Quiz : Les fondamentaux de l'algèbre et de la géométrie en Seconde

Question 1 sur 10 10:00

[{"id":69542,"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":"3x - 5 = 7 ⇒ 3x = 12 ⇒ x = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69543,"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":"2x + 3 \u003E 7 ⇒ 2x \u003E 4 ⇒ x \u003E 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69544,"question":"Quelle est la distance entre les points A(1, 2) et B(4, 6) dans le plan ?","option_a":"5","option_b":"√25","option_c":"√13","option_d":"7","option_e":"","option_f":"","bonne_reponse":"B","explication":"Distance = √[(4-1)² + (6-2)²] = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69545,"question":"Le milieu du segment [AB] avec A(-2, 3) et B(4, -1) a pour coordonnées :","option_a":"(1, 1)","option_b":"(2, -2)","option_c":"(1, -1)","option_d":"(3, 1)","option_e":"","option_f":"","bonne_reponse":"B","explication":"Milieu = ((-2+4)\/2, (3-1)\/2) = (1, 1).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69546,"question":"L'équation x² - 5x + 6 = 0 admet pour solutions :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont x = 2 et x = 3, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69547,"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 = (x - 3)(x + 3) (identité remarquable).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69548,"question":"L'inégalité -3x + 2 ≤ 8 a pour solution :","option_a":"x ≥ -2","option_b":"x ≤ -2","option_c":"x ≥ 2","option_d":"x ≤ 2","option_e":"","option_f":"","bonne_reponse":"B","explication":"-3x + 2 ≤ 8 ⇒ -3x ≤ 6 ⇒ x ≥ -2 (attention au changement de sens).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69549,"question":"Le point M(2, -1) appartient-il à la droite d'équation y = 2x - 5 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Pour x = 2, y = 2*2 - 5 = -1. Le point M(2, -1) appartient donc à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69550,"question":"Quelle est la solution de l'inéquation x² - 4x + 3 \u003C 0 ?","option_a":"x ∈ ]1, 3[","option_b":"x ∈ ]-∞, 1[ ∪ ]3, +∞[","option_c":"x ∈ ]-∞, 3[","option_d":"x ∈ ]1, +∞[","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les racines sont x = 1 et x = 3. Le polynôme est négatif entre les racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":69551,"question":"La droite passant par A(1, 1) et B(3, 5) a pour coefficient directeur :","option_a":"2","option_b":"1\/2","option_c":"4","option_d":"-2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Coefficient directeur = (5-1)\/(3-1) = 4\/2 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]