Quiz — Devoir Synthèse N1 (Math)(1).pdf

Question 1 sur 10 20:00

[{"id":22679,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = 12\/3","option_c":"x = 2","option_d":"x = 4\/3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 7, on ajoute 5 des deux côtés : 3x = 12, puis on divise par 3 : x = 4.","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 = 4\", \"b\": \"x = 12\/3\", \"c\": \"x = 2\", \"d\": \"x = 4\/3\"}}","_debug_options_count":4},{"id":22680,"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, ce qui est le cas ici avec a = 2 et b = 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":22681,"question":"Quel est le coefficient directeur de la droite d'équation y = -4x + 1 ?","option_a":"1","option_b":"-4","option_c":"4","option_d":"0","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient directeur d'une droite d'équation y = ax + b est le nombre a, ici -4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"1\", \"b\": \"-4\", \"c\": \"4\", \"d\": \"0\"}}","_debug_options_count":4},{"id":22682,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à :","option_a":"La somme des carrés des deux autres côtés","option_b":"Le produit des deux autres côtés","option_c":"La différence des carrés des deux autres côtés","option_d":"La moitié de la somme des deux autres côtés","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est le théorème de Pythagore : dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"La somme des carrés des deux autres côtés\", \"b\": \"Le produit d","_debug_options_count":4},{"id":22683,"question":"L'inéquation 2x + 5 \u003E 11 a pour solution :","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":"Résolvons : 2x \u003E 6 → x \u003E 3. L'inégalité est stricte, 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":22684,"question":"Un quadrilatère dont les diagonales se coupent en leur milieu est toujours un parallélogramme.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété caractéristique du parallélogramme : ses diagonales se coupent en leur milieu.","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":22685,"question":"Quelle est l'image de 5 par la fonction f(x) = -2x + 7 ?","option_a":"-3","option_b":"17","option_c":"3","option_d":"-17","option_e":"","option_f":"","bonne_reponse":"a","explication":"Calculons f(5) = -2*5 + 7 = -10 + 7 = -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\": \"-3\", \"b\": \"17\", \"c\": \"3\", \"d\": \"-17\"}}","_debug_options_count":4},{"id":22686,"question":"La distance entre les points A(2; 3) et B(-1; 5) dans un repère orthonormé est :","option_a":"√13","option_b":"√5","option_c":"√17","option_d":"√29","option_e":"","option_f":"","bonne_reponse":"a","explication":"La distance est √[(2 - (-1))² + (3 - 5)²] = √[9 + 4] = √13.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"√13\", \"b\": \"√5\", \"c\": \"√17\", \"d\": \"√29\"}}","_debug_options_count":4},{"id":22687,"question":"Si sin(θ) = 0,5, alors θ mesure toujours 30°.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(θ) = 0,5 a plusieurs solutions dans [0°; 360°], dont 30° et 150°.","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":22688,"question":"Le milieu du segment [AB] avec A(-3; 4) et B(5; -2) a pour coordonnées :","option_a":"(1; 1)","option_b":"(2; 1)","option_c":"(1; -1)","option_d":"(4; -6)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le milieu a pour coordonnées ((-3+5)\/2; (4-2)\/2) = (1; 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(1; 1)\", \"b\": \"(2; 1)\", \"c\": \"(1; -1)\", \"d\": \"(4; -6)\"}}","_debug_options_count":4}]