Week 1:  Sketch the graph of x=3cos(2t), y=1+cos² (2t); be sure to explain how you were able to eliminate the t parameter.  WARNING: Think carefully about the values of x that actually occur when you plug in t.  Do you ever get, say, x=5?
Week 2:  What is the quadric surface 0=xy+yz+xz?  Hint:  Don't try to change variables; instead, if (a,b,c) is a point on the surface, think about t(a,b,c).  For this question, full credit for the right answer --- you don't need to show your work.  No credit will be given for the wrong answer.
Week 3:  Let u be any function of x and y, with x=s+t and y=s-t.  Show that u_ss=u_tt if and only if u_xy=0 (this means you have to show that if u_xy=0, then automatically u_ss=u_tt , and conversely, if instead u_ss=u_tt, then automatically u_xy=0.)  Hint: Compute u_ss and u_tt using the chain rule.
_{Week 4:  Let f(x,y)=xsin(x)y.  Compute the double integral of f over the square wth vertices (0,0), (0,1) , (1,0) and (1,1)
Week 6:  Let f(x,y,z)=x.  Compute the triple integral of f over the solid ball of radius 1 centered at (5,0,0).}  
Week 7:  See the attachment below.