Quiz — Exercices d'Algèbre 1ère année Dunod (1997).pdf

Question 1 sur 10 20:00

[{"id":6171,"question":"Quelle est la solution de l'équation 3x - 5 = 7 ?","option_a":"x = 4","option_b":"x = -4","option_c":"x = 12","option_d":"x = -12","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 = -4\", \"c\": \"x = 12\", \"d\": \"x = -12\"}}","_debug_options_count":4},{"id":6172,"question":"L'inéquation 2x + 3 \u003E 7 a pour solution :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La solution est x \u003E 2. En effet, 2x + 3 \u003E 7 ⇒ 2x \u003E 4 ⇒ x \u003E 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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":6173,"question":"Quel est le développement de (x + 3)(x - 2) ?","option_a":"x² + x - 6","option_b":"x² - x - 6","option_c":"x² + 5x - 6","option_d":"x² - 5x - 6","option_e":"","option_f":"","bonne_reponse":"b","explication":"En utilisant la formule (a + b)(a + c) = a² + (b + c)a + bc, on obtient x² + (3 - 2)x + (3 × -2) = x² + x - 6.","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 - 6\", \"b\": \"x² - x - 6\", \"c\": \"x² + 5x - 6\", \"d\": \"x² ","_debug_options_count":4},{"id":6174,"question":"La factorisation de x² - 9 est :","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":"Il s'agit d'une différence de carrés : 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":6175,"question":"L'équation x² + 4x + 4 = 0 admet :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation peut s'écrire (x + 2)² = 0, donc elle admet une solution double : x = -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\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":6176,"question":"Quelle est la solution de l'inéquation -2x + 5 ≤ 1 ?","option_a":"x ≥ 2","option_b":"x ≤ 2","option_c":"x ≥ -2","option_d":"x ≤ -2","option_e":"","option_f":"","bonne_reponse":"b","explication":"En résolvant -2x + 5 ≤ 1, on obtient -2x ≤ -4 ⇒ x ≥ 2 (attention au changement de sens de l'inégalité).","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 ≥ 2\", \"b\": \"x ≤ 2\", \"c\": \"x ≥ -2\", \"d\": \"x ≤ -2\"}}","_debug_options_count":4},{"id":6177,"question":"Le polynôme x³ - 2x² + x se factorise en :","option_a":"x(x² - 2x + 1)","option_b":"x(x - 1)(x - 1)","option_c":"(x - 1)³","option_d":"x(x² + 2x - 1)","option_e":"","option_f":"","bonne_reponse":"b","explication":"En factorisant par x, on obtient x(x² - 2x + 1), puis x² - 2x + 1 = (x - 1)², donc x(x - 1)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(x² - 2x + 1)\", \"b\": \"x(x - 1)(x - 1)\", \"c\": \"(x - 1)³\", \"d\": ","_debug_options_count":4},{"id":6178,"question":"La fonction f(x) = 2x + 3 est 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 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":6179,"question":"Quelle est la solution de l'équation 4x² - 12x + 9 = 0 ?","option_a":"x = 3\/2","option_b":"x = -3\/2","option_c":"x = 1","option_d":"x = 0","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'équation est un carré parfait : (2x - 3)² = 0 ⇒ 2x - 3 = 0 ⇒ x = 3\/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\": \"x = 3\/2\", \"b\": \"x = -3\/2\", \"c\": \"x = 1\", \"d\": \"x = 0\"}}","_debug_options_count":4},{"id":6180,"question":"L'inégalité x² \u003E 4 est équivalente à :","option_a":"x \u003E 2 ou x \u003C -2","option_b":"x \u003E 2 et x \u003C -2","option_c":"-2 \u003C x \u003C 2","option_d":"x = 2 ou x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"x² \u003E 4 ⇒ x \u003E 2 ou x \u003C -2, car le carré d'un nombre est supérieur à 4 si ce nombre est en dehors de l'intervalle [-2, 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\": \"x \u003E 2 ou x \u003C -2\", \"b\": \"x \u003E 2 et x \u003C -2\", \"c\": \"-2 \u003C x \u003C 2\", \"d\":","_debug_options_count":4}]