UBC Wiki - User contributions [en]

User:DeborahMa

2011-01-28T17:47:18Z

DeborahMa:

I'm '''Deborah'''. I'm a '''3rd years Arts student majoring in Sociology and applying for a Commerce Minor.'''

A parabola as '''stated in class''' is a conic section, the locus of all pints equidistant (equal distance) to a given line and a given point as well as all the points (x,y) satisfying an equation of the type y = ax^2 +bx + c

According to '''Wikipedia''' under the keyword “parabola”, parabola are all around us in the physical world, for example, a bouncing ball reflects a parabola shape when it bounces from the ground to midair and back to the ground again captured through a stroboscopic flash at 25 images per second. Also, you can see parabola trajectories of water in fountains. When water is trajected from the fountain, the shape as which is shoots out is similar to the shape of a parabola. Lastly, according to '''Wikipedia''', parabolas can also be found in the shape of main cables on a suspension bridge. It is stated in Wikipedia that “the curve of the chains of a suspension bridge is always an intermediate curve between an parabola.”

From looking up images under the keyword “parabola” on '''Google''', I found that when jugglers juggle balls and objects in the air, the curve that it makes from when the object leaves the jugglers hand to when it is midair to the other hand of the juggler, it makes a curve similar to that of a parabola. The McDonalds “M” logo can to some degree I suppose reflect two upside-down parabola curve.

='''Homework 12 Problem #3'''=

: On your profile page within the wiki, write an essay describing a particular use of calculus in your ﬁeld of study, or in a ﬁeld of interest to you. Feel free of course to add pictures, links and/or videos on the page (that's the advantage of writing online versus on paper). Your essay should be at least 500 words long (think a nice and interesting full page of text).

'''Field of interest:''' Economics

: In this essay, I wanted to discuss about my interests in economics and how it affects everyday consumers. I am the type of person that looks to look around for good and cheap bargains before settling on a particular product, so in a way prices of products and merchandise influence the way I feel about the brand and the product and most of the time, if I feel I can find a cheaper price elsewhere, I will go that distance to lower my costs.
: A recent example is buying textbooks for the semester; university textbooks are only getting more and more expensive each year and it is only ideal to think twice and shop around between settling on one.
''So what does this all have to do with economics?''
I feel that calculus in the field of economics plays a very important role because it is through rules such as elasticity that enable economist to come up with the supply and demand model, the marginal cost and marginal revenue charts.

[[File:Supply and demand.gif|400px|thumb|left|In this illustration you can see what happens when we move along the supply and demand curve. At p* and Q* is Equilibrium, which mean there is the right amount of supply for the right amount that consumers are demanding. When there is too much demand and little supply, there will be a SHORTAGE. When there is little demand and excess supply, we have a surplus amount of goods.]]

: In business, calculus and math in general can allow companies to maximize their profit.

[[File:Profitmax1.gif|375px|thumb|left|In this diagram, companies are PROFIT if they are able to keep their average total cost above the average cost curve and if their price is above marginal cost. The area on the y-axis between P and ATC is PROFIT, and companies can either choose to lower their average total cost (ATC) or raise their prices in order to maximize profit but risk low demands from consumers.]]

With the prices of gasoline dropping once in a while, it encourages consumers and car owners to fill up more.
But what happens when there is a lot of demand and very minimal supply of gasoline?

[[File:Gasoline-supply-demand.jpg|300px|thumb|left]]

Just as a speedometer monitors the rate-of-change of a car, similar calculations can be applied to stocks. Although there is no true "instantaneous rate of change" required of a first derivative, rate-of-change calculations using stock prices of today compared with say 200 days ago can provide meaningful values to plot.
When prices trend down, the rate-of-change indicator will be in a negative position -- similar to how the first derivative of a quadratic behaves. Just as parabolas have linear first derivatives, stocks on a parabolic trajectory up or down will have a pseudo-first-derivative that maintains a linear shape. By definition, this first derivative will have to break its trend before the market's actual prices do.
The shape of a rate-of-change plot will often carry hidden value too. Stocks, once leaving the base, are free to climb to the target (reflected) point. Once there, traders have little incentive to hang on, expecting higher prices, so they reverse their positions. This does lead to abrupt melt-ups and melt-downs, but rarely without some re-testing of the highs(lows).

'''<big>Further applications of calculus in economics include costs, marginal costs and revenues.</big>'''

{{#ev:youtube|LmftTXTE3Fw|400}}
{{#ev:youtube|52ANs_PZQjI|400}}

User:DeborahMa

2011-01-28T17:30:34Z

DeborahMa:

I'm '''Deborah'''. I'm a '''3rd years Arts student majoring in Sociology and applying for a Commerce Minor.'''

A parabola as '''stated in class''' is a conic section, the locus of all pints equidistant (equal distance) to a given line and a given point as well as all the points (x,y) satisfying an equation of the type y = ax^2 +bx + c

According to '''Wikipedia''' under the keyword “parabola”, parabola are all around us in the physical world, for example, a bouncing ball reflects a parabola shape when it bounces from the ground to midair and back to the ground again captured through a stroboscopic flash at 25 images per second. Also, you can see parabola trajectories of water in fountains. When water is trajected from the fountain, the shape as which is shoots out is similar to the shape of a parabola. Lastly, according to '''Wikipedia''', parabolas can also be found in the shape of main cables on a suspension bridge. It is stated in Wikipedia that “the curve of the chains of a suspension bridge is always an intermediate curve between an parabola.”

From looking up images under the keyword “parabola” on '''Google''', I found that when jugglers juggle balls and objects in the air, the curve that it makes from when the object leaves the jugglers hand to when it is midair to the other hand of the juggler, it makes a curve similar to that of a parabola. The McDonalds “M” logo can to some degree I suppose reflect two upside-down parabola curve.

='''Homework 12 Problem #3'''=

: On your profile page within the wiki, write an essay describing a particular use of calculus in your ﬁeld of study, or in a ﬁeld of interest to you. Feel free of course to add pictures, links and/or videos on the page (that's the advantage of writing online versus on paper). Your essay should be at least 500 words long (think a nice and interesting full page of text).

'''Field of interest:''' Economics

: In this essay, I wanted to discuss about my interests in economics and how it affects everyday consumers. I am the type of person that looks to look around for good and cheap bargains before settling on a particular product, so in a way prices of products and merchandise influence the way I feel about the brand and the product and most of the time, if I feel I can find a cheaper price elsewhere, I will go that distance to lower my costs.
: A recent example is buying textbooks for the semester; university textbooks are only getting more and more expensive each year and it is only ideal to think twice and shop around between settling on one.
''So what does this all have to do with economics?''
I feel that calculus in the field of economics plays a very important role because it is through rules such as elasticity that enable economist to come up with the supply and demand model, the marginal cost and marginal revenue charts.

[[File:Supply and demand.gif|400px|thumb|left|In this illustration you can see what happens when we move along the supply and demand curve. At p* and Q* is Equilibrium, which mean there is the right amount of supply for the right amount that consumers are demanding. When there is too much demand and little supply, there will be a SHORTAGE. When there is little demand and excess supply, we have a surplus amount of goods.]]

: In business, calculus and math in general can allow companies to maximize their profit.

[[File:Profitmax1.gif|375px|thumb|left|In this diagram, companies are PROFIT if they are able to keep their average total cost above the average cost curve and if their price is above marginal cost. The area on the y-axis between P and ATC is PROFIT, and companies can either choose to lower their average total cost (ATC) or raise their prices in order to maximize profit but risk low demands from consumers.]]

With the prices of gasoline dropping once in a while, it encourages consumers and car owners to fill up more.
But what happens when there is a lot of demand and very minimal supply of gasoline?

[[File:Gasoline-supply-demand.jpg|300px|thumb|left]]

'''<big>Further applications of calculus in economics include costs, marginal costs and revenues.</big>'''

{{#ev:youtube|LmftTXTE3Fw|400}}
{{#ev:youtube|52ANs_PZQjI|400}}

File:Gasoline-supply-demand.jpg

2011-01-28T17:22:29Z

DeborahMa:

File:Profitmax1.gif

2011-01-28T17:16:35Z

DeborahMa:

User:DeborahMa

2011-01-28T17:14:13Z

DeborahMa:

File:Supply and demand.gif

2011-01-28T17:10:36Z

DeborahMa:

User:DeborahMa

2011-01-28T17:08:32Z

DeborahMa:

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-27T07:03:58Z

DeborahMa:

='''<big>Homework 12</big>'''=

Start with the Function

<math>P(t)=\frac{1}{1+e^{-t}}\quad</math>

1) Change the height of the horizontal asymptote on the right and denote it by K.

2) Change the y-intercept to any number between 0 and K.

*BONUS - Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical.

'''<big>Solution</big>'''

1) We first found where the graph displays horizontal asymptotes. In order to do this we took the limit of the function as t approaches infinity. This told us as t becomes larger and larger, the function f(x) or "y" becomes arbitrarily close to 1, proving to us we had a horizontal asymptote on the right side of the graph. In order to raise this horizontal asymptote on the right side of the graph, we multiplied the whole function by a factor K. Since the numerator is 1, you can simplify and change the graph to:

<math>P(t)=\frac{K}{1+e^{-t}}\quad</math>

K must be equal to or larger than 1, or the horizontal asymptote will lower.

2) To change the y-intercept and to ensure it stays between 0 and K, we shifted the graph to the right. To do this we added any constant h to the the variable t. rewriting the equation:

<math>P(t)=\frac{K}{1+e^{(-t+h)}}\quad</math>

K can be any value from negative INF to positive INF

In the following graph we set K to 3.

'''Red''' = original graph

'''Green''' = Shifting of horizontal asymptote higher

'''Blue''' = Changing the y-intercept

[[File:Shifting of graph to the right.jpg]]

='''BONUS'''=

* Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical. (If you graph it, it should be quite clear).
Once you've played with the function enough, try to find an application of the graph to model something. It can be anything which starts at a value and then goes to another one (think for a population, it goes from 0 to it's carrying capacity). Explain what you are modelling and how you decide to attribute a numerical value to each of the 2 or 3 parameters that you researched just above. Then use the model to make a prediction. For example, if your model is suppose to describe a population for which you have its initial population and carrying capacity (potentially its rate of increase if you solved the bonus part), then use that data to make a prediction for the population in 20 years, or use the model to predict when will the population reach 95% of its carrying capacity).
When doing this last part, explain well where you're taking your data from (real data or imagined data), what it is that you're modelling and how you are doing the math to answer a predictive question.

'''<big>BONUS Solution</big>'''

In order to shift the slope of the graph, we must alter the t variable. By adding a coefficient in front of t, you can either increase the slope to almost one (m > 0), or decrease the slope (m < 0).

<math>P(t)=\frac{K}{1+e^{(-mt+h)}}\quad</math>

'''Red''' = original equation

'''Green''' = Heightened horizontal asymptote on right side and increased slope to near 1

[[File:Slope change.jpg]]

'''<big>Model</big>'''

You can use this function for any type of logistical growth, commonly applied to population growth (whether it be humans, bacteria, animal, or even tumor cells).

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 13

2011-01-27T06:55:58Z

DeborahMa: Created page with "='''<big>Homework 13</big>'''= Pick one of the topic offered below and then explain in your own words what it means that these concepts work on a logarithmic scal..."

='''<big>Homework 13</big>'''=

Pick one of the topic offered below and then explain in your own words what it means that these concepts work on a logarithmic scale. Create a wiki page with all your explanations. The length of that page is up to you, but it should feel like the work of four people thinking about a topic and trying to make sense of it. If you drafted something and would like some comments (within 24 hours), send me an email and a link where to look at, I'll post comments).
Topics:
* Decibels
* Richter magnitude scale
* Brightness of stars
* pH

If you have another idea, please send me an email to confirm your choice of topic.

Course:MATH110/Archive/2010-2011/003/Teams/Geneve

2011-01-27T06:52:05Z

DeborahMa:

{{
Infobox MATH110 Teams
| team name = Geneve
| member 1 = Agnes Luong
| member 2 = Deborah Ma
| member 3 = Megan Bontogon
| member 4 = Stephanie Urness
}}
In workshop J.

'''<big><big>Homework 11</big></big>'''

[[/Course:Math110/003/Teams/Geneve/Homework11/]]

<big><big>'''Homework 12'''</big></big>

[[Course:MATH110/003/Teams/Geneve/Homework_12]]

<big><big>'''Homework 13'''</big></big>

[[Course:MATH110/003/Teams/Geneve/Homework_13]]

'''<big><big>Word of the day</big></big>'''

Agnes -

Deborah - ''Motivation''

Megan -

Stephanie -

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-26T03:08:55Z

DeborahMa:

='''<big>Homework 12</big>'''=

'''<big><big>Team Problem</big></big>'''

Start with the function
:<math>P(t) = \frac{1}{1+e^{-t}}</math>

Your goal is to modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:
:*Change the height of the horizontal asymptote on the right, we'll denote it by K. \
:*Change the y-intercept to any number between 0 and K
BONUS (just the point below, not what comes after)
:*Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical. (If you graph it, it should be quite clear).

Once you've played with the function enough, try to find an application of the graph to model something. It can be anything which starts at a value and then goes to another one (think for a population, it goes from 0 to it's carrying capacity). Explain what you are modelling and how you decide to attribute a numerical value to each of the 2 or 3 parameters that you researched just above. Then use the model to make a prediction. For example, if your model is suppose to describe a population for which you have its initial population and carrying capacity (potentially its rate of increase if you solved the bonus part), then use that data to make a prediction for the population in 20 years, or use the model to predict when will the population reach 95% of its carrying capacity).
When doing this last part, explain well where you're taking your data from (real data or imagined data), what it is that you're modelling and how you are doing the math to answer a predictive question.

'''<big><big>Solution</big></big>'''

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-26T03:08:37Z

DeborahMa:

='''<big>Homework 12</big>'''=

''<big><big>Team Problem</big></big>'''

Start with the function
:<math>P(t) = \frac{1}{1+e^{-t}}</math>

Your goal is to modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:
:*Change the height of the horizontal asymptote on the right, we'll denote it by K. \
:*Change the y-intercept to any number between 0 and K
BONUS (just the point below, not what comes after)
:*Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical. (If you graph it, it should be quite clear).

Once you've played with the function enough, try to find an application of the graph to model something. It can be anything which starts at a value and then goes to another one (think for a population, it goes from 0 to it's carrying capacity). Explain what you are modelling and how you decide to attribute a numerical value to each of the 2 or 3 parameters that you researched just above. Then use the model to make a prediction. For example, if your model is suppose to describe a population for which you have its initial population and carrying capacity (potentially its rate of increase if you solved the bonus part), then use that data to make a prediction for the population in 20 years, or use the model to predict when will the population reach 95% of its carrying capacity).
When doing this last part, explain well where you're taking your data from (real data or imagined data), what it is that you're modelling and how you are doing the math to answer a predictive question.

'''<big><big>Solution</big></big>'''

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-26T03:03:45Z

DeborahMa:

'''<big><big>Team Problem</big></big>'''

Start with the function
:<math>P(t) = \frac{1}{1+e^{-t}}</math>

Your goal is to modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:
:*Change the height of the horizontal asymptote on the right, we'll denote it by K. \
:*Change the y-intercept to any number between 0 and K
BONUS (just the point below, not what comes after)
:*Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical. (If you graph it, it should be quite clear).

Once you've played with the function enough, try to find an application of the graph to model something. It can be anything which starts at a value and then goes to another one (think for a population, it goes from 0 to it's carrying capacity). Explain what you are modelling and how you decide to attribute a numerical value to each of the 2 or 3 parameters that you researched just above. Then use the model to make a prediction. For example, if your model is suppose to describe a population for which you have its initial population and carrying capacity (potentially its rate of increase if you solved the bonus part), then use that data to make a prediction for the population in 20 years, or use the model to predict when will the population reach 95% of its carrying capacity).
When doing this last part, explain well where you're taking your data from (real data or imagined data), what it is that you're modelling and how you are doing the math to answer a predictive question.

'''<big><big>Solution</big></big>'''

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-26T03:03:04Z

DeborahMa:

Start with the function
:<math>P(t) = \frac{1}{1+e^{-t}}</math>

Your goal is to modify the function so that we can use it to model a real-life problem. We want to be able to control the following things:
:*Change the height of the horizontal asymptote on the right, we'll denote it by K. \
:*Change the y-intercept to any number between 0 and K
BONUS (just the point below, not what comes after)
:*Change the slope of the curved part. Find a way so that the slope can go from very close to zero to almost vertical. (If you graph it, it should be quite clear).

Once you've played with the function enough, try to find an application of the graph to model something. It can be anything which starts at a value and then goes to another one (think for a population, it goes from 0 to it's carrying capacity). Explain what you are modelling and how you decide to attribute a numerical value to each of the 2 or 3 parameters that you researched just above. Then use the model to make a prediction. For example, if your model is suppose to describe a population for which you have its initial population and carrying capacity (potentially its rate of increase if you solved the bonus part), then use that data to make a prediction for the population in 20 years, or use the model to predict when will the population reach 95% of its carrying capacity).
When doing this last part, explain well where you're taking your data from (real data or imagined data), what it is that you're modelling and how you are doing the math to answer a predictive question.

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-26T03:02:13Z

DeborahMa:

'''<big><big>Team Problem</big></big>'''

Start with the function
:<math>P(t) = \frac{1}{1+e^{-t}}</math>

'''<big><big>Solution</big></big>'''

File:B532d798ec926e169adf3c1a55f0cdf0.png

2011-01-26T02:58:11Z

DeborahMa:

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 12

2011-01-26T02:56:19Z

DeborahMa: Created page with "A"

Course:MATH110/Archive/2010-2011/003/Teams/Geneve

2011-01-26T02:52:50Z

DeborahMa:

{{
Infobox MATH110 Teams
| team name = Geneve
| member 1 = Agnes Luong
| member 2 = Deborah Ma
| member 3 = Megan Bontogon
| member 4 = Stephanie Urness
}}
In workshop J.

'''<big><big>Homework 11</big></big>'''

[[/Course:Math110/003/Teams/Geneve/Homework11/]]

<big><big>'''Homework 12'''</big></big>

[[Course:MATH110/003/Teams/Geneve/Homework_12]]

'''<big><big>Word of the day</big></big>'''

Agnes -

Deborah - ''Motivation''

Megan -

Stephanie -

Course:MATH110/Archive/2010-2011/003/Teams/Geneve

2011-01-26T02:48:11Z

DeborahMa:

{{
Infobox MATH110 Teams
| team name = Geneve
| member 1 = Agnes Luong
| member 2 = Deborah Ma
| member 3 = Megan Bontogon
| member 4 = Stephanie Urness
}}
In workshop J.

[[/Course:Math110/003/Teams/Geneve/Homework11/]]

'''<big><big>Word of the day</big></big>'''

Agnes -

Deborah - ''Motivation''

Megan -

Stephanie -

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T14:26:25Z

DeborahMa: /* Model */

='''<big>Homework 11</big>'''=
=='''Model'''==
:At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

:When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

:We then can determine the equation of our model using slope-intercept form (y=mx+b).

:In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

:Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

===='''<big>What does our model predict for a production of 150 items?</big>'''====

:Since x= # of items produced, x=150. Therefore our model predicts:

:y= 7(150)-40

:y= 1050-40

:y= 1010

:Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

:Using our model we found that the average cost per item increases as production levels increase.

:Since using the original values we were given (20,100), the average cost per item is $5.

:Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

<big>1)</big><big> '''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

[[File:CYCLEOFFIXEDCOSTS.jpg|400px|thumb|left|'''In this diagram, we see that as companies increase their production, this increase in production will lower the price and fixed cost which will in turn make more affordable products for consumers which will lead to higher market shares and revenue and more money to spend on production from the profits made and the cycle continues.''']]

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

[[File:330px-Economies of scale.PNG|400px|thumb|left|'''In this illustration you can see 'Output' on the x-axis and 'Average cost' on the y-axis. The long run average cost is depicted as the the rate of change as output increases and average cost is lowered. At Q outputs, your average cost is C, but when you increase your output to Q2, your average cost is C1 (economies of scale), therefore average cost continues to decrease as output increases to a certain point; approximately Q2, and then the more you make afterwards, will result in higher average cost (diseconomies of scale).''']]

:For example, larger companies have purchasing power to get better deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

[[File:Diseconomiesofscale.gif|400px|thumb|left|'''This is another illustration of the economies and diseconomies of scale. Economies of scale: when an increase in output leads to lower average cost (AC) and when to a certain point (Q* in this illustration), any further increase in output will lead to a higher AC.''']]

<big>2)</big> '''''<big>Economic production quantity</big>'''''
:Economic Production Quantity model (also known as the EPQ model) determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. This method is an extension of the Economic Order Quantity model (also known as the EOQ model). The difference between these two methods is that the EPQ model assumes the company will produce its own quantity or the parts are going to be shipped to the company while they are being produced, therefore the orders are available or received in an incrementally manner while the products are being produced. While the EOQ model assumes the order quantity arrives complete and immediately after ordering, meaning that the parts are produced by another company and are ready to be shipped when the order is placed.

:EPQ only applies where the demand for a product is constant over the year and that each new order is delivered/produced incrementally when the inventory reaches zero. There is a fixed cost charged for each order placed, regardless of the number of units ordered. There is also a holding or storage cost for each unit held in storage (sometimes expressed as a percentage of the purchase cost of the item).

:We want to determine the optimal number of units of the product to order so that we minimize the total cost associated with the purchase, delivery and storage of the product

[[File:EPQ Graph.jpg|400px|thumb|left|'''This is the Economic Production Quantity Model (EPQ model). This graph illustrates the total cost, the holding cost and the set up cost. On the x-axis, we have "Order quantity" and on the y-axis we have "Annual cost". This graph helps to determine the optimal number of units of the product to order so that we minimize the total cost associated with the purchase, delivery and storage of the product.''']]

File:EPQ Graph.jpg

2011-01-19T14:23:09Z

DeborahMa:

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T14:21:14Z

DeborahMa: /* Examples of Other Models */

='''<big>Homework 11</big>'''=
=='''Model'''==
:At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

:When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

:We then can determine the equation of our model using slope-intercept form (y=mx+b).

:In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

:Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

===='''<big>What does our model predict for a production of 150 items?</big>'''====

:Since x= # of items produced, x=150. Therefore our model predicts:

:y= 7(150)-40

:y= 1050-40

:y= 1010

:Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

:Using our model we found that the average cost per item increases as production levels increase.

:Since using the original values we were given (20,100), the average cost per item is $5.

:Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

<big>1)</big><big> '''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

[[File:CYCLEOFFIXEDCOSTS.jpg|400px|thumb|left|'''In this diagram, we see that as companies increase their production, this increase in production will lower the price and fixed cost which will in turn make more affordable products for consumers which will lead to higher market shares and revenue and more money to spend on production from the profits made and the cycle continues.''']]

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

[[File:330px-Economies of scale.PNG|400px|thumb|left|'''In this illustration you can see 'Output' on the x-axis and 'Average cost' on the y-axis. The long run average cost is depicted as the the rate of change as output increases and average cost is lowered. At Q outputs, your average cost is C, but when you increase your output to Q2, your average cost is C1 (economies of scale), therefore average cost continues to decrease as output increases to a certain point; approximately Q2, and then the more you make afterwards, will result in higher average cost (diseconomies of scale)''']]

:For example, larger companies have purchasing power to get better deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

[[File:Diseconomiesofscale.gif|400px|thumb|left|'''This is another illustration of the economies and diseconomies of scale. Economies of scale: when an increase in output leads to lower average cost (AC) and when to a certain point (Q* in this illustration), any further increase in output will lead to a higher AC''']]

<big>2)</big> '''''<big>Economic production quantity</big>'''''
:Economic Production Quantity model (also known as the EPQ model) determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. This method is an extension of the Economic Order Quantity model (also known as the EOQ model). The difference between these two methods is that the EPQ model assumes the company will produce its own quantity or the parts are going to be shipped to the company while they are being produced, therefore the orders are available or received in an incrementally manner while the products are being produced. While the EOQ model assumes the order quantity arrives complete and immediately after ordering, meaning that the parts are produced by another company and are ready to be shipped when the order is placed.

:EPQ only applies where the demand for a product is constant over the year and that each new order is delivered/produced incrementally when the inventory reaches zero. There is a fixed cost charged for each order placed, regardless of the number of units ordered. There is also a holding or storage cost for each unit held in storage (sometimes expressed as a percentage of the purchase cost of the item).

:We want to determine the optimal number of units of the product to order so that we minimize the total cost associated with the purchase, delivery and storage of the product

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T14:10:28Z

DeborahMa: /* Model */

='''<big>Homework 11</big>'''=
=='''Model'''==
:At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

:When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

:We then can determine the equation of our model using slope-intercept form (y=mx+b).

:In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

:Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

===='''<big>What does our model predict for a production of 150 items?</big>'''====

:Since x= # of items produced, x=150. Therefore our model predicts:

:y= 7(150)-40

:y= 1050-40

:y= 1010

:Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

:Using our model we found that the average cost per item increases as production levels increase.

:Since using the original values we were given (20,100), the average cost per item is $5.

:Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

* <big>'''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

[[File:CYCLEOFFIXEDCOSTS.jpg|400px|thumb|left|'''In this diagram, we see that as companies increase their production, this increase in production will lower the price and fixed cost which will in turn make more affordable products for consumers which will lead to higher market shares and revenue and more money to spend on production from the profits made and the cycle continues.''']]

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

[[File:330px-Economies of scale.PNG|400px|thumb|left|'''In this illustration you can see 'Output' on the x-axis and 'Average cost' on the y-axis. The long run average cost is depicted as the the rate of change as output increases and average cost is lowered. At Q outputs, your average cost is C, but when you increase your output to Q2, your average cost is C1 (economies of scale), therefore average cost continues to decrease as output increases to a certain point; approximately Q2, and then the more you make afterwards, will result in higher average cost (diseconomies of scale)''']]

:For example, larger companies have purchasing power to get better deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

[[File:Diseconomiesofscale.gif|400px|thumb|left|'''This is another illustration of the economies and diseconomies of scale. Economies of scale: when an increase in output leads to lower average cost (AC) and when to a certain point (Q* in this illustration), any further increase in output will lead to a higher AC''']]

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T14:05:48Z

DeborahMa: /* Model */

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T13:57:04Z

DeborahMa: /* Homework 11 */

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T13:56:12Z

DeborahMa: /* Model */

=Homework 11=
=='''<big>Model</big>'''==
:At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

:When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

:We then can determine the equation of our model using slope-intercept form (y=mx+b).

:In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

:Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

===='''<big>What does our model predict for a production of 150 items?</big>'''====

:Since x= # of items produced, x=150. Therefore our model predicts:

:y= 7(150)-40

:y= 1050-40

:y= 1010

:Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

:Using our model we found that the average cost per item increases as production levels increase.

:Since using the original values we were given (20,100), the average cost per item is $5.

:Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

* <big>'''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

:For example, larger companies have purchasing power to get ebtter deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T13:54:53Z

DeborahMa: /* According to our model, what happens to the average cost per item as production levels increase? */

=Homework 11=
==Model==
At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

We then can determine the equation of our model using slope-intercept form (y=mx+b).

In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

===='''<big>What does our model predict for a production of 150 items?</big>'''====

:Since x= # of items produced, x=150. Therefore our model predicts:

:y= 7(150)-40

:y= 1050-40

:y= 1010

:Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

:Using our model we found that the average cost per item increases as production levels increase.

:Since using the original values we were given (20,100), the average cost per item is $5.

:Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

* <big>'''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

:For example, larger companies have purchasing power to get ebtter deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T13:54:30Z

DeborahMa: /* What does our model predict for a production of 150 items? */

=Homework 11=
==Model==
At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

We then can determine the equation of our model using slope-intercept form (y=mx+b).

In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

===='''<big>What does our model predict for a production of 150 items?</big>'''====

:Since x= # of items produced, x=150. Therefore our model predicts:

:y= 7(150)-40

:y= 1050-40

:y= 1010

:Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

Using our model we found that the average cost per item increases as production levels increase.

Since using the original values we were given (20,100), the average cost per item is $5.

Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

* <big>'''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

:For example, larger companies have purchasing power to get ebtter deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T13:53:08Z

DeborahMa: /* According to our model, what happens to the average cost per item as production levels increase? */

=Homework 11=
==Model==
At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

We then can determine the equation of our model using slope-intercept form (y=mx+b).

In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

====What does our model predict for a production of 150 items?====

Since x= # of items produced, x=150. Therefore our model predicts:

y= 7(150)-40

y= 1050-40

y= 1010

Therefore our model predicts that for a production of 150 items, it costs $1010.

===='''<big>According to our model, what happens to the average cost per item as production levels increase?</big>'''====

Using our model we found that the average cost per item increases as production levels increase.

Since using the original values we were given (20,100), the average cost per item is $5.

Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

* <big>'''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

:For example, larger companies have purchasing power to get ebtter deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

Course:MATH110/Archive/2010-2011/003/Teams/Geneve/Homework 11

2011-01-19T13:52:34Z

DeborahMa: /* Examples of Other Models */

=Homework 11=
==Model==
At the current production level of 20 items the cost is 100 items and the marginal cost is $7 per unit.

When creating a graph of this model we can say that the x-axis refers to the number of items, and the y-axis refers to the cost of production. The marginal cost per each item is $7 so we can say that the slope at (20,100) is equal to 7.

We then can determine the equation of our model using slope-intercept form (y=mx+b).

In order to solve for "b" we substitute y and x for the values (20,100). For "m" we substitute in the slope which is 7.

We get:
100= 7(20)+ b
100= 140 + b
b= -40

Since we know the value of "b" and "m" the equation of our model is: y= 7x-40 assuming y is greater than or equal to 20.

====What does our model predict for a production of 150 items?====

Since x= # of items produced, x=150. Therefore our model predicts:

y= 7(150)-40

y= 1050-40

y= 1010

Therefore our model predicts that for a production of 150 items, it costs $1010.

====According to our model, what happens to the average cost per item as production levels increase?====

Using our model we found that the average cost per item increases as production levels increase.

Since using the original values we were given (20,100), the average cost per item is $5.

Whereas the values we obtained for the production of 150 items (150,1010), the average cost per item is approx. $6.73

====<big>Examples of Other Models</big>====

* <big>'''''Economies of Scale'''''</big>
:'''Economies of Scale''' mean the increase in efficiency of production as the number of goods being produced increases. Typically, a company that achieves economies of scale lowers the average cost per unit through increased production since fixed costs are shared over an increased number of goods.
:'''"The more you buy, the more you save".'''

:Larger companies and firms often are able to produce work more cost-efficiently than smaller ones. Economy of scale is when anything that you produce helps save costs if the scale of operation increases.

:For example, larger companies have purchasing power to get ebtter deals from supplies and lower cost of manufacturing because bigger factor have lower costs per unit produced. Larger companies also have better logistics leading to lower distribution cost.Economics of scale do not necessarily happen because a company is bigger. For example, you can combine two completely unrelated businesses together which is likely to lead to a higher costs by adding more management levels and worse management because you reduce focus on each business.

:In retail stores, such as Superstore and Save-on-foods, the more orders of soft drinks the manufacturer receives, the more savings it makes, as it will in turn get cheaper prices for the materials it needs to produce its drinks (e.g. plastic, aluminium, sugar) as it will be buying them in larger quantities and receiving discounts, the manufacturing company in turn would give its customers cheaper prices for the more orders for drinks they make for this very reason, as they will gain the discounts, they can pass a saving onto their customers, making themselves stronger, a more respected company from its suppliers as it is buying in higher volumes and its turnover becomes higher. All these factors contribute to the benefits of economies of scale.

File:CYCLEOFFIXEDCOSTS.jpg

2011-01-19T13:45:09Z

DeborahMa:

File:330px-Economies of scale.PNG

2011-01-19T13:44:49Z

DeborahMa:

File:Economyofscale.gif

2011-01-19T13:44:26Z

DeborahMa:

File:Diseconomiesofscale.gif

2011-01-19T13:43:52Z

DeborahMa:

Thread:Course talk:MATH110/003/Math Forum/Web work 11/reply (3)

2011-01-18T22:50:22Z

DeborahMa: Reply to Webwork 11 - problem 11

I had the same problem with #11 too. Webwork doesn't seem to accept any statement that I input for the 4 blanks for Question #11.

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T07:26:48Z

DeborahMa:

[[File:MathStudentAnimation.gif|1000px|thumb|right|alt text]]

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

=Polynomial Long Division=

=== Definition of Polynomial Long Division ===
[[File:Provide a short definition of polynomial division as well as a summary of the theory behind polynomial division.pdf|150px|thumb|left|alt text]]

===How to Perform Polynomial Long Divison in Just 10 EASY STEPS===
[[File:pdfpd.pdf|150px|thumb|none]]

===Video Tutorial: How to Perform Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|150px|Five practice questions and tips]]

=== Usefulness of Polynomial Long Division in Other Problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|150px|thumb|none]]

=== Using Polynomial Long Division and Finding Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|150px|thumb|none|alt text]]

===Video Tutoral: Slant Asymptotes===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

'''''Solution'''''
[[File:Solution to Practice Problem 1.pdf|150px|thumb|none|alt text]]

2. <math>\frac{x^4-1}{x-1}</math>

'''''Solution'''''
[[File:Solution to Practice Problem 2.pdf|150px|thumb|none|alt text]]

===Video Tutorial: What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T07:25:03Z

DeborahMa: /* Definition of Polynomial Long Division */

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T06:55:24Z

DeborahMa: /* PRACTICE PROBLEMS */

[[File:MathStudentAnimation.gif|1000px|thumb|right|alt text]]

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

=== Definition of polynomial division ===
* Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. Polynomial division allows for a polynomial to be written in a divisor–quotient form which is often advantageous.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|150px|thumb|none]]

===Video Tutorial: How to do Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|150px|thumb|none]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|150px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|150px|thumb|none|alt text]]

===Video Tutoral: SLANT ASYMPTOTES===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===
[[File:Group8practice_problem.pdf|150px|thumb|none]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

'''''Solution'''''
[[File:Solution to Practice Problem 1.pdf|150px|thumb|none|alt text]]

2. <math>\frac{x^4-1}{x-1}</math>

'''''Solution'''''
[[File:Solution to Practice Problem 2.pdf|150px|thumb|none|alt text]]

===Video Tutorial: What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T06:55:02Z

DeborahMa:

[[File:MathStudentAnimation.gif|1000px|thumb|right|alt text]]

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

=== Definition of polynomial division ===
* Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. Polynomial division allows for a polynomial to be written in a divisor–quotient form which is often advantageous.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|150px|thumb|none]]

===Video Tutorial: How to do Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|150px|thumb|none]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|150px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|150px|thumb|none|alt text]]

===Video Tutoral: SLANT ASYMPTOTES===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===
[[File:Group8practice_problem.pdf|150px|thumb|none]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

'''''Solution'''''
[[File:Solution to Practice Problem 1.pdf|150px|thumb|none|alt text]]

2. <math>\frac{x^4-1}{x-1}</math>

'''''Solution'''''
[[File:Solution to Practice Problem 2.pdf|150px|thumb|none|alt text]]

===Video Tutorial: What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T06:52:03Z

DeborahMa:

[[File:MathStudentAnimation.gif|1000px|thumb|right|alt text]]

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

=== Definition of polynomial division ===
* Polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. Polynomial division allows for a polynomial to be written in a divisor–quotient form which is often advantageous.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|150px|thumb|none]]

===Video Tutorial: How to do Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|150px|thumb|none]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|150px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|150px|thumb|none|alt text]]

===Video Tutoral: SLANT ASYMPTOTES===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===
[[File:Group8practice_problem.pdf|150px|thumb|none]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

2. <math>\frac{x^4-1}{x-1}</math>

===PRACTICE PROBLEMS: SOLUTIONS===
1. [[File:Solution to Practice Problem 1.pdf|150px|thumb|none|alt text]]

2. [[File:Solution to Practice Problem 2.pdf|150px|thumb|none|alt text]]

===Video Tutorial: What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T04:28:46Z

DeborahMa:

[[File:MathStudentAnimation.gif|1000px|thumb|right|alt text]]

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|150px|thumb|none]]

===Video Tutorial: How to do Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|150px|thumb|none]]

=== Definition of polynomial division ===
[[File:Provide a short definition of polynomial division as well as a summary of the theory behind polynomial division.pdf|150px|thumb|none|Definition of polynomial division]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|150px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|150px|thumb|none|alt text]]

===Video Tutoral: SLANT ASYMPTOTES===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===
[[http://wiki.ubc.ca/images/3/37/Group8practice_problem.pdf]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

2. <math>\frac{x^4-1}{x-1}</math>

===PRACTICE PROBLEMS: SOLUTIONS===
1. [[File:Solution to Practice Problem 1.pdf|150px|thumb|none|alt text]]

2. [[File:Solution to Practice Problem 2.pdf|150px|thumb|none|alt text]]

===Video Tutorial: What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

File:MathStudentAnimation.gif

2010-12-03T04:25:44Z

DeborahMa:

Course:MATH110/Archive/2010-2011/003/Groups/Group 08

2010-12-03T04:24:34Z

DeborahMa:

{{Infobox MATH110 Groups
| group number = 8
| member 1 = [[User:DeborahMa|Deborah Ma]]
| member 2 = [[User:MartinPalanca|Martin Palanca]]
| member 3 = [[User:CassandraTravlos|Cassandra Travlos]]
| member 4 = [[User:JustineVallieres|Justine Vallieres]]
| member 5 = [[User:PhilipLauFaiWong|Philip Wong]]
| member 6 =
}}

[[File:Math sign.gif|500px|thumb|right|alt text]]

== Basic Skills Project ==

[[Course:MATH110/003/Groups/Group 08/Basic Skills Project|Basic Skills Project]]

== [[Course:MATH110/003/Groups/Group 08/GROUP 8 - Basic Skills Assignment HW|Group 8 - Basic Skills Assignment HW #5 - Due Oct 29]] ==

== [[Course:MATH110/003/Groups/Group_08/PROBLEM_SOLVING_QUESTIONS_1-25_HW4|PROBLEM SOLVING QUESTIONS 1-25 HW4]] ==

File:Math sign.gif

2010-12-03T04:20:05Z

DeborahMa:

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T04:10:00Z

DeborahMa:

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|150px|thumb|none]]

===Video Tutorial: How to do Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|150px|thumb|none]]

=== Definition of polynomial division ===
[[File:Provide a short definition of polynomial division as well as a summary of the theory behind polynomial division.pdf|150px|thumb|none|Definition of polynomial division]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|150px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|150px|thumb|none|alt text]]

===Video Tutoral: SLANT ASYMPTOTES===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===
[[http://wiki.ubc.ca/images/3/37/Group8practice_problem.pdf]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

2. <math>\frac{x^4-1}{x-1}</math>

===PRACTICE PROBLEMS: SOLUTIONS===
1. [[File:Solution to Practice Problem 1.pdf|150px|thumb|none|alt text]]

2. [[File:Solution to Practice Problem 2.pdf|150px|thumb|none|alt text]]

===Video Tutorial: What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T04:06:49Z

DeborahMa:

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|200px|thumb|none]]

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|200px|thumb|none]]

=== Definition of polynomial division ===
[[File:Provide a short definition of polynomial division as well as a summary of the theory behind polynomial division.pdf|200px|thumb|none|Definition of polynomial division]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|200px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|200px|thumb|none|alt text]]

===Video Tutoral: SLANT ASYMPTOTES===
{{#ev:youtube|X8EyevWmmrg|300}}
{{#ev:youtube|--vh9zgZZmQ|300}}

=== Practice Problems ===
[[http://wiki.ubc.ca/images/3/37/Group8practice_problem.pdf]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

2. <math>\frac{x^4-1}{x-1}</math>

===PRACTICE PROBLEMS: SOLUTIONS===
1. [[File:Solution to Practice Problem 1.pdf|200px|thumb|none|alt text]]

2. [[File:Solution to Practice Problem 2.pdf|200px|thumb|none|alt text]]

===How to do Polynomial Long Division===
{{#ev:youtube|l6_ghhd7kwQ|300}}
{{#ev:youtube|4e9ugZCc4rw|300}}

===What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|300}}

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T03:52:36Z

DeborahMa:

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|200px|thumb|none]]

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|200px|thumb|none]]

=== Definition of polynomial division ===
[[File:Provide a short definition of polynomial division as well as a summary of the theory behind polynomial division.pdf|200px|thumb|none|Definition of polynomial division]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|200px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|200px|thumb|none|alt text]]

=== Practice Problems ===
[[http://wiki.ubc.ca/images/3/37/Group8practice_problem.pdf]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

2. <math>\frac{x^4-1}{x-1}</math>

===PRACTICE PROBLEMS: SOLUTIONS===
1. [[File:Solution to Practice Problem 1.pdf|200px|thumb|none|alt text]]

2. [[File:Solution to Practice Problem 2.pdf|200px|thumb|none|alt text]]

===How to do Polynomial Long Division===
{{#ev:youtube|4e9ugZCc4rw|400}}

===What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|400}}

File:Solution to Practice Problem 2.pdf

2010-12-03T03:50:08Z

DeborahMa:

File:Solution to Practice Problem 1.pdf

2010-12-03T03:47:43Z

DeborahMa:

Course:MATH110/Archive/2010-2011/003/Groups/Group 08/Basic Skills Project

2010-12-03T03:41:42Z

DeborahMa:

=Group 8 Plan to Improve our Basic Skills=

As a group, we will contribute to the Basic Skills page on “polynomial division”. This is a section that not everyone in the group is comfortable with, however this will give us an opportunity to understand it, where those of us who do understand can help those in our group who do not. In the process of group teaching we will better be able to come up with multiple ways to explain how to do polynomial division in a hopefully comprehensive and simplified manner.

As a group we came up with a basic but effective plan to help others understand:

* Since the wiki pages are very useful resources we thought we could post a set of notes outlining the following in a section called “Basic Skills Notes” on the wiki:

* Firstly, we would provide a short definition of polynomial division that is simple enough for everyone to understand but also comprehensive, as well as a summary of the theory behind polynomial division.

* This will be followed by one simple practice example – where we will provide an explanation for each line or step in the work out process of the equation like we do in part 2 of the homework – this will also include useful tips and tricks

* After this simple example we will demonstrate another, harder, example with the same layout as the easy example (with the explanations for each step and tips and tricks)

* Next we will provide a few practice problems for everyone to try for themselves

* At the end of the set of notes we will have a summary box of all the useful tips and tricks in order to reinforce the information given above

* Then we will have a problem solving question where polynomial division would be used to solve the question in order to not only understand but also apply this process to a more complicated question

* Finally we will present a practice quiz for everyone to try out.

We as a group feel that this would be very useful to have up on the wiki because if every group does this for one of the basic skills topics then we can go online and print all these notes out. These notes will then let us understand and also practice lots of problems.

===How to Perform Polynomial Divison in Just 10 STEPS===
[[File:pdfpd.pdf|200px|thumb|none]]

=== Usefulness of polynomial long division in other problems ===
[[File:Find where can polynomial long division be useful in other problems.pdf|200px|thumb|none]]

=== Definition of polynomial division ===
[[File:Provide a short definition of polynomial division as well as a summary of the theory behind polynomial division.pdf|200px|thumb|none|Definition of polynomial division]]

=== Five Practice Questions and Tips ===
[[File:4_Practice_Questions_and_Useful_Tips.pdf|thumb|none|200px|Five practice questions and tips]]

=== Vertical and Slant Asymptotes ===
[[File:Polynomial_Long_Division_and_Finding_Vertical_and_Slant_Asymptotes.pdf‎|200px|thumb|none|alt text]]

=== Practice Problems ===
[[http://wiki.ubc.ca/images/3/37/Group8practice_problem.pdf]]

===PRACTICE PROBLEMS===
1. <math>{3x^3-x^2+x-2}\div{x+2}</math>

2. <math>\frac{x^4-1}{x-1}</math>

===How to do Polynomial Long Division===
{{#ev:youtube|4e9ugZCc4rw|400}}

===What to do if there's a MISSING TERM in your polynomial?===
{{#ev:youtube|BWCI0pc2bDQ|400}}

===STEP BY STEP