Algebra 2/Trigonometry Honors
Review (MP3)
Name:
CHAPTER 9 – POLYNOMIALS AND POLYNOMIAL FUNCTIONS






Remainder and Factor Theorems
Rational Zeros Theorem
Real Zeros of Polynomial Functions
Four Useful Theorems
The Binomial Theorem
Standard Deviation and Chebyshev’s Theorem
1. Find the quotient and remainder: (3x4  3x3  x2  x  12)  ( x  1)
2. Find all rational zeros of the function: f ( x)  24 x3  14 x 2  x  1
3. Expand the expression: (4n + 5m)4
4. Find the standard deviation: 3
5
9
7
2
6
8
4
5
7
5. Suppose that F(x) = ax2 +bx + c and that F(0) = -3, F(1) = 4, and F(-1) = 8. Find (a, b, c).
6. Use synthetic division to completely factor P( x)  x 4  x3  11x 2  9 x  18
7. Find the 4th term in the 15th row of Pascal’s Triangle.
8. Solve for x: 2 2 x 1  10
CHAPTER 10 – RATIONAL EXPRESSIONS, EQUATIONS, AND FUNCTIONS




Multiplying and Dividing Rational Expressions
Rational Equations and Inequalities
Adding and Subtracting Rational Expressions
Complex Fractions
9. Simplify and state any restrictions:
x 2  25
x2  4 x  3

x2  2 x  3 x  3

x2  4 x  5 x  5
10. Solve for x:
11. Simplify:
14
( x  1)2
1
2
x  3x

3
6
x 1

2
2
x 9
1
x 3
12. Simplify:
2
x
x 1
x
13. Let f ( x) 
2x
2
x 5
and g ( x) 
4
2
x 5
. Find x such that f(x) – g(x) = 0.
3
f ( x  h)  f ( x )
14. Let f ( x)  , find
x
h
CHAPTER 11 – EXPONENTIAL AND LOGARITHMIC FUNCTIONS





Definitions of exponential and logarithmic functions
Properties of logarithms
Solving exponential and logarithmic equations
Applications
Binomials and Binomial Distribution
15. Solve for x: log4 x = log3 27
16. Solve for x: Find the value of log5 21
17. Rewrite as a single logarithm: 2log3 5 + 3log3 4 – log3 7
18. Find the value of log5 21
19. Solve for x: log4 x + log4 (x – 2) = 1
4
of the time. If the coin is tossed four times, what is the
5
probability that it will turn up heads at least twice?
20. A weighted coin turns up heads
21. Sam deposited $10,000 into a savings account earning 5.75% interest, compounded
continuously. How long must he leave the money in the bank before it doubles its amount?
22. Solve for x: 37 x 12  5 x 9
23. Radioactive iodine has a half-life of 60 days. Find the amount of iodine that will remain of
10 oz after 40 days.
24. Find x to the nearest hundredth: 4e2 x  5
CHAPTER 13 – SEQUENCES AND SERIES




Sequences
Series
Arithmetic Sequences and Series
Geometric Sequences and Series
n
25. If  ak  n(n  3) , what is an ?
k 1
26. {Sn} is the sequence of partial sums of {an}. If S10 = 115 and S11 = 136, what is a11?
27. Insert three arithmetic means between 4 and 12.
28. Insert three geometric means between 3 and
100
29. Evaluate:  5n
n 1
3
16