Quiz Mathématiques — 4ème Année Secondaire : Algèbre, Géométrie & Fonctions

Question 1 sur 10 10:00

[{"id":27198,"question":"Quelle est la solution de l'équation 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 ou x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation x² - 5x + 6 = 0 se factorise en (x-2)(x-3)=0. Les solutions sont donc x=2 et x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27199,"question":"La fonction f(x) = 3x² - 2x + 1 est-elle toujours positive ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant de f(x) est Δ = (-2)² - 4*3*1 = 4 - 12 = -8 \u003C 0. Comme le coefficient de x² est positif, la fonction est toujours positive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27200,"question":"Quel est le volume d'un cube dont l'arête mesure 4 cm ?","option_a":"16 cm³","option_b":"32 cm³","option_c":"64 cm³","option_d":"128 cm³","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le volume d'un cube est donné par V = arête³. Ici, V = 4³ = 64 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27201,"question":"L'équation sin(x) = 0,5 admet-elle des solutions dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans l'intervalle [0, π], sin(x) = 0,5 admet deux solutions : x = π\/6 et x = 5π\/6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27202,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 4x² + 2x - 1 ?","option_a":"f'(x) = 3x² - 8x + 2","option_b":"f'(x) = 3x² - 4x + 2","option_c":"f'(x) = x² - 8x + 2","option_d":"f'(x) = 3x² - 8x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de f(x) = x³ - 4x² + 2x - 1 est f'(x) = 3x² - 8x + 2 (dérivée terme à terme).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27203,"question":"Un angle de 150° est-il un angle aigu ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un angle aigu mesure entre 0° et 90°. 150° est un angle obtus.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27204,"question":"Résoudre l'inéquation 2x - 3 \u003E 5.","option_a":"x \u003E 1","option_b":"x \u003E 4","option_c":"x \u003C 4","option_d":"x \u003C 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x - 3 \u003E 5 ⇒ 2x \u003E 8 ⇒ x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27205,"question":"La droite d'équation y = 2x + 3 passe-t-elle par le point A(1, 5) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x=1, y = 2*1 + 3 = 5. Le point A(1,5) appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27206,"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 : f(-x) = -f(x). Son centre de symétrie est donc l'origine O(0,0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":27207,"question":"L'aire d'un triangle rectangle de côtés 3 cm et 4 cm est-elle égale à 6 cm² ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un triangle rectangle est (base * hauteur)\/2 = (3*4)\/2 = 6 cm². L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]