Quiz : Maths 3ème année secondaire — Série 13

Question 1 sur 10 10:00

[{"id":80492,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle : (ax^n)' = n*ax^(n-1). Ici, f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80493,"question":"L'équation x² - 4x + 4 = 0 admet-elle deux solutions réelles distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = b² - 4ac = 16 - 16 = 0, donc l'équation admet une solution double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80494,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"x² + C","option_c":"2x² + x + C","option_d":"x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale d'une fonction linéaire s'obtient en appliquant la formule ∫(ax + b) dx = (a\/2)x² + bx + C. Ici, ∫(2x + 1) dx = x² + x + C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80495,"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":80496,"question":"Quelle est la solution de l'inéquation 3x - 7 \u003E 2x + 5 ?","option_a":"x \u003E 12","option_b":"x \u003C 12","option_c":"x \u003E -12","option_d":"x \u003C -12","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant l'inéquation : 3x - 7 \u003E 2x + 5 → x \u003E 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80497,"question":"Le triangle ABC avec AB = 5 cm, BC = 12 cm et AC = 13 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérifions avec le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Le triangle est donc rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80498,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/6) = 1\/2, valeur à connaître par cœur dans le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80499,"question":"La fonction f(x) = x³ est-elle paire ou impaire ?","option_a":"Paire","option_b":"Impaire","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction est impaire si f(-x) = -f(x). Ici, f(-x) = (-x)³ = -x³ = -f(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80500,"question":"Quel est le résultat de (2x + 3)(x - 4) ?","option_a":"2x² - 5x - 12","option_b":"2x² + 5x - 12","option_c":"2x² - 11x - 12","option_d":"2x² - 5x + 12","option_e":"","option_f":"","bonne_reponse":"C","explication":"En développant : (2x + 3)(x - 4) = 2x² - 8x + 3x - 12 = 2x² - 5x - 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":80501,"question":"La droite d'équation y = 2x + 1 a-t-elle un coefficient directeur égal à 1 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur (pente) de la droite y = 2x + 1 est 2, pas 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]