## Precalculus 2 Practice Exam

Test 3 Time: 1.5 hours

1. Find the partial fraction decomposition of

2. Identify the sequence (in the sum) as arithmetic, geometric, or neither and find the sum:

3. Identify the sequence as arithmetic, geometric, or neither and find the sum of the first 25 terms using techniques described in class. Round your answer to two decimal places:

4. In an arithmetic sequence, and .
• Find the formula which describes the nth term of this sequence.
• Using the formula found, write the first three terms of the sequence.

5. Use mathematical induction to prove the given formula for every positive integer n:

6. An experiment consists of studying the number of boys and girls in families with exactly 3 children. Let b represent boys and g represent girls.

• Describe the sample space that considers the ordering of the births of the 3 children.
• Describe the event that the family has exactly 2 girls.

7. Consider the expression .
• Using the Binomial Theorem, write out the binomial expansion of the given expression and compute the third binomial coefficient by hand (show all steps).
• Using any method (calculator or by hand) find the rest of the coefficients, and simplify the expansion in the above part.

8. A child has a set of different shaped plastic objects. There are 3 pyramids, 4 cubes, and 7 spheres.
• In how many ways can she arrange them in a row if they are all different colors?
• In how many distinguishable ways can they be arranged in a row if objects of the same shape are also the same color?

9. One card is selected from a standard deck of 52 playing cards. What is the probability that the card is a heart or a two?

10. From a group of 16 smokers and 20 nonsmokers, a researcher wants to randomly select 8 smokers and 8 nonsmokers for a study. In how many ways can the study group be selected?