Quiz Mathématiques : Équations, Fonctions et Géométrie — 4ème Année Secondaire

Question 1 sur 10 10:00

[{"id":12138,"question":"Quelle est la solution de l'équation du second degré x² - 5x + 6 = 0 ?","option_a":"x = 2 ou x = 3","option_b":"x = -2 ou x = -3","option_c":"x = 1 ou x = 6","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions s'obtiennent en factorisant : (x-2)(x-3)=0, donc x=2 ou x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12139,"question":"La fonction f(x) = x² - 4x + 3 est-elle croissante sur l'intervalle [2, +∞[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x)=2x-4 est positive pour x\u003E2, donc la fonction est croissante sur cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12140,"question":"Quel est le volume d'un cylindre de rayon r=3 cm et de hauteur h=5 cm ?","option_a":"45π cm³","option_b":"9π cm³","option_c":"15π cm³","option_d":"30π cm³","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le volume d'un cylindre est V=πr²h = π×3²×5 = 45π cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12141,"question":"L'inéquation 2x - 3 \u003E 5 a pour solution x \u003E 4.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x \u003E 8, on obtient x \u003E 4, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12142,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 1 ?","option_a":"f'(x) = 9x² - 4x + 1","option_b":"f'(x) = 3x² - 2x + 1","option_c":"f'(x) = 6x² - 4x + 1","option_d":"f'(x) = 9x² - 4x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée se calcule terme par terme : f'(x)=9x²-4x+1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12143,"question":"Le triangle ABC avec AB=5 cm, BC=12 cm et AC=13 cm est un triangle rectangle.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vérification par Pythagore : 5²+12²=13², donc c'est un triangle rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12144,"question":"Quelle est la solution de l'inéquation -2x + 7 ≤ 3 ?","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x ≥ -2","option_d":"x ≤ -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"En résolvant -2x ≤ -4, on obtient x ≥ 2 (attention au changement de sens de l'inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12145,"question":"La fonction f(x) = 1\/x est-elle définie pour x=0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction 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":12146,"question":"Quel est le centre de symétrie de la fonction f(x) = x³ - 3x ?","option_a":"O(0,0)","option_b":"A(1, -2)","option_c":"B(-1, 2)","option_d":"C(0, -3)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x)=x³-3x est impaire, donc son centre de symétrie est l'origine O(0,0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":12147,"question":"L'aire d'un disque de rayon r=4 cm est égale à 16π cm².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire est πr² = π×4² = 16π cm², donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]