Did you read my tips on how to study and learn this course?  If not, here is a link to those important suggestions:

Here is a link to the actual assignment, in case you don't have it:

Classic definition of derivative question.  VERY similar to my Lesson 4, Practise Problem 5(e).

Classic differentiation rules practice as I teach in Lesson 5.

However, I think he goofed in part (d).  The 2^θ term is an a^u derivative which I don't teach until Lesson 8.  The derivative of a^u is a^u*u'*lna.  So the derivative of 2^θ is 2^θ*ln2.

These are trig limits using the principles I illustrate in Lesson 2, question 16.  Both are a matter of exploiting the sinh/h pattern.  Make sure you state right at the beginning that the limit of sinh/h as h approaches 0 = 1 (in other words state the limit I tell you to memorize on the first page of Lesson 2). 

Factor that trinomial on the bottom and you should nicely discover that the "h" inside the sinh above is already present.  Just split the problem into two factors.  For example, if you have sinh on top and (h)(p) as two multiplying factors on the bottom, you can separate it into sinh/h times 1/(p).  In other words, just slide that second factor (p) over to the side as the denominator of its own separate fraction.

First, use the conjugate to simplify the bottom.  And factor the top: cos^2 y -1 can be factored as a difference of squares, just like x^2 -1.  That totally sets you up for the second memorized trig limit I give at the start of Lesson 2.  The limit as h goes to 0 of (cosh - 1)/h =0.  You can split off that exact limit (just y instead of h).  The rest of the stuff on top is just a separate fraction whose limit is trivial.

Read my section on Velocity and Acceleration starting on page 149.  Look at my Lesson 5, question 5 and Practise Problems 86 and 87.

v is simply the derivative of h(t); v = h'(t).

The arrow stops rising when its velocity is 0.  Find t where v=0. Just leave the answer as a mess. You can't be expected to get an exact answer without a calculator and calculators aren't allowed on the exam. You can use a calculator to give a neater, rounded off answer, but state the perfect answer, too.

The arrow hits the ground when h=0.  Find t when h=0.  If you do it correctly, there will be two answers for t, but one of those answers will clearly be inappropriate.  That is because the arrow is on the ground twice, once at the start, and once at the end.  Once you have found the value for t, sub it into your v equation to find the velocity.  If you do it right, you will get a negative answer for v and it will be pretty neat if you simplify.

Classic tangent line application of derivatives.  Like my Lesson 5, question 2 and Practice Problems 75 to 82.

Look at my Lesson 5, question 6 and Practise Problem 88.

Classic implicit diff as taught in my Lesson 6.  Best examples of this specific problem are in my Lesson 8, though!  Be sure you also look at my Lesson 8 Practise Problems 5, 9, and 12 for similar examples.

Classic related rates (Lesson 7) similar to my Lecture Problem 6.

More related rates, similar to my Lesson 7, Lecture Problem 3.  However, he wants dA/dt where A=πr^2.  Suggestion: Do just like I do in my problem, but use the similar triangles to eliminate h from the volume formula rather than r, so that you can solve dr/dt first, using dV/dt.  Then, you can use the area formula to solve dA/dt since you now know dr/dt.