Download Algebra 2 Connections

Algebra 2 Connections
Appendix A Review Worksheet
Name ________________________
Date ______________ Period ____
1) Consider the following sequence: 128, 96, 72,…
a) Write the next three terms of the sequence ___________________________________
b) Is this sequence arithmetic, geometric, or neither? Explain your answer using a complete sentence.
c) Write a recursive and explicit equation for this sequence.
2) Given the recursive equation:
a)
t (1)  9
t (n  1)  t (n)  6
Write the first four terms of the sequence __________________________________
b) Write the explicit equation for the sequence ________________________________
3) Given the recursive equation:
a)
a1  5
a n 1  3  a n
Write the first four terms of the sequence __________________________________
b) Write the explicit equation for the sequence ________________________________
4)
Multiply each of the following expressions. Check that each result is equivalent to the given expression.
2 w( w  3)
a.
b. 3(2 x  1)( x  7)
c. (q  3)(q 2  4q  5)
5.
If f(x) = -2x2 + 11x + 2, find the following:
b. Evaluate f(-3)
b. What values of x will make f(x) = 7?
6) Decide whether each of the following pairs of expressions is equivalent for all values of x. If they are
equivalent, show how you can be sure. If they are not, justify your reasoning completely.
a. ( x  2)2 and x 2  4
b. (2 x  5)2 and 4x 2  20 x  25
7) Solve the systems of equations algebraically. Show all your work.
a.
3x  2 y  6


1
y  x4


2
3x  2 y  7
5 x  3 y  2
b. 
8) Investigate each of the following functions using multiple representations (tables and graphs). Determine the x
and y – intercepts, the domain and range, and any asymptotes for each function, if applicable.
a. f  x   2 x2  5x  3
b. g  x   3(2) x
9) Digger Dog hides the same number of bones each Friday in his favorite hiding spot.
a. What type of sequence represents his total number of saved bones? How can you tell?
b. After week 4, he had 23 bones, and after week 8, he had 35 bones. How many did he start with?
Display this data in a table and write an explicit rule.
c. Use your rule to determine whether or not it is possible for him to save exactly100 bones.