Title

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

Learning Objectives

 After completing this tutorial, you should be able to: Take a test on topics covered in tutorials 54A - 58 in this website.

 Special Notes about Tutorial 59: I can not guarantee you will pass your test after going though any of the tutorials in this website or this practice test. However, it will definitely help you to better understand the topics covered better. Disclaimer: WTAMU and Kim Seward are not responsible for how a student does on any test or any class for any reason including not being able to access the website due to any technology problems.  There are no videos on this page.

Introduction

It is important to note that chances are I'm not your math instructor. You need to check with your math teacher as to things like when your next math test is and what it covers.  It may cover more material on the test than what is in this practice test.  Just note that there are other practice tests at this website. So, after finding out what is on your test (if you have one) do the practice test(s) problems that go with the test you are preparing for.  If you are not in a class or are not having a test soon, this practice test is still good practice to go through and check to make sure you are understanding this material before moving on - kind of like a spot check.  The material on this practice test goes with  Tutorial 54A:  Sequences , Tutorial 54B: Series, Tutorial 54C: Arithmetic Sequences and Series , Tutorial 54D: Geometric Sequences and Series , Tutorial 54: The Binomial Theorem , Tutorial 55: The Fundamental Counting Principle , Tutorial 56: Permutations , Tutorial 57: Combinations , and Tutorial 58: Probability.

Also note that your teacher may word the problems on their test a little differently, may have some different kinds of problems, or may have a different number of problems than what is in this practice test.  Again, since I'm probably not your math instructor, I don't know exactly how your teacher will set up your math test.  Just note that these problems will help you build an understanding of the concepts presented and the terms used in math problems.  If you have an understanding of the problems instead of just memorizing them, then you should do fine on these concepts, no matter how the test is set up.

 Steps to Studying for a Math Test
1. Work through problems.  If you are in a class, you should have done this on completion of any homework you have done.  For anyone,  you can accomplish this by doing the practice problems found in each tutorial.

2. Check work on problems.  The practice problems in each tutorial have links to the answers to them so you can instantly check how you are doing.  Also, in most math books, the odd answers are found in the back of the book.

3. Review concepts.  Whether you got the problems right or wrong, make sure you review over them.  If you did get a problem wrong, make sure you either review that concept in it's respective tutorial or ask your math teacher about it.  If you don't ask about a problem before a test,  you are going to kick yourself when it comes up on the test.

4. Work through problems as if you were taking the test - no notes, book, webpages, etc.  This practice test is a perfect way to do that. After taking this practice test, check your answers by clicking on the link to the answer key found at the bottom of the practice test (before the 'need extra help on these topics' section)

 During the Test

It is to your benefit to show as much of the work as possible on the problems that have several steps involved.

Make sure that you read the directions carefully,  you wouldn't believe how many points get taken off  math tests for people not following directions.

Pace yourself.  You do not have to be the first one done to do well on the test.  Do not panic if there is still time left to take the test and others are turing it in.  Sometimes that means they do not know the material and left some of the answers blank.  Do not worry about anyone else but yourself.

Don't rush through a problem.  Another thing that math teachers take points off for are careless mistakes made by people that rush through a problem.  When those students get their tests back, they bonk themselves on the head at some of the things that got counted wrong,  things that they knew how to do.

Remember to breathe!!!!  I know some of you are scared to death at the thought of having to take a math test of any kind.  For you guys, try to relax and don't forget to breathe.  (Even if you aren't scared to take a math test,  it is probably a good idea to remember to breathe,  I wouldn't want you to pass out during the test). If it feels like your brain has left the building during your test, just close your eyes and breathe in and out and in and out and your brain will return.

Good luck on your test.  If you are taking a math test soon, don't panic, you are going to do great!!!

Practice Test

 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.

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

Need Extra Help on these Topics?

The following are web pages that can assist you in the topics that were covered on this page: