Quiz Maths : Maîtrisez les exercices de la Série 1 en 3ème année secondaire

Question 1 sur 10 10:00

[{"id":57421,"question":"Quelle est la solution de l’équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12","option_c":"x = -4","option_d":"x = 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4. Vérifiez en remplaçant x par 4 dans l’équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57422,"question":"La fonction f(x) = 2x² - 3x + 1 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction affine est de la forme ax + b. Ici, f(x) est un polynôme du second degré (terme en x²), donc ce n’est pas une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57423,"question":"Quel est le coefficient directeur de la droite d’équation y = -4x + 7 ?","option_a":"7","option_b":"-4","option_c":"4","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Dans l’équation y = mx + p, m est le coefficient directeur. Ici, m = -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57424,"question":"L’inéquation 5 - 2x \u003E 1 a pour solution :","option_a":"x \u003C 2","option_b":"x \u003E 2","option_c":"x ≤ 2","option_d":"x ≥ 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"5 - 2x \u003E 1 ⇒ -2x \u003E -4 ⇒ x \u003C 2 (en divisant par un nombre négatif, on change le sens de l’inégalité).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57425,"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":"Vérifiez le théorème de Pythagore : 5² + 12² = 25 + 144 = 169 = 13². Donc, le triangle est rectangle en B.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57426,"question":"Quelle est la dérivée de la fonction f(x) = x³ - 2x² + 5x - 1 ?","option_a":"f’(x) = 3x² - 4x + 5","option_b":"f’(x) = 3x² - 4x + 5x","option_c":"f’(x) = x² - 4x + 5","option_d":"f’(x) = 3x² - 2x + 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d’un polynôme est la somme des dérivées de chaque terme : (x³)’ = 3x², (-2x²)’ = -4x, (5x)’ = 5, (-1)’ = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57427,"question":"L’équation x² - 6x + 9 = 0 admet-elle deux solutions distinctes ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le discriminant Δ = (-6)² - 4×1×9 = 36 - 36 = 0. Une seule solution (solution double) : x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57428,"question":"Quel est le résultat de √(16) + √(9) ?","option_a":"7","option_b":"5","option_c":"10","option_d":"25","option_e":"","option_f":"","bonne_reponse":"A","explication":"√(16) = 4 et √(9) = 3, donc 4 + 3 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57429,"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 f(x) = 1\/x n’est pas définie en x = 0 car la division par zéro est interdite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":57430,"question":"Quelle est la solution du système { 2x + y = 5 ; x - y = 1 } ?","option_a":"x = 2, y = 1","option_b":"x = 1, y = 2","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. Vérifiez en remplaçant dans les deux équations.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]