Section 2

Section 1: Calculus 1. Compute the derivative of � ( � )=4 � 3−6 � 2+2 � +7 f ( x )=4 x 3 −6 x 2 +2 x +7 . Answer: � ′ ( � )=12 � 2−12 � +2 f ′ ( x )=12 x 2 −12 x +2 . 2. Evaluate the integral ∫03(2 � 2+3 � −4) ��∫ 03 (2 x 2 +3 x −4) dx . Answer: ∫03(2 � 2+3 � −4) �� =29 ∫ 03 (2 x 2 +3 x −4) dx =29 . Section 2: Linear Algebra 3. Solve the system of equations: 3 � +2 � =125 � −4 � =33 x +2 y 5 x −4 y =12=3 Answer: � =3, � =3 x =3, y =3 . 4. Find the determinant of the matrix: [2−134] [ 23−14 ] Answer: Determinant = 1111 . Section 3: Probability and Statistics 5. If P(A) = 0.7 and P(B) = 0.5, what is P(A and B) if A and B are independent events? Answer: � ( �  and  � )=0.35 P ( A  and  B )=0.35 . 6. Calculate the standard deviation of the following data set: 4, 6, 8, 10, 12. Answer: Standard deviation = 2.8282.828 . Section 4: Discrete Mathematics 7. Find the number of permutations of the word "COMBINATIONS." Answer: Number of permutations = 12!2!2! 2!2!12! . 8. In a group of 20 people, how many different committees of 4 people can be formed? Answer: Number of committees = (204) ( 420 ) . Section 5: Differential Equations 9. Solve the differential equation ���� =2 � dxdy =2 x . Answer: � = � 2+ � y = x 2 + C , where � C is the constant of integration. 10. Solve the initial value problem: ���� =3 � dxdy =3 y , � (0)=5 y (0)=5 . Answer: � =5 � 3 � y =5 e 3 x . Section 6: Geometry