Quiz — 220.._67551_1582491008_Magazine-27-revision synthese n°2.pdf

Question 1 sur 10 20:00

[{"id":23764,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"La solution s'obtient en utilisant la formule des racines d'une équation du second degré : x = [5 ± √(25 - 16)] \/ 4 = [5 ± 3]\/4. Les racines sont donc 0,5 et 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 ou x = 2\", \"b\": \"x = 0,5 ou x = 2\", \"c\": \"x = -1 ou x = 2\",","_debug_options_count":4},{"id":23765,"question":"La fonction f(x) = x³ - 3x est décroissante sur l'intervalle [-1, 1].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 3x² - 3 est négative sur [-1, 1] car 3x² ≤ 3. La fonction est donc décroissante sur cet intervalle.","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":23766,"question":"Quelle est la limite de la fonction f(x) = (2x² + 3x) \/ (x² - 1) lorsque x tend vers l'infini ?","option_a":"2","option_b":"∞","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"En divisant le numérateur et le dénominateur par x², on obtient f(x) = (2 + 3\/x) \/ (1 - 1\/x²). Lorsque x tend vers l'infini, les termes 3\/x et 1\/x² tendent vers 0, donc la limite est 2\/1 = 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\": \"2\", \"b\": \"∞\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":23767,"question":"Dans un triangle rectangle, si sin(θ) = 3\/5, alors cos(θ) est égal à :","option_a":"4\/5","option_b":"2\/5","option_c":"√(1 - (3\/5)²)","option_d":"Les deux réponses A et C sont correctes","option_e":"","option_f":"","bonne_reponse":"d","explication":"D'après le théorème de Pythagore, cos(θ) = √(1 - sin²(θ)) = √(1 - 9\/25) = 4\/5. Les réponses A et C sont donc équivalentes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"d\", \"options\": {\"a\": \"4\/5\", \"b\": \"2\/5\", \"c\": \"√(1 - (3\/5)²)\", \"d\": \"Les deux répons","_debug_options_count":4},{"id":23768,"question":"La dérivée de la fonction f(x) = ln(x) est f'(x) = 1\/x.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée de la fonction logarithme népérien est bien f'(x) = 1\/x pour x \u003E 0.","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":23769,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 5 ?","option_a":"x ≤ 12","option_b":"x ≥ 12","option_c":"x ≤ -12","option_d":"x ≥ -12","option_e":"","option_f":"","bonne_reponse":"a","explication":"En soustrayant 2x des deux côtés, on obtient x - 7 ≤ 5. Puis en ajoutant 7, on a 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 ≥ 12\", \"c\": \"x ≤ -12\", \"d\": \"x ≥ -12\"}}","_debug_options_count":4},{"id":23770,"question":"Dans une urne contenant 3 boules rouges et 2 boules bleues, quelle est la probabilité de tirer une boule bleue ?","option_a":"2\/5","option_b":"3\/5","option_c":"1\/5","option_d":"5\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il y a 2 boules bleues sur un total de 5 boules. La probabilité est donc 2\/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\": \"2\/5\", \"b\": \"3\/5\", \"c\": \"1\/5\", \"d\": \"5\/2\"}}","_debug_options_count":4},{"id":23771,"question":"La fonction f(x) = e^x est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La fonction exponentielle e^x est strictement positive pour tout x réel.","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":23772,"question":"Quelle est l'équation de la tangente à la courbe y = x² + 2x au point d'abscisse x = 1 ?","option_a":"y = 4x - 1","option_b":"y = 2x + 1","option_c":"y = 4x + 1","option_d":"y = x + 2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La dérivée f'(x) = 2x + 2 donne le coefficient directeur de la tangente en x = 1 : f'(1) = 4. L'équation de la tangente est y = f(1) + f'(1)(x - 1) = 3 + 4(x - 1) = 4x - 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\": \"y = 4x - 1\", \"b\": \"y = 2x + 1\", \"c\": \"y = 4x + 1\", \"d\": \"y = x + ","_debug_options_count":4},{"id":23773,"question":"Le théorème de Thalès s'applique uniquement aux triangles rectangles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le théorème de Thalès s'applique à tous les triangles, pas seulement aux triangles rectangles.","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}]