The University of Connecticut, Storrs
Mathematics 1060Q Final Exam Study Guide December 11,
2008
Format: Twenty multiple-choice problems plus bonus problems. Some incorrect
answers will receive partial credit.
Students will need to know the trigonometric identities, addition formulas,
half-angle and double angle formulas,
inverse properties of exponentials and logarithms, and the compound interest
formula.
(These were supplied on Exam 3 but for the final exam, you will need to have a
working knowledge of them.)
The circle notation for a composite function will be used in the statement of
at least one problem, and
uncomplicated factoring and other fundamental properties from algebra will show
up.
The “Exercises for Calculus” problems will not be tested on the final exam.
Knowing the special values of the sine and cosine (at π/6, etc.), and the
periodic behavior of these functions will be helpful.
Topics:
- Solve
an absolute value equation.
- Use
factoring to locate the intercepts of a polynomial graph.
- Calculate
a difference quotient. Use algebra to simplify it.
- Solve
a linear inequality; answer using interval notation.
- Equations
of parallel lines.
- Translate
a graph. (Horizontal and vertical shifts.)
- Polynomial
division, quotient and remainder.
- Find
an inverse function algebraically.
- Use
basic algebra facts to simplify a composite function.
- Find
the domain of a rational function.
- Asymptote
analysis from descriptive data.
- Use natural
logarithms to solve a problem in continuously compounded interest.
- Complete
the square to find the center and radius of a circle.
- Apply
double angle formulas and periodicity of trigonometric functions.
- Compose
trig and inverse trig functions at a specific place. (Know the ranges!)
- Given
a trig value and quadrant of the angle, find another trig value.
- Compose
trig and inverse trig functions to obtain an algebraic function.
- Use
identities to simplify a trigonometric expression.
- Convert
between degrees and radians.
- Use
the Law of Sines.