Quiz Maths : 4ème Année Secondaire — Algèbre, Géométrie & Analyse

Question 1 sur 10 10:00

[{"id":34263,"question":"Quelle est la solution de l'équation 3x + 5 = 2x - 7 ?","option_a":"x = -12","option_b":"x = -2","option_c":"x = 12","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En soustrayant 2x des deux côtés, on obtient x + 5 = -7, puis en soustrayant 5, on trouve x = -12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34264,"question":"Le théorème de Pythagore s'applique-t-il à tous les triangles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore ne s'applique qu'aux triangles rectangles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34265,"question":"Quelle est la dérivée de la fonction f(x) = 4x³ - 2x² + 5 ?","option_a":"f'(x) = 12x² - 4x","option_b":"f'(x) = 12x² - 4x + 5","option_c":"f'(x) = 4x² - 2x","option_d":"f'(x) = 12x² - 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme par terme : 3*4x² - 2*2x + 0 = 12x² - 4x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34266,"question":"Dans un triangle ABC rectangle en A, si AB = 3 et AC = 4, quelle est la longueur de BC ?","option_a":"5","option_b":"7","option_c":"6","option_d":"4","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore : BC² = AB² + AC² = 9 + 16 = 25, donc BC = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34267,"question":"La fonction f(x) = x² est-elle toujours croissante ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = x² est décroissante sur ]-∞, 0] et croissante sur [0, +∞[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34268,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 7 ?","option_a":"x \u003E 5","option_b":"x \u003C 5","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En ajoutant 3 des deux côtés, on obtient 2x \u003E 10, puis en divisant par 2, x \u003E 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34269,"question":"Le cosinus d'un angle aigu dans un triangle rectangle est-il toujours inférieur à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le cosinus d'un angle aigu est toujours compris entre 0 et 1, car il représente le rapport de deux longueurs.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34270,"question":"Quelle est la limite de la fonction f(x) = (3x² + 2x - 1)\/(x² - 4) quand x tend vers +∞ ?","option_a":"3","option_b":"0","option_c":"1\/4","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"A","explication":"En divisant numérateur et dénominateur par x², on obtient (3 + 2\/x - 1\/x²)\/(1 - 4\/x²), donc la limite est 3\/1 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34271,"question":"Un parallélogramme a-t-il toujours des diagonales de même longueur ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Seuls les rectangles (un type de parallélogramme) ont des diagonales de même longueur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":34272,"question":"Quelle est la probabilité de tirer un as dans un jeu de 52 cartes ?","option_a":"1\/13","option_b":"1\/4","option_c":"1\/52","option_d":"4\/52","option_e":"","option_f":"","bonne_reponse":"A","explication":"Il y a 4 as dans un jeu de 52 cartes, donc la probabilité est 4\/52 = 1\/13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]