8 = 0 → 4x = -8 → x = -2. La solution est donc x = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58353,"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":"Oui, une fonction constante est une fonction qui prend la même valeur pour tout x. Ici, f(x) = 5 est bien une fonction constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58354,"question":"Quel est le résultat de (√5)² ?","option_a":"5","option_b":"√10","option_c":"2√5","option_d":"25","option_e":"","option_f":"","bonne_reponse":"A","explication":"(√5)² = 5, car le carré d'une racine carrée redonne le nombre sous la racine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":58355,"question":"L'inégalité 2x + 3 \u003E 7 est-elle équivalente à x \u003E 2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 → 2x \u003E 4 → x \u003E 2. L'inégalité est donc bien équivalente à x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]