Teaching first year undergraduates, I've noticed that what gives them the most trouble is simple computations like factoring, expanding, handling fractions, powers, especially when variables and other parameters come into play.
Here in France these things are supposedly taught in middle school and high school but the degree of mastery that our first year students have of these topics can be very low.
I'm currently in the process of designing a new "calculus 1" course for those students and would like to include in the first two weeks some material to have student work their computational muscles. However I'm afraid if those exercises look too much like high school the students might get bored. So I'd like to give them exercises that look like small computational challenges but rely only on these elementary precalculus topics.
So the question is :
Question : What are some good resources of reasonably challenging problems of mostly computational problems which involves only the pre-calculus tools listed above ?
Disclaimer : I did browse MESE but didn't find anything, though I might just use the wrong keywords. Also I'm not too familiar with MESE and hope this question is not too broad.
I'm an assistant professor in a university in France. I need to design a calculus course for first year students in Maths, Engineering, Physics, Computer Science and Chemistry.
Up until now, calculus topics where scattered in with more formal analysis and algebra courses, which had the unfortunate side-effect that student came to know that they could focus on the computational techniques to have a decent grade rather than get hands with definitions and proofs.
French high school pupils do have a basic exposure to calculus, they know how to compute simple limits (though they have no idea of the definition) and derivatives of not too complicated (they don't know the chain rule for instance, but know how to differentiate $u^\alpha$ or $e^u$ for instance), they can study the variations of functions using the derivative and have seen that there is a thing called "integral" that you can compute using antiderivatives.
University curriculum in France is not centralized so we are not tied in the topics we can cover.