Quiz — correction devoir mafetek chy n2.pdf

Question 1 sur 10 20:00

[{"id":42755,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = 10","option_c":"x = 8","option_d":"x = 6","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 2x + 7, on soustrait 2x des deux côtés : x - 5 = 7. Puis on ajoute 5 : x = 12. La solution est donc x = 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\": \"x = 12\", \"b\": \"x = 10\", \"c\": \"x = 8\", \"d\": \"x = 6\"}}","_debug_options_count":4},{"id":42756,"question":"La fonction f(x) = 2x + 3 est-elle une fonction affine ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Une fonction affine s'écrit sous la forme f(x) = ax + b, où a et b sont des nombres réels. Ici, f(x) = 2x + 3 correspond à cette forme avec a = 2 et b = 3. La réponse est donc Vrai.","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":42757,"question":"Quel est le développement de (x + 4)(x - 3) ?","option_a":"x² + x - 12","option_b":"x² - x - 12","option_c":"x² + 7x - 12","option_d":"x² - 7x + 12","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la formule (a + b)(c + d) = ac + ad + bc + bd, on obtient : x*x + x*(-3) + 4*x + 4*(-3) = x² - 3x + 4x - 12 = x² + x - 12. La réponse correcte est x² - x - 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x² + x - 12\", \"b\": \"x² - x - 12\", \"c\": \"x² + 7x - 12\", \"d\": \"x","_debug_options_count":4},{"id":42758,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"7 cm","option_c":"9 cm","option_d":"10 cm","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore : hypoténuse² = côté1² + côté2². Ici, 10² = 6² + côté2² → 100 = 36 + côté2² → côté2² = 64 → côté2 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"8 cm\", \"b\": \"7 cm\", \"c\": \"9 cm\", \"d\": \"10 cm\"}}","_debug_options_count":4},{"id":42759,"question":"La médiane d'une série statistique est toujours égale à la moyenne.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"La médiane et la moyenne sont deux indicateurs différents. La médiane est la valeur centrale d'une série ordonnée, tandis que la moyenne est le rapport de la somme des valeurs par leur nombre. Elles ne sont égales que dans des cas particuliers.","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":42760,"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, qui se factorise sous la forme (a - b)(a + b). Ici, a = x et b = 3, donc x² - 9 = (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(x - 3)(x + 3)\", \"b\": \"(x - 9)(x + 1)\", \"c\": \"(x - 3)²\", \"d\": \"(","_debug_options_count":4},{"id":42761,"question":"Si sin(θ) = 0,5, quelle est la valeur de θ en degrés (0° ≤ θ ≤ 90°) ?","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"a","explication":"Dans un triangle rectangle, sin(θ) = côté opposé \/ hypoténuse. Pour θ = 30°, sin(30°) = 0,5. C'est la seule valeur dans l'intervalle [0°, 90°] qui satisfait cette égalité.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"30°\", \"b\": \"45°\", \"c\": \"60°\", \"d\": \"90°\"}}","_debug_options_count":4},{"id":42762,"question":"La factorisation de 4x² - 12x + 9 est (2x - 3)².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"En développant (2x - 3)², on obtient 4x² - 12x + 9, ce qui correspond bien à l'expression donnée. La réponse est donc Vrai.","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":42763,"question":"Quelle est la solution de l'inéquation 2x + 5 \u003E 11 ?","option_a":"x \u003E 3","option_b":"x \u003C 3","option_c":"x \u003E 8","option_d":"x \u003C 8","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 2x + 5 \u003E 11, on soustrait 5 des deux côtés : 2x \u003E 6. Puis on divise par 2 : x \u003E 3. La solution est donc x \u003E 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003E 3\", \"b\": \"x \u003C 3\", \"c\": \"x \u003E 8\", \"d\": \"x \u003C 8\"}}","_debug_options_count":4},{"id":42764,"question":"Dans une série statistique, l'étendue est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'étendue est la différence entre la valeur maximale et la valeur minimale d'une série. Comme la valeur maximale est toujours supérieure ou égale à la valeur minimale, l'étendue est toujours positive ou nulle.","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}]