I actually start my students on Day 1 teaching them the fundamentals of both derivatives and integration. 
It’s exciting and it shows them (via my Mad Farmer worksheet) that they already know a lot about Calculus and that it’s relevant to real life (they’ll argue with me that a mad farmer on a tractor doesn’t seem relevant but you get my point). I feel if you jump right into Limits (or worse, a boring PreCalculus review), it just sets a tone of boredom (and sometimes despair). To be fair, I actually assign it as homework and then discuss all of Day 2. I even include an actual free response problem that they can do after they finish part 1 of this worksheet!
The Worksheet for Day 1 of Calculus
The Mad Farmer worksheet uses the velocity and position of a tractor to teach them a plethora (fave vocab word as a kid) of fundamentals in one worksheet. The best part is that as we encounter these topics again on practice exams, assessments, etc. we always refer back to the “Tractor problem” – and these fundamentals come flooding back. It’s like when we use money in middle school to discuss fractions or adding positive and negative numbers – a car driving example makes complex calculus real, manageable, and understandable.
When we start the first fundamental theorem of Calculus later in the year, we take out this worksheet again and refer back to it. It’s important to reference this worksheet (either physically or just verbally) throughout the year.
In 2009 my students completely bombed a problem (AB Calc 2009 Question 1). After that, I really had to reevaluate how taught this course. After a few iterations of this worksheet (and a lot of other changes to how I did things) I began to see the big pay-off year after year in their scores. Try it and let me know what you think (contact me for the Word version if you’d like to change it)
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