Mathematics · Grades 11–12
Derivatives, accumulated change and units · Revision sheet
Connect calculations to their meanings and domains.
Learn the idea
Derivative
A derivative describes a local rate of change with respect to the independent variable.
Units
If position is measured in metres and time in seconds, its time derivative has units m/s.
Signed integral
A definite integral of velocity gives signed displacement, not automatically total distance.
Critical points
A zero derivative is a candidate for an extremum, not a guarantee. Check the surrounding behavior.
Explain without looking
- Why must an indefinite integral normally include an arbitrary constant?
- Explain why an integral of a negative velocity can be negative while distance traveled is not.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.