Final Exam Review Sheet for
Colorado State University, Pueblo
Math 224 — Calculus II — Fall 2014
Prior Material
Remember the final exam is comprehensive, meaning that the material
from all parts of the course will be covered, roughly in proportion to the
course time we spent on it. Therefore it is important to review and be
comfortable with all the material tested in the three course midterms, for
which:
- This midterm was on Chapter 7 of the textbook, including:
- inverses, one-to-one, graphing, restricted domains
- the natural log and exponential functions, their definitions, algebra,
and calculus with them
- logs and exponentials with other bases
- inverse trig functions, domains, compositions, derivatives,
- L'Hôpital's Rule
- hyperbolic functions and their inverses
- This midterm was on Chapter 8 [Integration Techniques] of the
textbook, including:
- basic approaches with algebra (long division, completing the square,
etc.) and substitution
- integration by parts
- trigonometric integrals
- trigonometric substitution
- partial fractions
- improper integrals
- This midterm had its own review sheet.
In addition,
- After the third midterm, we covered
- parametric equations, graphing, calculus (slope of tangent lines)
- polar coordinates, converting to and from Cartesian, graphing,
calculus (slope of tangent lines and areas inside figures)
- Fourier series, calculating them and a theorem about their convergence
Format and content of the final exam
Each day of the exam will have well more than 100 points. Your total final
exam score will be half the sum of the scores on the two exam days, but with
a maximum of 100. Points above 100 will, as usual, go into over-all course
extra credit.
On the first day of the final exam (Wednesday) will be the questions
directly relating to the parts of the course covered in midterms I and II.
There will be a page of formulæ at the end of the test for you to
consult — the same page as was on the back of the second midterm (which
had some trigonometric identities, some basic trigonometric integrals and
derivatives, and some guides to good trigonometric substitutions). Other
formulæ you think you might like — derivatives of inverse functions,
definitions of hyperbolic functions, derivatives of hyperbolic functions and
logs or exponentials with different bases, ... — are up to you to learn.
The second final exam day (Thursday) will have all questions directly
relating to the part of the course covered in midterm III and in the short,
post-midterm III unit. The same reference page on convergence tests from
midterm III will be included on this part of the final. But you must learn
any formulæ from the post-midterm III unit you think you might need
(slopes of tangent lines and areas in polar coordinates, Fourier series, ...).
You may use a calculator (graphing but not symbolic) during the whole final
exam, but it will be unnecessary. You must explain and show all your work, as
always.