Quiz Maths 3ème Année : Algèbre, Analyse et Géométrie

Question 1 sur 10 10:00

[{"id":11478,"question":"Quelle est la solution de l'équation 2x² - 5x + 2 = 0 ?","option_a":"x = 1 ou x = 2","option_b":"x = 0,5 ou x = 2","option_c":"x = -1 ou x = 2","option_d":"x = 1 ou x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"On utilise la formule du discriminant Δ = b² - 4ac = 25 - 16 = 9. Les solutions sont x = (5 ± 3)\/4, soit x = 2 ou x = 0,5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11479,"question":"La dérivée de la fonction f(x) = x³ - 3x² + 2x est f'(x) = 3x² - 6x + 2.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée correcte est f'(x) = 3x² - 6x + 2, donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11480,"question":"Quelle est l'équation de la tangente à la courbe y = x² au point d'abscisse x = 1 ?","option_a":"y = 2x - 1","option_b":"y = x + 1","option_c":"y = 2x + 1","option_d":"y = x - 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"La tangente a pour équation y = f'(1)(x - 1) + f(1) = 2(x - 1) + 1 = 2x - 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11481,"question":"Dans un triangle rectangle, si cos(θ) = 3\/5, alors sin(θ) = ?","option_a":"4\/5","option_b":"3\/4","option_c":"5\/3","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"D'après le théorème de Pythagore, sin(θ) = √(1 - cos²(θ)) = √(1 - 9\/25) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11482,"question":"La fonction f(x) = 1\/x est dérivable sur son ensemble de définition.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La fonction f(x) = 1\/x est dérivable sur ℝ* (x ≠ 0), donc l'affirmation est vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11483,"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 de l'équation x² - 4x + 3 = 0 sont x = 1 et x = 3. Le polynôme est négatif entre ces racines.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11484,"question":"Soit f(x) = ln(x). Quelle est la valeur de f'(2) ?","option_a":"1\/2","option_b":"2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de ln(x) est f'(x) = 1\/x, donc f'(2) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11485,"question":"Un vecteur directeur de la droite d'équation 2x - 3y + 5 = 0 est (3 ; 2).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Un vecteur directeur est (3 ; 2) car 2*3 - 3*2 + 5 = 5 ≠ 0, mais le vecteur (3 ; 2) est bien parallèle à la droite.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11486,"question":"Quelle est la primitive de f(x) = 3x² - 2x + 1 ?","option_a":"F(x) = x³ - x² + x + C","option_b":"F(x) = 6x - 2 + C","option_c":"F(x) = x³ - x² + C","option_d":"F(x) = 3x³ - x² + x + C","option_e":"","option_f":"","bonne_reponse":"A","explication":"La primitive est F(x) = x³ - x² + x + C, car F'(x) = 3x² - 2x + 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":11487,"question":"Dans un repère orthonormé, la distance entre les points A(1 ; 2) et B(4 ; 6) est ?","option_a":"5","option_b":"√13","option_c":"√25","option_d":"√34","option_e":"","option_f":"","bonne_reponse":"D","explication":"La distance est √((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]