Maths 4ème secondaire : Algèbre, Géométrie et Analyse

Question 1 sur 10 10:00

[{"id":39705,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 15","option_e":"","option_f":"","bonne_reponse":"B","explication":"En ajoutant 5 des deux côtés, on obtient 3x = 15. En divisant par 3, x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39706,"question":"Le théorème de Pythagore s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore est valable uniquement pour les triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39707,"question":"Quelle est la forme canonique de la fonction f(x) = 2x² - 8x + 5 ?","option_a":"f(x) = 2(x - 2)² - 3","option_b":"f(x) = 2(x - 4)² + 5","option_c":"f(x) = 2(x - 1)² - 1","option_d":"f(x) = 2(x - 2)² + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"En complétant le carré, on obtient f(x) = 2(x² - 4x) + 5 = 2[(x - 2)² - 4] + 5 = 2(x - 2)² - 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39708,"question":"Si A et B sont deux événements incompatibles, alors P(A ∪ B) = P(A) + P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour des événements incompatibles, la probabilité de leur réunion est la somme de leurs probabilités.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39709,"question":"Quelle est l'équation de la droite passant par les points A(1, 2) et B(3, 4) ?","option_a":"y = x + 1","option_b":"y = 2x - 1","option_c":"y = x","option_d":"y = 2x + 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le coefficient directeur est (4-2)\/(3-1) = 1. L'équation est y = x + 1 (car 2 = 1*1 + 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39710,"question":"La fonction f(x) = 1\/x est définie pour 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":39711,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","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":"En soustrayant 3 des deux côtés, on obtient 2x \u003E 4. En divisant par 2, x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39712,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par Δ = b² - 4ac.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est bien Δ = b² - 4ac, utilisé pour déterminer le nombre de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39713,"question":"Quelle est la probabilité d'obtenir un nombre pair en lançant un dé équilibré ?","option_a":"1\/6","option_b":"1\/2","option_c":"1\/3","option_d":"2\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Il y a 3 nombres pairs (2, 4, 6) sur 6 faces possibles, donc la probabilité est 3\/6 = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":39714,"question":"La dérivée de la fonction 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, selon la règle de dérivation des puissances.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]