Quiz Maths 4ème : Trigonométrie et Géométrie à l'épreuve

Question 1 sur 10 10:00

[{"id":77042,"question":"Quelle est la valeur de sin(30°) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La valeur exacte de sin(30°) est 1\/2, selon le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77043,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 5 cm et un côté mesure 3 cm, l'autre côté mesure 4 cm.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai, car 3² + 4² = 5² (théorème de Pythagore).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77044,"question":"Quelle formule permet de calculer l'aire d'un triangle connaissant deux côtés et l'angle entre eux ?","option_a":"A = (a + b) \/ 2","option_b":"A = (a × b × sin(C)) \/ 2","option_c":"A = a × b","option_d":"A = π × r²","option_e":"","option_f":"","bonne_reponse":"B","explication":"La formule correcte est A = (a × b × sin(C)) \/ 2, où a et b sont les côtés et C l'angle entre eux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77045,"question":"La tangente d'un angle est toujours supérieure à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux, car tan(30°) = 1\/√3 ≈ 0,577, qui est inférieur à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77046,"question":"Quelle est la valeur de cos(60°) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La valeur exacte de cos(60°) est 1\/2, selon le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77047,"question":"Dans un triangle équilatéral de côté 6 cm, l'aire est de 9√3 cm².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai, car l'aire d'un triangle équilatéral est (√3\/4) × côté² = (√3\/4) × 36 = 9√3 cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77048,"question":"Quelle est la formule de la dérivée de sin(x) ?","option_a":"cos(x)","option_b":"-cos(x)","option_c":"sin(x)","option_d":"1\/cos(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77049,"question":"La somme des angles d'un triangle est toujours égale à 180°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai, c'est une propriété fondamentale de la géométrie euclidienne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77050,"question":"Quelle est la valeur de tan(45°) ?","option_a":"0","option_b":"1","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La valeur de tan(45°) est 1, car sin(45°) = cos(45°) = √2\/2, donc tan(45°) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":77051,"question":"Dans un cercle de rayon 5 cm, l'aire est de 25π cm².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai, car l'aire d'un cercle est π × r² = π × 25 = 25π cm².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]