Quiz Mathématiques : 4ème année secondaire — Série 22

Question 1 sur 10 10:00

[{"id":50981,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = 4\/3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50982,"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":"La fonction est un polynôme du second degré avec un discriminant positif (4), donc elle change de signe. Elle n'est pas toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50983,"question":"Quel est le coefficient directeur de la droite d'équation y = 2x + 5 ?","option_a":"2","option_b":"5","option_c":"-2","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'équation y = mx + p, m est le coefficient directeur. Ici, m = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50984,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E 5","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x + 3 \u003E 7, on obtient 2x \u003E 4, puis x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50985,"question":"La dérivée de f(x) = x³ est f'(x) = 3x².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de x³ est bien 3x², d'après la formule de dérivation des puissances.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50986,"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":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50987,"question":"Si f(x) = 2x + 1, alors f(3) = 7.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par 3 dans f(x) = 2x + 1, on obtient f(3) = 2*3 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50988,"question":"Le discriminant d'un polynôme du second degré ax² + bx + c est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = a² - 4bc","option_c":"Δ = b - 4ac","option_d":"Δ = 4a² - b²","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est bien Δ = b² - 4ac, formule fondamentale pour étudier les racines d'un polynôme.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50989,"question":"La fonction f(x) = 1\/x est-elle définie en x = 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":50990,"question":"Quelle est la limite de (3x² + 2x - 1)\/(x² + 1) quand x tend vers l'infini ?","option_a":"3","option_b":"2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 + 1\/x²), qui tend vers 3 quand x tend vers l'infini.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]