Maths 4ème année secondaire : Évaluation de synthèse

Question 1 sur 10 10:00

[{"id":33573,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x - 5","option_d":"6x + 2x","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme s'obtient en appliquant la règle de dérivation terme à terme : f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33574,"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 = 0, donc l'équation admet une solution réelle double (x = 2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33575,"question":"Quel est le volume d'un cube d'arête 3 cm ?","option_a":"9 cm³","option_b":"12 cm³","option_c":"27 cm³","option_d":"81 cm³","option_e":"","option_f":"","bonne_reponse":"C","explication":"Le volume d'un cube est donné par V = arête³ = 3³ = 27 cm³.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33576,"question":"La fonction f(x) = x³ est-elle paire ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = -x³ ≠ f(x), donc elle est impaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33577,"question":"Quelle est la solution de l'inéquation 2x - 3 \u003E 5 ?","option_a":"x \u003E 1","option_b":"x \u003E 4","option_c":"x \u003C 4","option_d":"x \u003E -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":33578,"question":"Le point A(2, -1) appartient-il à la droite d'équation y = 3x - 7 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"En substituant x = 2 dans l'équation : y = 3(2) - 7 = -1, ce qui correspond aux coordonnées de A.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33579,"question":"Quelle est l'aire d'un triangle de base 5 cm et de hauteur 4 cm ?","option_a":"10 cm²","option_b":"20 cm²","option_c":"15 cm²","option_d":"25 cm²","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'aire d'un triangle est donnée par A = (base × hauteur) \/ 2 = (5 × 4) \/ 2 = 10 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33580,"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":33581,"question":"Quel est le résultat de l'intégrale ∫(2x + 1) dx ?","option_a":"x² + x + C","option_b":"2x² + x + C","option_c":"x² + 2x + C","option_d":"2x² + 2x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"∫(2x + 1) dx = x² + x + C, où C est la constante d'intégration.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":33582,"question":"Le triangle de côtés 3 cm, 4 cm et 5 cm est-il rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"3² + 4² = 9 + 16 = 25 = 5², donc le triangle est rectangle d'après le théorème de Pythagore.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]