>Should we supply on the exam paper such things as >sin^2 + cos^2 = 1, (ab)^n = a^n b^n, log(ab) = log a + log b, the chain >rule for differential calculus, etc,, and concentrate on whether students >can apply the correct rule correctly. Or are these part of the body of >mathematical knowledge that a good student should have at their fingertips? > >In Queensland, we have external exams for mature age learners. The Maths in >Society exam has the formulas supplied, the Maths B and Maths C exams >(roughly equivalent to Algebra II, and Calculus and Analytical Geometry) >don't. So even within our system there appears to be differing attitudes.
I am not a teacher at this level, but I have had a number of semi-technical jobs and hobbies where algebraic manipulation was necessary. If I did not know the formulas you give, I would be in sad shape. Or rather, I would, through practice, quickly learn them. I would hope that the course they took gave them enough practice so you wouldn't have to give them formulas like this. If they don't know that (ab)^n = a^n b^n or log(ab) = log a + log b, then how can you say they really know exponents or logarithms?
In the case of sin^2 + cos^2 = 1, this one is pretty basic to doing any kind of trig calculations, but for trig identities in general, there are so many of them and they are so interrelated that no one can expect to know them all. Maybe give them the standard identities, but problems that depend not on those, but identities that can be derived from them.
In the case of the chain rule, and in general, the answer depends on what you want them to know when the course is over. If the Maths in Society course -- like many similarly-named courses in the USA -- is intended for people who are going no further with math, giving them the formulas may be appropriate. If you are training scientists and engineers, they obviously need to know the chain rule after their first calculus course; they will need it soon and often.
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