Math 1313 Course Objectives

 

Chapter.Section

Objective and Examples

Material Covered by End of Week #

1.3

Given a linear depreciation problem, find the rate of

depreciation, the expression that expresses the book

value at the end of t years and the value of the asset

after a given amount of years.

 

Example:  A company purchased a car in 2000 for $13,000.  The car is depreciated linearly for 5 years.  The scrap value of the car is $4,000.  What is the rate of depreciation?  Write the expression that expresses the book value of the car after t years of use.  What is the value of the car in 2003?

 

Given the production cost, selling price of a product

and the fixed costs of the company, find the cost

function, revenue function, profit function, and

compute the profit or loss corresponding to certain

production levels.

 

Example  A company has a fixed cost of $100,000 and a production cost of $14 for each unit produced.  The product sells for $20 per unit. 

What is the cost function?

What is the revenue function?

What is the profit function?

What is the break-even point?

What is the profit or loss corresponding to a production level of 12,000 and 20,000 units?

 

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

1.4

Given a word problem find break-even quantity,

break-even revenue and break-even point of the

company.

 

Example  A company has a fixed cost of $100,000 and a production cost of $14 for each unit produced.  The product sells for $20 per unit. 

What is the break-even quantity?

What is the break-even revenue?

What is the break-even point?

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

1.5

Given a set of data or a word problem, find the

equation for the least-square line of the data and

use this equation to predict a certain future value.

 

Example:  The size of the average farm in a certain town has been growing steadily over the years.  The accompanying data was collected and gives the size of the average farm y (in acres) from 1945 to 1995.  (Here x = 0 corresponds to the beginning of the year 1945.)

Year, x                         0          10        20        30        40           

Number of Acres, y     57        63        76        88        92           

 

a.   Find the equation of the least-squares line for these data.

b.   Use the result in part (a) to estimate the size of the average farm in the year 1998.

 

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

3.2, 3.3

Set up and solve a linear programming problem.

 

Example:  A company manufactures two products, A and B, on two machines I and II.  It has been determined that the company will realize a profit of $3 on each unit of product A and a profit of $4 on each unit of product B.  To manufacture a unit of product A requires 6 min on machine I and 5 min on machine II.  To manufacture a unit of product B requires 9 min on machine I and 4 min on machine II.  The company has 5 hours of machine time on machine I and 3 hours of machine time on machine II in each work shift.  How many units of each product should be produced in each shift to maximize the company’s profit?  Set up the linear programming problem then solve it.

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

5.1-5.3

Given a certain math of finance problem, recognize

what kind of problem it is and solve it.  The kind of

problems given will be:  simple interest, future value

or present value with simple interest, effective rate,

future value or present value with compound interest,

future value or present value of an annuity,

amortization, or sinking fund.

 

Example:  A company would like to have $50,000 in 2 years to replace machinery.  The account they wish to invest in earns 3.45% per year compounded quarterly.  How much should they deposit into this account each quarter to have the desired funds in 2 years? 

a.       What kind of problem is this?

b.      Solve the problem.

 

Example:  Karen has decided to deposit $300 each month into an account that earns 2.34% per year compounded monthly.  How much will she have in this account after 3 years?

a.       What kind of problem is this?

b.      Solve the problem.

 

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

6.1

Given sets, list the subsets and proper subsets of a set. 

Find the union, intersection and/or complement of

certain given sets.

 

Example:  Let U = {1,2,3,4,5,6,7,a,b,c,d,e}A = {1,2,3,4,5,a,b,c}, B = {1,3,5,6,a,c,d}, and C = {2,4,7,b,d,e}, and D = {1,2,a}

a.   List the subsets of D.

b.   Find

          

 

Use Venn diagram shading to find the union,

intersection and/or complement of certain given sets.

 

Example:  Given the following Venn diagram, shade the given set.

     

                                                                  U

                          A                        B

                                                 

 

 

                                       C

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

6.2

Find the number in sets by using formulas or Venn

diagram shading.

 

Example:  Of 30 elementary school children, 15 read a book last summer, 17 practiced math last summer and 7 read a book and practiced math last summer. 

How many of the 30 children:

a.   did not read a book last summer?

b.   read a book but did not practice math last summer?

c.   did not read a book and did not practice math last summer?

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

6.3, 6.4

Solve word problems by using counting technique(s)

such as the multiplication principle, combination or

permutation.

 

Example:  A coin is tossed 20 times, how many    outcomes are there?

 

Example:  In how many ways can you arrange 3 different pictures from 5 available on a wall from left to right?

Example:  In how many ways can you choose 3 mystery books from a collection of 15 mystery books and 5 romance books from a collection of 20 romance books?

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

7.1, 7.2

Given a set of data or a certain experiment, list the

simple events, find the probability of each of the

simple events, find the probability distribution, and

find the probability of an event that consists of more

than one simple event.

 

Example:  A pair of dice is cast.  List the simple events.  Assign probabilities to each of the simple events.  Find the probability distribution of the experiment.  Find the probability that the sum of the numbers is even.

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

7.3

Given a word problem, use formulas or Venn

diagram shading to find the probability of the union,

intersection and/or complement of certain events.

 

Example:  Of 30 elementary school children, 15 read a book last summer, 17 practiced math last summer and 7 read a book and practiced math last summer. 

What is the probability that a child selected at random

a.   did not read a book last summer?

b.   read a book but did not practice math last summer?

c.   did not read a book and did not practice math last summer?

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

7.4

Use counting techniques to find the probability of

certain events.

 

Example:  A box contains 25 batteries of which 5 are defective.  A random sample of 4 is chosen.  What is the probability that at least 2 are defective?

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

7.5

Use the conditional probability formula or tree diagrams to aid in finding certain probabilities. 

 

Example:  A group of senators is comprised of 48 Democrats and 52 Republicans.  Seventy-one percent of the Democrats served in the military, whereas 68% of the Republicans served in the military.  What is the probability that a senator chosen at random

a.   is Republican?

b.   Is a Democrat and did not serve in the military?

c.   served in the military?

d.   did not serve in the military, given that he/she is a Democrat?

 

Given that certain events are independent, find the probability of the intersection of those independent events.

 

Example:  If A and B are independent events and P(A)=0.4 and P(B)=0.6, find P(AB).

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

7.6

Use tree diagrams and Bayes’ formulas to find certain

conditional probabilities.

 

Example:  A group of senators is comprised of 48 Democrats and 52 Republicans.  Seventy-one percent of the Democrats served in the military, whereas 68% of the Republicans served in the military.  What is the probability that a senator chosen at random is a Republican, given that he/she served in the military?

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

8.1

Given a probability distribution, find certain

probabilities and draw a histogram associated with

the given probability distribution.   Construct the

probability distribution of a random variable.

 

 

Example:  The probability distribution of the random variable X is shown below.

 x                        P(X=x)

  1            0.2

  2            0.3

  3            0.5

 

 

    a.  Find P(1 < X < 3).

b.  Draw the histogram corresponding to the given probability distribution.

 

 

 

 

 

Example:  Given the following frequency table, construct the probability distribution associated with the random variable X.

x             P(X=x)

  1            45

  2            20

  3            32

 

 

 

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

8.2

Find the expected value of a given probability

distribution or of a word problem. 

 

Example:  The following probability distribution tables describes the number of cars, x, that a certain car dealer will sell in a given day along with its associated probability.

x             P(X=x)

   1            0.2

   2            0.3

   3            0.5

 

Find the expected number of cars the car dealer will sell in a given day.

 

Given a word problem, find the odds in favor, odds

against or given the odds find a certain probability.

 

 

Example:  The odds in favor of an event occurring are 4 to 5.  What is the probability of the event not occurring?

 

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

8.3

Given a probability distribution or a word problem,

find the variance and standard deviation. 

 

Example:  Given

x                  P(X=x)

1            0.2

2           0.3

3            0.5

 

Find the variance and standard deviation.

Use Chebychev’s inequality to estimate a certain

probability.

 

 

Example:  The expected lifetime of a certain machine is 24 mo and the standard deviation is 3 mo.  Use Chebychev’s inequality to estimate the probability that one of these machines will last between 20 and 28 mo.

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

8.4

Given a binomial experiment, find certain

probabilities, the mean, the variance, and the standard deviation.

 

Example:  The probability that a certain CD player will be defective is 0.04.  If a sample of 15 CD players is chosen at random, what is the probability that the sample contains

a.   no defective CD players?

b.   at most 3 defective CD players?

c.   Find the mean, variance and standard deviation of this experiment.

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

8.5

Given a standard normal distribution, find certain

probabilities or given the probability find the value of

z. 

 

Example:  Let Z be a standard normal random variable.  Find:

a.       P(Z < 1.34)

b.      P(Z> -2.33)

c.       P(-0.23 < Z < 1.22)

 

Example:  Let Z be a standard normal random variable.  Find the value of z if:

 

a.       P(Z > z) = 0.8749

b.      P(-z < Z < z) = 0.4908

 

Given a normal distribution, possibly a word problem, standardize it to find certain probabilities.

Example:  Let X be a normal random variable.  The mean is 25 and the standard deviation is 4.  Find:

 

a.        P(X < 30)

b.       P(X > 10)

c.       P(15 < X < 25)

 

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Chapter.Section

Objective and Examples

Material Covered by End of Week #

8.6

Use the normal distribution to approximate a binomial distribution.

Example:  Use the normal distribution to approximate the following binomial distribution.  A biased coin is tossed 100 times.  The probability of obtaining a head is 30%.  What is the probability that the coin will land heads at least 90 times?

 

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