Honors Trig/PreCalc
Final Test Review
Name ____________________________
This packet is meant to serve as a guide for your studying and may not contain everything that is on
the test. Be sure to study your notes and do additional practice problems from the book. This will be
a 2 day 100 point test. The purpose of both this study guide and the test is to ensure that you are
prepared to be successful in AP Calculus next year. Below is a list of the key topics that you need to
know.

Solving equations (Logarithmic, Exponential, Trig, Quadratic, Polynomial)

Graphing (Piecewise, Greatest Integer Function, Logarithmic, Exponential, Trig, Quadratic,
Polynomial, Rational, Conics)

Algebraic skills (avg. rate of change, function composition, factoring, inverses, complex fractions,
domain, writing equations of lines, rationalizing numerators and denominators, partial fractions)

Trig skills (exact values of trig and inverse trig functions, identities, Law of Sines and Cosines,
applications, vectors)

Limits and Derivatives
1. Find the average rate of change of f ( x)  x 2  4 x from x1  5 to x2  9 .
2. Use the properties of logs and exponents to simplify expressions:
a.
ln e
b. ln e2
d. log3 32
c. log1
3. Find exact values of all trig functions:
a.
 3 
cos  
 2 
 

2
b. tan 
 

6
c. sin 
4. Simplifying rational expressions:
a.
1
1

xh4 x4
h
2
2

b. x  h  3 x  3
h
5. Solve trig equations:
a.
2sin x  3
b. 2cos2 x  3sin x  0
6. Factor:
a.
9 x2  5x  4
b. 16a 2 x  25 y  25x  16a 2 y
c. x3  27
7. Graph trig functions:
a. y  sin x
b. y  2cos( x   )
8. Determine limits:
a.
x5
x5 ( x  5)( x  4)
lim
x2  x  2
x1
x 1
b. lim
9. Solve each equation (factoring, quadratic formula, or rational root theorem):
a.
2 x2  7 x  4
c. 2 x 2  6 x  1
b.
2 x3  9 x 2  7 x  1  0
d. 4 x 4  7 x 2  2  0
10. Graph functions:
a. With asymptotes and points
y
x2  2 x  3
x 3
b. With transformations
f ( x)  x  1  2
11. Find the derivative:
a.
f ( x)  2 x 3  7 x
b. f ( x) 
2
x7
c. f ( x)  2 x  9
12. Partial fraction decomposition:
a.
x2
 x  1  x  1
2
b.
4 x 2  3x  14
x3  8