1]
Use the binomial formula to expand
     

2]
Use the binomial formula to find the fifth and twelfth terms in the expansion of
     .

3]
a) Solution
How many 4-letter code words are possible using the first 10 letters of the alphabet if
(i) No letter can be repeated?
(ii) Letters can be repeated?
(iii) Adjacent letters cannot be alike?
b) Solution
Find the number of permutations of 25 objects taken 8 at a time.
Compute the answer to 4 significant digits using a calculator.

4]
a) Solution
How many 4-letter code words are possible from the first 6 letters of the alphabet,
with no letter repeated? Allowing letters to repeat?
b) Solution
How many different license plates are possible if each contains 3 letters followed by 3 digits? How many of these license plates contain no repeated letters and no repeated digits?

5]
a)
Write the following without the summation notation and find the sum.
     

b)
     

c)
     

d)
Write
     
using summation notation, and find .

6]
Represent the repeating decimal as the quotient of two integers.

     

7]
Let    be a geometric sequence. Find the the indicated quantity.

                                                          

8]
Let   be an geometric sequence. Find the indicated quantity.

                                                           

9]
Find
     

10]
Let     be an arithmetic sequence. Find the indicated quantities.

                                                         

11]
Given  

(i) Write the first four terms of the sequence.
(ii) Find .
(iii) Find .
Note:
This is an example of a sequence in which the definition of the general term is given recursively. That is, a term is defined by reference to another term. In this case,
is defined by reference to the previous term, .

12]
Use synthetic division to find the quotient and remainder resulting from dividing

           by .

13]
Find all the rational zeros for  .

14]
a)
Find all zeros exactly fo r .

b)
Given that    and that    is a zero,
write    as a product of linear terms.

15]
Find all vertical, horizontal, and oblique asymptotes. Do not graph.

     

16]
Solve    and check.

NOTE:
Recall that means , which are called common logarithms. The base is 10.

17]
Solve the equations and give your answers to 3 significant digits.
a)
          

NOTE:
Recall that and that means .
Logarithms to the base are called natural logarithms.


b)
          

18]
Graph
               

19] Simplify the complex fraction

     

20]
Write the following in the standard form for complex numbers,

     




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