Algèbre et Géométrie : Testez vos connaissances en 3ème année secondaire

Question 1 sur 10 10:00

[{"id":46336,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 3 ?","option_a":"x = 8","option_b":"x = 2","option_c":"x = -2","option_d":"x = 5","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x : 3x - 2x = 3 + 5 → x = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46337,"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 f(x) = ax + b. Ici, le terme x² montre qu'il s'agit d'une fonction polynôme du second degré.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46338,"question":"Quel théorème permet de calculer une longueur dans un triangle rectangle ?","option_a":"Théorème de Thalès","option_b":"Théorème de Pythagore","option_c":"Théorème des milieux","option_d":"Théorème de la droite des milieux","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Pythagore s'applique aux triangles rectangles pour calculer une longueur manquante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46339,"question":"Si cos(θ) = 0,5, quelle est la valeur de sin(θ) dans un triangle rectangle ?","option_a":"√3\/2","option_b":"1\/2","option_c":"√2\/2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle, si cos(θ) = 0,5 alors θ = 60° et sin(60°) = √3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46340,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"2x + 3 \u003E 7 → 2x \u003E 4 → x \u003E 2. La solution est donc x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46341,"question":"Quelle est la forme factorisée de x² - 9 ?","option_a":"(x - 3)(x + 3)","option_b":"(x - 9)(x + 1)","option_c":"(x - 3)²","option_d":"(x + 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46342,"question":"Dans un triangle ABC, si AB = 5 cm, BC = 4 cm et AC = 3 cm, alors le triangle est :","option_a":"Rectangle en A","option_b":"Rectangle en B","option_c":"Rectangle en C","option_d":"Non rectangle","option_e":"","option_f":"","bonne_reponse":"C","explication":"On vérifie avec le théorème de Pythagore : 3² + 4² = 5² → 9 + 16 = 25. Le triangle est rectangle en C.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46343,"question":"La dérivée de la fonction f(x) = 4x³ est :","option_a":"12x²","option_b":"12x³","option_c":"4x²","option_d":"3x²","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de xⁿ est n·xⁿ⁻¹. Ici, f'(x) = 4·3x² = 12x².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46344,"question":"Si deux droites sont parallèles, alors leurs coefficients directeurs sont égaux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont le même coefficient directeur (pente).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":46345,"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":"On factorise : (x - 2)(x - 3) = 0 → x = 2 ou x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]