MATH 21B, WINTER 2011
PRACTICE FINAL EXAM
INSTRUCTOR: GABRIEL AMOS
EXAM DATE: MARCH, 2011
The final exam will be a cumulative exam with 10 problems covering everything we’ve seen this
quarter, with an emphasis on the material from the last two weeks. You should study your
previous exams and homework problems to ensure you understand everything you missed there.
A list of topics that
be covered on the exam:
Antiderivatives, basic integration rules, fundamental theorem of calculusparts 1 and 2.
Definition of integral as limit of Riemann sums.
Areas and area between curves (includes integration of absolute values).
Volumes by disks, washers, and shells.
Lengths of curves and surface area.
Moments and centers of mass.
Work, force, and fluid pressure.
Exponential growth models; solutions to
Advanced techniques; integration by parts, partial fractions, trig integrals and trig
Approximations by trapezoidal and Simpson’s rules.