# College Algebra Tutorial 59

College Algebra
Tutorial 59: Practice Test on Tutorials 54A - 58

Problem 1a: Write a formula for the nth term of the infinite sequence.  Do not use a recursion formula.

1a.

Problem 2a: Find the first four terms and the 10th term of the arithmetic sequence.

2a.

Problem 3a: Find the first four terms AND the common ratio of the geometric sequence.

3a.

The common ratio is -2.

Problem 4a: Write the geometric series in summation notation.

4a.

Problem 5a: Find the sum of the arithmetic series.

5a.

Problem 6a: Find the sum of the infinite geometric series.

6a.

Problem 7a: Evaluate the given binomial coefficient.

7a.

Problem 8a:  Use the Binomial Theorem to expand the binomial and express the result in simplified form.

8a.

Problem 9a:  Find the term indicated in the expansion.

9a. ;   fifth term

Problems 10a - 10f:  Solve by the method of your choice.

10a.  Next semester you are going to take one business class, one math class, one political science class one english class and one fine arts class.  According to the schedule you have 3 different business classes, 5 different math classes, 1 political science class, 4 different English classes, and 2 Fine Arts classes to choose from.  Assuming no scheduling conflicts, how many different five-course selections can you make?

10b.  In how many ways can 8 employees be assigned to 8 different jobs?

10c.  A computer password can use any letter of the alphabet, and a sequence of 5 different letters must be selected for the password.  How many computer passwords are possible?

10d.   A boss has 8 employees and 5 are chosen to give a presentation.  How many different ways can the boss choose the presenters if the order of the presenters is important?

10e.  A boss has 8 employees and 5 are chosen to give a presentation.  How many different ways can the boss choose the presenters if the order of the presenters is not important?

10f.  15 students of whom 9 are seniors, 4 are juniors, and 2 are sophomores, are selected as semi-finalists for a literary award.  Of the 15 students, 5 finalists will be selected.

1)  In how many ways can 5 finalists be selected from the 15 students?

2)  In how many ways can the 5 finalists contain only seniors?

3)  In how many ways can the 5 finalist contain exactly 1 sophomore and 4 juniors?

Problems 11a - 11b:  200 college students took a survey on their favorite soda pop.  The results are as follows: 125 said their favorite was Coke.  25 said their favorite is Diet Coke.  30 said their favorite is Dr. Pepper.  15 said their favorite was Sprite.  And 5 said their favorite was Mountain Dew.

If each student picked only one favorite, find the following probabilities.

11a. A student's favorite soda pop is Diet Coke.

11b.  A student’s favorite soda pop is Sprite.

Problems 12a - 12b:  From a group of  7 seniors and 9 juniors, 4 people are selected at random to form a committee.  Find the probability that

12a. Only seniors are selected.

12b. Exactly 2 seniors and 2 juniors are selected.

Problems 13a - 13c:  An employee’s name will be picked at random to go on a business trip with the boss.  There are 20 senior level executives, 15 junior level executives, 18 senior level programmers, 12 junior level programmers, 5 senior level assistants and 5 junior level assistants.

Find the probability that

13a.  a programmer OR an assistant will be picked.

Mutually exclusive:

13b.  a senior level employee OR an executive will be picked.

Not mutually exclusive:

13c.  a junior level employee will not be picked.

Problem 14a:  Find the probability.

14a.   If 1 card is drawn from a deck of cards and 1 die is rolled find the probability that the card drawn is a diamond AND the number rolled on the die is even.

Sets are independent of each other:

Last revised on May 21, 2011 by Kim Seward.