## Description

# MAT 222 INTERMEDIATE ALGEBRA COMPLETE CLASS

**MAT 222 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material – Ashford**

**Week 1 Assignment Solving Proportions**

Read the following instructions in order to complete this assignment:

a. Solve problem 56 on page 437 of *Elementary and Intermediate Algebra*. Set up the two ratios and write your equation choosing an appropriate variable for the bear population.

b. Complete problem 10 on page 444 of *Elementary and Intermediate Algebra*. Show all steps in solving the problem and explain what you are doing as you go along.

c. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:

§ Your solution to the above problems, making sure to include all mathematical work, and an explanation for each step

§ A discussion of the following: What form of an equation do you end up with in problem 10? What do you notice about the coefficient of x compared to the original problem? Do you think there might be another way to solve this equation for y than with the proportion method? How would you do it?

§ An incorporation of the following four math vocabulary words into your paper. Use **bold **font to emphasize the words in your writing. (**Do not write definitions for the words; use them appropriately in sentences describing your math work**.):

o Extraneous

o Proportion

o Cross multiply

o Extreme-means

The paper must be at least two pages in length and formatted according to APA style. Cite your resources in text and on the reference page. For information regarding APA samples and tutorials, visit the Ashford Writing Center, within the Learning Resources tab on the left navigation toolbar, in your online course.

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**Week 1 DQ Accounting and the Business Environment**

In this discussion, you are assigned two rational expressions with which you will then do a variety of math work. Remember that each polynomial must be fully factored and that you can only cancel factors; **you cannot cancel terms**. Read the following instructions in order and view the example to complete this discussion:

Find your two rational expressions in the list below based on your first initial.

Find and state the common denominator between the two expressions. Build up each expression so that it has the common denominator. (Remember not to do any canceling at this point since you need those extra factors for the common denominator.)

Add the two rational expressions together. Factor again if possible, and present the answer in lowest terms.

Incorporate the following five math vocabulary words into your discussion. Use **bold **font to emphasize the words in your writing (**Do not write definitions for the words; use them appropriately in sentences describing your math work**.):

§ Domain

§ Lowest terms

§ Opposites

§ LCD

§ Build up

Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references. Respond to at least two of your classmates’ posts by Day 7. Is their work similar to your own? Did they factor and cancel correctly? Are their answers in lowest terms?

**Week 2 Assignment Two-Variable Inequalities**.

Read the following instructions in order to complete this assignment:

a. Solve problem 68 on page 539 of *Elementary and Intermediate Algebra*, and make sure to study the given graph. For the purposes of the assignment, it would be helpful to copy the graph onto your own scratch paper.

b. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:

§ An answer to the three questions asked about given real-world situation.

§ An application of the given situation to the following two scenarios:

o The Burbank Buy More store is going to make an order which will include *at most *60 refrigerators. What is the maximum number of TVs which could also be delivered on the same 18-wheeler? Describe the restrictions this would add to the existing graph.

o The next day, the Burbank Buy More decides they will have a television sale so they change their order to include *at least *200 TVs. What is the maximum number of refrigerators which could also be delivered in the same truck? Describe the restrictions this would add to the original graph.

c. An incorporation of the following math vocabulary words into your discussion. Use **bold **font to emphasize the words in your writing (**Do not write definitions for the words; use them appropriately in sentences describing your math work**.):

§ Solid line

§ Dashed line

§ Parallel

§ Linear inequality

§ Test point

**Week 2 DQ One-Variable Compound Inequalities**.

In this discussion, you will be demonstrating your understanding of compound inequalities and the effect that dividing by a negative has on an inequality. Read the following instructions in order and view the example to complete this discussion:

a. According to the first initial of your last name, find the pair of compound inequalities assigned to you in the table below.

b. Solve the compound inequalities as demonstrated in *Elementary and Intermediate Algebra *and the Instructor Guidance in the left navigation toolbar, in your online course, being careful of how a negative x-term is handled in the solving process. Show all math work arriving at the solutions.

c. Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set as demonstrated in the Instructor Guidance in the left navigation toolbar, in your online course.

d. Incorporate the following five math vocabulary words into your discussion. Use **bold **font to emphasize the words in your writing (

§ Compound inequalities

§ And

§ Or

§ Intersection

§ Union

**Week 3 Assignment Real World Radical Formulas**.

Read the following instructions in order to complete this assignment:

a. Solve parts *a *and *b *of problem 103 on page 605 and problem 104 on page 606 of *Elementary and Intermediate Algebra*.

b. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:

§ An explanation of what the parts of the formula mean before using it to get your answers. Study the Instructor Guidance examples to learn how to solve the formula for another variable.

§ Your solution to the above problems, making sure to include all mathematical work.

§ A discussion of how and why these concepts are important in the “real world.” Describe another situation that could be evaluated using these concepts.

**Week 3 DQ Simplifying Radicals**.

In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents. Read the following instructions in order and view the example to complete this discussion:

a. Find the rational exponent problems assigned to you in the table below.

*If the last letter of your first name is*

*On pages 576 – 577, do the following problems*

A or L

42 and 101

B or K

96 and 60

C or J

46 and 104

D or I

94 and 62

E or H

52 and 102

F or G

90 and 64

M or Z

38 and 72

N or Y

78 and 70

O or X

44 and 74

P or W

80 and 68

Q or V

50 and 76

R or U

84 and 66

S or T

54 and 100

b. Simplify each expression using the rules of exponents and examine the steps you are taking.

c. Incorporate the following five math vocabulary words into your discussion. Use **bold **font to emphasize the words in your writing (**Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work**.):

§ Principal root

§ Product rule

§ Quotient rule

§ Reciprocal

§ *n*th root

Refer to Inserting Math Symbols for guidance with formatting. Be aware that with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have √12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not. Thus we must specify whether we mean it to say √(12) + 9 or √(12 + 9). As there is a big difference between the two, this distinction is important in your notation.

Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or “sqrt(12 + 9)” depending on what we needed it to say.

**Week 4 Assignment Real World Quadratic Functions**.

Read the following instructions in order to complete this assignment:

a. Solve problem 56 on pages 666-667 of *Elementary and Intermediate Algebra*.

b. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay, please make sure to include:

§ An explanation of the basic shape and location of the graph and what it tells us about the Profit function.

§ Your solutions (it is a double question) to the above problem, making sure to include all mathematical work for both problems.

§ Discuss how and why this is important for managers to know, and explain what could happen if the ideal conditions were not met.

**Week 4 DQ Solving Quadratic Equations**.

In this discussion, you will solve quadratic equations by two main methods: factoring and using the Quadratic Formula. Read the following instructions in order and view the example to complete this discussion:

a. Find the problems assigned to you in the table below.

b. For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation.

c. For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to Inserting Math Symbols for guidance with formatting.

d. Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.

e. Incorporate the following four math vocabulary words into your discussion. Use **bold **font to emphasize the words in your writing (

§ Quadratic formula

§ Factoring

§ Completing the square

§ Discriminant

**Week 5 Assignment Composition and Inverse**.

Read the following instructions in order to complete this assignment:

a. We define the following functions: *f(x) *= 2*x *+ 5 *g(x) *= *x*2 – 3 *h(x*) = 7 – *x*

3

§ Compute (*f – h*)(4).

§ Evaluate the following two compositions: (*f g*)(*x*) and (*h g*)(*x*).

§ Transform the *g(x) *function so that the graph is moved 6 units to the right and 7 units down.

§ Find the inverse functions *f -1(x) *and *h-1(x)*.

§ Your solutions to the above problems, making sure to include all mathematical work for both problems, as well as explaining each step.

§ A discussion of the applicability of functions to the real world, based upon your reading of Chapter 11 of*Elementary and Intermediate Algebra*. Be sure to use specific examples, a brief discussion of why your examples are important, and to cite your sources.

**Week 5 DQ Relations and Functions**. In this discussion, you will be assigned two equations with which you will then do a variety of math work having to do with mathematical functions. Read the following instructions in order and view the example to complete this discussion:

a. Find your two equations in the list below based on the last letter of your last name.

There are many ways to go about solving math problems. For this assignment you will be required to do some work that will not be included in the discussion. First, you need to graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.

b. Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)

c. Discuss the general shape and location of each of your graphs.

d. State the domain and range for each of your equations. Write them in interval notation.

e. State whether each of the equations is a function or not giving your reasons for the answer.

f. Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.

g. Incorporate the following five math vocabulary words into your discussion. Use **bold **font to emphasize the words in your writing (**Do not write definitions for the words; use them appropriately in sentences describing the thought behind your math work**.):

§ Function

§ Relation

§ Domain

§ Range

§ TransportationMAT

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