Section 4: Calculus

Q31. The first differential of the function is given by:

A.

B.

C.

D.

E.

Q32. Solve the following differential equation , y(0)=0 and hence decide which of the following is closest to the value of y(1).

A. 16.3

B. 17.3

C. 18.3

D. 19.3

E. 20.3

Q33. By solving the corresponding characteristic equation show that the general solution to the linear differential equation is:

A.

B.

C.

D.

E.

Q34. The general solution to the differential equation is given by

A.

B.

C.

D.

E.

Q35. The differential equation in above is used to model the assets, £S million, of a bank t years after it was set up. Given that the initial assets of the bank were £200 million, and using your answer to the above, the assets of the bank 10 years after it was set up, to the nearest £ million are:

A. £524

B. £534

C. £544

D. £554

E. £564

Q36. By using integration show that the volume of the shape made by rotating the function , between x=-1 and x=1, 360 degrees about the x axis is given by:

A.

B.

C.

D.

E.

Q37. The curve C has polar equation . The area of the region bounded by C is given by.

A. a/2

B. a/4

C. a

D. 2a

E. 4a

Q38. The integral of the function is given by:

A.

B.

C.

D.

E.

Q39. Using partial fractions or otherwise show that the following integral: is closest to:

A. 0.04

B. 0.05

C. 0.06

D. 0.07

E. 0.08

Q40. Using integration by substitution, state which of the following gives the closest answer to the integral of

A. 1/10

B. 1/15

C. 1/20

D. -1/15

E. -1/10