Quiz : Équations, fonctions et géométrie — 2ème année secondaire

Question 1 sur 10 10:00

[{"id":16068,"question":"Quelle est la solution de l'équation 2x² - 8x + 6 = 0 ?","option_a":"x = 1 ou x = 3","option_b":"x = 2 ou x = 4","option_c":"x = 0 ou x = 4","option_d":"x = -1 ou x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"On utilise la formule des racines du second degré : Δ = b² - 4ac = 64 - 48 = 16. Les solutions sont x = (8 ± 4)\/4, soit x = 3 ou x = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16069,"question":"La fonction f(x) = 3x - 5 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. Ici, a = 3 et b = -5, donc c'est bien une fonction affine.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16070,"question":"Quel est le coefficient directeur de la droite d'équation y = -2x + 7 ?","option_a":"7","option_b":"-2","option_c":"2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le coefficient directeur d'une droite d'équation y = ax + b est le nombre a. Ici, a = -2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16071,"question":"Si deux droites sont parallèles, leurs coefficients directeurs sont :","option_a":"égaux","option_b":"opposés","option_c":"inverses","option_d":"nuls","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites parallèles ont le même coefficient directeur, car elles ont la même pente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16072,"question":"L'inéquation 3x - 7 \u003E 5 a pour solution :","option_a":"x \u003E 4","option_b":"x \u003C 4","option_c":"x \u003E 12","option_d":"x \u003C 12","option_e":"","option_f":"","bonne_reponse":"A","explication":"On isole x : 3x \u003E 12 → x \u003E 4. La solution est donc x \u003E 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16073,"question":"Le théorème de Pythagore s'applique-t-il dans un triangle rectangle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le théorème de Pythagore stipule que 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},{"id":16074,"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 : a² - b² = (a - b)(a + b). Ici, a = x et b = 3, donc (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16075,"question":"Si f(x) = 2x + 1, alors f(3) = ?","option_a":"5","option_b":"7","option_c":"6","option_d":"4","option_e":"","option_f":"","bonne_reponse":"B","explication":"On remplace x par 3 : f(3) = 2*3 + 1 = 7.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16076,"question":"Les droites d'équations y = 2x + 1 et y = -0.5x + 3 sont-elles perpendiculaires ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites sont perpendiculaires si le produit de leurs coefficients directeurs est égal à -1. Ici, 2 * (-0.5) = -1, donc elles sont perpendiculaires.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":16077,"question":"Quelle est la solution de l'inéquation -x + 4 ≤ 2x - 1 ?","option_a":"x ≥ 1","option_b":"x ≤ 1","option_c":"x ≥ 5\/3","option_d":"x ≤ 5\/3","option_e":"","option_f":"","bonne_reponse":"C","explication":"On isole x : -x - 2x ≤ -1 - 4 → -3x ≤ -5 → x ≥ 5\/3 (en divisant par un nombre négatif, le sens de l'inégalité change).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]