1. Two ropes hold a boat at a dock. The tension in the ropes can be represented by 40 + 10j N and 50 – 25j N. Find the resultant force.
2. The total power P (in watts) transmitted by an AM radio station is given by
   
   P = 500 + 250 m^2 ,
   where m is the modulation index. Find the instantaneous rate of change of P with respect to m for m = 0.92
3. Find the derivative of the following polynomials:
   i. y = 4 x^2 + 7 x + 3
   ii. y = 4 x^ -6 - 5 x^3 + x
4. Find the derivative of the following trigs:
   a. y = 6 sin Ө
   b. y = 7 sin Ө + 3 cos Ө
5. Determine the gradient of each of the given functions at the given point.
   a) s = 2t^3 - 5t^2 + 4 (-1,-3)
   b) y = 5 sin Ө where Ө = 38◦
6. Find the area under the curve y = x^3 that is between the lines x = 1 and x = 2.
   
7. Integrate the following
   i) 4x^6 + 3x^ -4 + 1
   ii) 2 cos Ө
8. The electric field E at a distance r from a point charge is E = k/(r2), where k is a constant. Find an expression for the instantaneous rate of change of the electric field with respect to r.
9. The blade of a saber saw moves vertically up and down, and its displacement y (in cm) is given by y = 1.85 sin t, where t is the time (in s). Find the velocity of the blade for t = 0.025 s.
10. An open-top container is to be made from a rectangular piece of cardboard 24 cm by 38 cm. Equal squares of side x cm are to be cut from each corner, then the sides are to be bent up and taped together. Find the instantaneous rate of change of the volume V of the container with respect to x for x = 4 cm.
11. An analysis of a company’s records shows that in a day the rate of change of profit (in dollars) in producing x generators is dp/dx = 60(30 – 4x^5). Find the profit in producing x generators if a loss of $500 is incurred if none are produced.
12. The vertical displacement y (in cm) of the end of an industrial robot arm for each cycle is y = 2t^1.5 – cos t, where t is the time (in s). Find its vertical velocity for t = 15s.