Maths Bac : Évaluation des notions clés du 1er trimestre

Question 1 sur 10 10:00

[{"id":23838,"question":"Quelle est la solution de l'équation 3x - 5 = 10 ?","option_a":"x = 5","option_b":"x = 15\/3","option_c":"x = 5\/3","option_d":"x = 3","option_e":"","option_f":"","bonne_reponse":"A","explication":"3x - 5 = 10 → 3x = 15 → x = 15\/3 = 5. La solution est donc x = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23839,"question":"La fonction f(x) = x² - 4x + 3 admet un minimum en x = 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée f'(x) = 2x - 4 s'annule en x = 2. Comme f''(x) = 2 \u003E 0, il s'agit bien d'un minimum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23840,"question":"Quelle est la forme factorisée de l'expression 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 : x² - 3² = (x - 3)(x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23841,"question":"L'équation 2x² + 4x - 6 = 0 admet deux solutions réelles.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le discriminant Δ = 16 - 4*2*(-6) = 64 \u003E 0, donc deux solutions réelles distinctes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23842,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/6) = sin(30°) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23843,"question":"La droite d'équation y = 2x + 1 est parallèle à la droite d'équation y = 2x - 3.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Deux droites sont parallèles si elles ont le même coefficient directeur. Ici, les deux droites ont un coefficient directeur de 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23844,"question":"Quelle est la solution de l'inéquation 2x + 3 \u003E 7 ?","option_a":"x \u003E 2","option_b":"x \u003E 4","option_c":"x \u003C 2","option_d":"x \u003C 4","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":23845,"question":"La fonction f(x) = 1\/x est définie pour x = 0.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction f(x) = 1\/x n'est pas définie en x = 0 car la division par zéro est impossible.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23846,"question":"Quelle est la dérivée de la fonction f(x) = 3x³ - 2x² + x - 5 ?","option_a":"9x² - 4x + 1","option_b":"6x² - 4x + 1","option_c":"3x² - 2x + 1","option_d":"3x² - 4x + 1","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de f(x) = 3x³ - 2x² + x - 5 est f'(x) = 9x² - 4x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":23847,"question":"L'aire d'un triangle de base 6 cm et de hauteur 4 cm est de 24 cm².","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'aire d'un triangle est (base × hauteur) \/ 2 = (6 × 4) \/ 2 = 12 cm². L'affirmation est donc fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]