| Subject | %(approx) | Sections | Typical Problems |
| Basic derivative(s) - Free from Gateway | 30% | 3.1 | |
| Differentiation - definition, formulas etc | 15% | 3.1,3.2 | p169/59-63
p234/13,16,102 |
| Continuity (def, theory - including Bolzano, IVT) | 15% | 2.5 | p146/45-50,62 |
| Higher derivatives, chain rule
(Also: limits of expressions involving trig functions) |
15% | 3.2, 3.4, 3.5, 3.8 | p185/41, 55
p234/1-3,7-9,11,61,65,67 p192/11, 25, 49, 58, 65, 68, 69 p209/12, 21, 25, 33, 55 |
| Implicit differentiation | 10% | 3.6 | p198/16, 17, 40, 41 |
| Rates and related rates | 10% | 3.3, 3.10 | p178/10
p219/look at all of them! |
| Vectors, parametrics, etc | 5% | 3.7, 3.9 | p203/21; find r'(t) for problems 5, 8
p214/9, 15, 21 |
| Approximations, linearization | 5% | 3.11 (handout) | p236/94, 95 (use handout approach) |
You can definitely expect problems of the following form:
While you should understand Bolzano's Thm and the IVT, I will not require you to reproduce the proofs on this exam. Possibly next one...