Maths 2ème année : Algèbre et Géométrie — Quiz interactif

Question 1 sur 10 10:00

[{"id":66622,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 3","option_b":"x = 5","option_c":"x = 15\/3","option_d":"x = 10\/3","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour résoudre 3x - 5 = 10, on ajoute 5 aux deux côtés : 3x = 15, puis on divise par 3 : x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66623,"question":"Le discriminant d'une équation du second degré ax² + bx + c = 0 est donné par :","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = a² - 4bc","option_d":"Δ = 2b - 4a","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant est calculé par la formule Δ = b² - 4ac, qui détermine le nombre de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66624,"question":"Vrai ou Faux ? L'équation x² + 4 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = 0² - 4(1)(4) = -16 est négatif, donc il n'y a pas de solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66625,"question":"Quelle est la distance entre les points A(2, 3) et B(-1, 5) dans un repère orthonormé ?","option_a":"√13","option_b":"√17","option_c":"5","option_d":"√5","option_e":"","option_f":"","bonne_reponse":"B","explication":"La distance est calculée par √[(xB - xA)² + (yB - yA)²] = √[(-1-2)² + (5-3)²] = √[9 + 4] = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66626,"question":"Vrai ou Faux ? La droite d'équation y = 2x + 3 a un coefficient directeur égal à 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur (pente) est le coefficient de x, soit 2, et non 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66627,"question":"Quelle est la solution du système d'équations { 2x + y = 5 ; x - y = 1 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 3","option_c":"x = 3, y = -1","option_d":"x = 0, y = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant le système, on trouve x = 2 et y = 1 (par substitution ou combinaison linéaire).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66628,"question":"Vrai ou Faux ? L'inéquation 2x - 3 \u003E 7 a pour solution x \u003E 5.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant 2x \u003E 10, on obtient x \u003E 5, donc la solution est correcte.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66629,"question":"Quelle est l'aire d'un triangle de base 6 cm et de hauteur 4 cm ?","option_a":"10 cm²","option_b":"12 cm²","option_c":"24 cm²","option_d":"8 cm²","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire d'un triangle est (base × hauteur) \/ 2 = (6 × 4) \/ 2 = 12 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66630,"question":"Vrai ou Faux ? La fonction f(x) = x² est une fonction affine.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine s'écrit f(x) = ax + b. Ici, f(x) = x² est une fonction du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":66631,"question":"Quelle est la solution de l'inéquation -3x + 6 ≤ 0 ?","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x \u003E 2","option_d":"x \u003C 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"En résolvant -3x ≤ -6, on obtient x ≥ 2 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]