Quiz — مواضيع أولمبياد الرياضيات 2025 بالإنجليزية - موقع الأستاذ راحيس عمر.pdf

Question 1 sur 10 20:00

[{"id":35870,"question":"Quel est le résultat de l'expression (3 + 5) × 2 − 4 ?","option_a":"12","option_b":"14","option_c":"16","option_d":"18","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculons étape par étape : (3 + 5) = 8, puis 8 × 2 = 16, enfin 16 − 4 = 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"12\", \"b\": \"14\", \"c\": \"16\", \"d\": \"18\"}}","_debug_options_count":4},{"id":35871,"question":"Un triangle rectangle a des côtés de longueurs 3 et 4. Quelle est la longueur de l'hypoténuse ?","option_a":"5","option_b":"6","option_c":"7","option_d":"8","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : hypoténuse² = 3² + 4² = 9 + 16 = 25, donc hypoténuse = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"5\", \"b\": \"6\", \"c\": \"7\", \"d\": \"8\"}}","_debug_options_count":4},{"id":35872,"question":"Vrai ou Faux ? La somme des angles d'un triangle est toujours égale à 180 degrés.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est un théorème fondamental en géométrie euclidienne.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":35873,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x − 5 ?","option_a":"6x + 2","option_b":"3x + 2","option_c":"6x² + 2","option_d":"3x² + 2x","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de 3x² est 6x, celle de 2x est 2, et celle de −5 est 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"6x + 2\", \"b\": \"3x + 2\", \"c\": \"6x² + 2\", \"d\": \"3x² + 2x\"}}","_debug_options_count":4},{"id":35874,"question":"Vrai ou Faux ? L'équation x² + 1 = 0 a deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'équation x² = −1 n'a pas de solution réelle, car un carré est toujours positif ou nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":35875,"question":"Quel est le résultat de 2⁵ ?","option_a":"10","option_b":"16","option_c":"32","option_d":"64","option_e":"","option_f":"","bonne_reponse":"c","explication":"2⁵ = 2 × 2 × 2 × 2 × 2 = 32.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"10\", \"b\": \"16\", \"c\": \"32\", \"d\": \"64\"}}","_debug_options_count":4},{"id":35876,"question":"Vrai ou Faux ? La médiane d'un triangle est toujours perpendiculaire à la base.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane relie un sommet au milieu du côté opposé, mais elle n'est pas toujours perpendiculaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":35877,"question":"Quelle est la solution de l'équation 2x + 3 = 7 ?","option_a":"x = 1","option_b":"x = 2","option_c":"x = 3","option_d":"x = 4","option_e":"","option_f":"","bonne_reponse":"b","explication":"2x = 7 − 3 = 4, donc x = 4 \/ 2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = 1\", \"b\": \"x = 2\", \"c\": \"x = 3\", \"d\": \"x = 4\"}}","_debug_options_count":4},{"id":35878,"question":"Vrai ou Faux ? Le périmètre d'un cercle est donné par la formule P = 2πr.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule du périmètre (circonférence) d'un cercle est bien P = 2πr.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":35879,"question":"Quel est le résultat de (a + b)² ?","option_a":"a² + b²","option_b":"a² + 2ab + b²","option_c":"a² − 2ab + b²","option_d":"(a + b)(a − b)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le développement de (a + b)² donne a² + 2ab + b².","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"a² + b²\", \"b\": \"a² + 2ab + b²\", \"c\": \"a² − 2ab + b²\", \"d\"","_debug_options_count":4}]