Quiz : Maîtrisez les bases des mathématiques en seconde !

Question 1 sur 10 10:00

[{"id":22848,"question":"Quelle est la forme canonique de la fonction f(x) = x² - 4x + 5 ?","option_a":"A. (x - 2)² + 1","option_b":"B. (x - 2)² + 5","option_c":"C. (x + 2)² + 1","option_d":"D. x² - 4x + 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique s'obtient par complétion du carré : f(x) = (x² - 4x + 4) + 1 = (x - 2)² + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22849,"question":"L'équation x² - 5x + 6 = 0 admet deux solutions réelles distinctes.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 25 - 24 = 1 \u003E 0, donc l'équation admet deux solutions réelles distinctes : x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22850,"question":"Quelle est la solution de l'inéquation 3x - 7 ≤ 2x + 1 ?","option_a":"A. x ≤ 8","option_b":"B. x ≥ 8","option_c":"C. x ≤ -8","option_d":"D. x ≥ -8","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 2x ≤ 1 + 7 → x ≤ 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22851,"question":"Dans un triangle rectangle, le carré de l'hypoténuse est égal à la somme des carrés des deux autres côtés. Cette propriété s'appelle :","option_a":"A. Théorème de Thalès","option_b":"B. Théorème de Pythagore","option_c":"C. Formule des aires","option_d":"D. Loi des cosinus","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est l'énoncé du théorème de Pythagore, applicable uniquement dans un triangle rectangle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22852,"question":"La fonction f(x) = 2x + 3 est une fonction affine. Son coefficient directeur est :","option_a":"A. 2","option_b":"B. 3","option_c":"C. 2x","option_d":"D. 3x","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour une fonction affine f(x) = ax + b, a est le coefficient directeur. Ici, a = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22853,"question":"L'équation |x - 4| = 2 admet deux solutions.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont x - 4 = 2 → x = 6 et x - 4 = -2 → x = 2. Donc deux solutions réelles.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22854,"question":"Quelle est la factorisation de l'expression x² - 9 ?","option_a":"A. (x - 3)(x + 3)","option_b":"B. (x - 9)(x + 1)","option_c":"C. x(x - 9)","option_d":"D. (x - 3)²","option_e":"","option_f":"","bonne_reponse":"A","explication":"x² - 9 est une différence de carrés : (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22855,"question":"La droite d'équation y = -2x + 5 passe par le point A(1 ; 3).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour x = 1, y = -2(1) + 5 = 3. Donc le point A(1 ; 3) appartient bien à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22856,"question":"Quelle est la solution de l'équation 2(x + 1) = 3x - 4 ?","option_a":"A. x = 6","option_b":"B. x = -6","option_c":"C. x = 2","option_d":"D. x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"2x + 2 = 3x - 4 → 2 + 4 = 3x - 2x → x = 6. Attention, la solution correcte est x = 6, mais l'option B est -6 (erreur de signe).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":22857,"question":"La fonction f(x) = x³ est une fonction paire.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction paire vérifie f(-x) = f(x). Ici, f(-x) = (-x)³ = -x³ ≠ f(x). Donc f n'est pas paire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]