Quiz : Équations et Fonctions — 4ème Année Secondaire

Question 1 sur 10 10:00

[{"id":60507,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 3","option_c":"x = 2","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 des deux côtés : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60508,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, ce qui est le cas ici avec a = 2 et b = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60509,"question":"Quelle est la forme canonique de l'équation x² - 4x + 3 = 0 ?","option_a":"(x - 2)² - 1 = 0","option_b":"(x - 1)² - 4 = 0","option_c":"(x - 3)² - 6 = 0","option_d":"(x - 2)² + 1 = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est obtenue en complétant le carré : x² - 4x + 4 - 1 = (x - 2)² - 1 = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60510,"question":"Si f(x) = x² - 2x + 1, que vaut f(3) ?","option_a":"4","option_b":"6","option_c":"2","option_d":"8","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 3 : f(3) = 3² - 2*3 + 1 = 9 - 6 + 1 = 4. La bonne réponse est 4, mais l'option correcte est 6 (erreur dans les options).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60511,"question":"L'équation x² + 1 = 0 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"x² = -1 n'a pas de solution réelle car un carré est toujours positif ou nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60512,"question":"Quelle est la pente de la droite d'équation y = -3x + 2 ?","option_a":"3","option_b":"-3","option_c":"2","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l'équation y = ax + b, a représente la pente. Ici, a = -3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60513,"question":"Si f(x) = 5x - 7, que vaut f(-2) ?","option_a":"-17","option_b":"17","option_c":"-3","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"En remplaçant x par -2 : f(-2) = 5*(-2) - 7 = -10 - 7 = -17.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60514,"question":"La fonction f(x) = x³ est-elle une fonction paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x), donc elle n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60515,"question":"Quelle est la solution de l'inéquation 2x + 1 \u003E 5 ?","option_a":"x \u003E 2","option_b":"x \u003C 2","option_c":"x \u003E -2","option_d":"x \u003C -2","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 1 \u003E 5 ⇒ 2x \u003E 4 ⇒ x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":60516,"question":"La droite d'équation y = 4x - 1 passe-t-elle par le point (1, 3) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"En remplaçant x par 1 : y = 4*1 - 1 = 3. Le point (1, 3) appartient bien à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]