Maths 4ème année : Testez vos connaissances sur les exercices corrigés

Question 1 sur 10 10:00

[{"id":31378,"question":"Quelle est la solution de l'équation 3x - 7 = 2x + 5 ?","option_a":"x = 12","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"Résolvez l'équation en isolant x : 3x - 2x = 5 + 7 → x = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31379,"question":"La fonction f(x) = x² - 4x + 3 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 16 - 12 = 4 \u003E 0, donc la fonction s'annule en deux points et change de signe.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31380,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 3 ?","option_a":"-2","option_b":"3","option_c":"1","option_d":"2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est le nombre devant x dans l'équation réduite de la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31381,"question":"La probabilité d'un événement impossible est égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La probabilité d'un événement impossible est 0, tandis que celle d'un événement certain est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31382,"question":"Résolvez l'inéquation 2(x - 3) ≤ 4x + 1.","option_a":"x ≥ -7\/2","option_b":"x ≤ -7\/2","option_c":"x ≥ 7\/2","option_d":"x ≤ 7\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Développez et isolez x : 2x - 6 ≤ 4x + 1 → -7 ≤ 2x → x ≥ -7\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31383,"question":"La dérivée de f(x) = 5x³ - 2x² + x est f'(x) = 15x² - 4x + 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée est bien 15x² - 4x + 1, car (5x³)' = 15x², (-2x²)' = -4x et (x)' = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31384,"question":"Quel est le résultat de ∫(3x² - 2x + 1) dx ?","option_a":"x³ - x² + x + C","option_b":"3x³ - x² + x + C","option_c":"x³ - x + C","option_d":"3x³ - 2x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"Calculez l'intégrale terme par terme : ∫3x² dx = x³, ∫-2x dx = -x², ∫1 dx = x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31385,"question":"Un triangle rectangle a des côtés de longueurs 3, 4 et 5. L'angle opposé au côté de longueur 5 est-il droit ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par le théorème de Pythagore, 3² + 4² = 5², donc l'angle opposé au côté 5 est droit.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31386,"question":"Quelle est la forme canonique de f(x) = x² - 6x + 5 ?","option_a":"(x - 3)² - 4","option_b":"(x - 6)² - 11","option_c":"(x - 2)² + 1","option_d":"(x + 3)² - 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"Complétez le carré : x² - 6x + 9 - 4 = (x - 3)² - 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":31387,"question":"La suite définie par uₙ = 2n + 1 est-elle arithmétique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La différence entre deux termes consécutifs est constante : uₙ₊₁ - uₙ = 2, donc la suite est arithmétique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]