q a rates

course Mth 164

I found this file that I had worked on last week. It looks like there might be part or all of qa asst 3 in there also, because I recognize some of the questions from what I worked on last night. I'm not sure how that happened. I have a qa asst 3 saved on this computer in another file and one at home that has all the questions answered because the questions did not skip when I worked on it at home.

w?????????????assignment #001

001. Rates

qa rates

01-26-2009

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08:47:19

`q001. You should copy and paste these instructions to a word processor for reference. However you can always view them, as well as everything else that has appeared in this box, by clicking the 'Display Everything' button.

1. For the next question or answer, you click on 'Next Question / Answer' button above the box at top left until a question has been posed. Once a question has been posed you are to answer before you click again on this button.

2. Before clicking for an answer, type your best answer to the current question into the box to the right, then clip on the 'Enter Answer' button.

3. After entering your answer you will click on 'Next Question / Answer' to view the answer to the question. Do not tamper with the information displayed in the left-hand box.

4. If your answer was incorrect, incomplete or would otherwise require revision, you will enter a self-critique. If you learned something from the answer, you need to restate it in your own words in order to reinforce your learning. If there is something you feel you should note for future reference, you should make a note in your own words. Go to the response box (the right-hand box) and type in a self-critique and/or notes, as appropriate. Do not copy and paste anything from the left-hand box, since that information will be saved in any case.

5. If you wish to save your response to your Notes file you may choose to click on the 'Save As Notes' button rather than the 'Enter Answer' button. Doing so will save your work for your future reference. Your work will be saved in a Notes file in the c:\vhmthphy folder. The title of the Notes file will also include the name you gave when you started the program.

6. After clicking either the 'Enter Response' or the 'Save as Notes' button, click on 'Next Question / Answer' and proceed in a similar manner.

In the right-hand box briefly describe your understanding of these instructions, then click 'Enter Answer'.

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RESPONSE -->

confidence assessment: 0

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08:47:51

`q001. You should copy and paste these instructions to a word processor for reference. However you can always view them, as well as everything else that has appeared in this box, by clicking the 'Display Everything' button.

1. For the next question or answer, you click on 'Next Question / Answer' button above the box at top left until a question has been posed. Once a question has been posed you are to answer before you click again on this button.

2. Before clicking for an answer, type your best answer to the current question into the box to the right, then clip on the 'Enter Answer' button.

3. After entering your answer you will click on 'Next Question / Answer' to view the answer to the question. Do not tamper with the information displayed in the left-hand box.

4. If your answer was incorrect, incomplete or would otherwise require revision, you will enter a self-critique. If you learned something from the answer, you need to restate it in your own words in order to reinforce your learning. If there is something you feel you should note for future reference, you should make a note in your own words. Go to the response box (the right-hand box) and type in a self-critique and/or notes, as appropriate. Do not copy and paste anything from the left-hand box, since that information will be saved in any case.

5. If you wish to save your response to your Notes file you may choose to click on the 'Save As Notes' button rather than the 'Enter Answer' button. Doing so will save your work for your future reference. Your work will be saved in a Notes file in the c:\vhmthphy folder. The title of the Notes file will also include the name you gave when you started the program.

6. After clicking either the 'Enter Response' or the 'Save as Notes' button, click on 'Next Question / Answer' and proceed in a similar manner.

In the right-hand box briefly describe your understanding of these instructions, then click 'Enter Answer'.

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RESPONSE -->

could not copy and paste instructions

confidence assessment:

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08:48:09

Your answer has been noted. Enter 'ok' in the Response Box and click on Enter Response, then click on Next Question/Answer for the first real question.

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RESPONSE -->

ok

confidence assessment: 0

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08:55:29

`q002. Note that there are 10 questions in this assignment. The questions are of increasing difficulty--the first questions are fairly easy but later questions are very tricky. The main purposes of these exercises are to refine your thinking about rates, and to see how you process challenging information. Continue as far as you can until you are completely lost. Students who are prepared for the highest-level math courses might not ever get lost.

If you make $50 in 5 hr, then at what rate are you earning money?

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RESPONSE -->

50/5 = $10/hr

confidence assessment: 3

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09:09:14

Most people will very quickly see that we need to divide $60,000 by 12 months, giving us 60,000 dollars / (12 months) = 5000 dollars / month. Note that again we have found a time rate, dividing the accumulated quantity by the time required to accumulate it.

You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.

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RESPONSE -->

Again, the problem was skipped and I didn't see it

confidence assessment: 0

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09:18:55

`q004. Suppose that the $60,000 is made in a year by a small business. Would be more appropriate to say that the business makes $5000 per month, or that the business makes an average of $5000 per month?

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RESPONSE -->

It would be more appropriate to say that the business makes $60000 a year because you don't know how much money the business made each month.

confidence assessment: 3

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09:20:10

`q006. If you use 60 gallons of gasoline on a 1200 mile trip, then at what average rate are you using gasoline, with respect to miles traveled?

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RESPONSE -->

question skipped - I couldn't see it to answer it

confidence assessment: 0

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09:20:59

`q008. In a study of how lifting strength is influenced by various ways of training, a study group was divided into 2 subgroups of equally matched individuals. The first group did 10 pushups per day for a year and the second group did 50 pushups per day for year. At the end of the year to lifting strength of the first group averaged 147 pounds, while that of the second group averaged 162 pounds. At what average rate did lifting strength increase per daily pushup?

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RESPONSE -->

confidence assessment:

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09:21:32

`q008. In a study of how lifting strength is influenced by various ways of training, a study group was divided into 2 subgroups of equally matched individuals. The first group did 10 pushups per day for a year and the second group did 50 pushups per day for year. At the end of the year to lifting strength of the first group averaged 147 pounds, while that of the second group averaged 162 pounds. At what average rate did lifting strength increase per daily pushup?

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RESPONSE -->

question disappeared before I had a chance to answer it !

confidence assessment:

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09:22:01

The runner traveled 100 meters between the two positions, and required 10 seconds to do so. The average rate at which the runner was covering distance was therefore 100 meters / (10 seconds) = 10 meters / second. Again this is an average rate; at different positions in his stride the runner would clearly be traveling at slightly different speeds.

You need to make note of anything in the given solution that you didn't understand when you solved the problem. If new ideas have been introduced in the solution, you need to note them. If you notice an error in your own thinking then you need to note that. In your own words, explain anything you didn't already understand and save your response as Notes.

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RESPONSE -->

didn't see problem

confidence assessment: 0

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09:23:56

`q011. During a race, a runner passes the 100-meter mark moving at 10 meters / second, and the 200-meter mark moving at 9 meters / second. What is your best estimate of how long it takes the runner to cover the 100 meter distance?

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RESPONSE -->

covered 100 meters at 10/meters/sec.

Is the race 100 meters or 1000 meters ?

(question doesn't seem to make sense)

confidence assessment: 1

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assignment #002

002. Describing Graphs

qa initial problems

01-26-2009

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assignment #003

003. PC1 questions

qa initial problems

01-26-2009

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10:21:10

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RESPONSE -->

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10:24:32

`q001 A straight line connects the points (3, 5) and (7, 17), while another straight line continues on from (7, 17) to the point (10, 29). Which line is steeper and on what basis to you claim your result?

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RESPONSE -->

the (7,17) (10, 29) line is steeper because the

slope is 4

confidence assessment: 3

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10:27:59

In order for the expression to be zero we must have 3x-6 = 0 or x+4=0 or x^2-4=0.

3x-6 = 0 is rearranged to 3x = 6 then to x = 6 / 3 = 2. So when x=2, 3x-6 = 0 and the entire product (3x - 6) * (x + 4) * (x^2 - 4) must be zero.

x+4 = 0 gives us x = -4. So when x=-4, x+4 = 0 and the entire product (3x - 6) * (x + 4) * (x^2 - 4) must be zero.

x^2-4 = 0 is rearranged to x^2 = 4 which has solutions x = + - `sqrt(4) or + - 2. So when x=2 or when x = -2, x^2 - 4 = 0 and the entire product (3x - 6) * (x + 4) * (x^2 - 4) must be zero.

We therefore see that (3x - 6) * (x + 4) * (x^2 - 4) = 0 when x = 2, or -4, or -2. These are the only values of x which can yield zero.**

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RESPONSE -->

skipped question 2 - these programs always skip question 2 !

self critique assessment: 0

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10:34:32

`q004. One straight line segment connects the points (3,5) and (7,9) while another connects the points (10,2) and (50,4). From each of the four points a line segment is drawn directly down to the x axis, forming two trapezoids. Which trapezoid has the greater area? Try to justify your answer with something more precise than, for example, 'from a sketch I can see that this one is much bigger so it must have the greater area'.

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RESPONSE -->

question 3 was also skipped

4. Just the distance between the line segments would show that the second trapezoid has the greater area - 50-10 =40.

confidence assessment: 2

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10:36:36

Your sketch should show that while the first trapezoid averages a little more than double the altitude of the second, the second is clearly much more than twice as wide and hence has the greater area.

To justify this a little more precisely, the first trapezoid, which runs from x = 3 to x = 7, is 4 units wide while the second runs from x = 10 and to x = 50 and hence has a width of 40 units. The altitudes of the first trapezoid are 5 and 9,so the average altitude of the first is 7. The average altitude of the second is the average of the altitudes 2 and 4, or 3. So the first trapezoid is over twice as high, on the average, as the first. However the second is 10 times as wide, so the second trapezoid must have the greater area.

This is all the reasoning we need to answer the question. We could of course multiply average altitude by width for each trapezoid, obtaining area 7 * 4 = 28 for the first and 3 * 40 = 120 for the second. However if all we need to know is which trapezoid has a greater area, we need not bother with this step.

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RESPONSE -->

I did not take into account the altitude, even though I got the correct answer. Since the graph was going to be so big, and the directions said not to just look at the graph and say it was bigger, I just didn't graph it. This could have been a trick question !

self critique assessment: 1

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11:22:20

* `q005. Sketch graphs of y = x^2, y = 1/x and y = `sqrt(x) [note: `sqrt(x) means 'the square root of x'] for x > 0. We say that a graph increases if it gets higher as we move toward the right, and if a graph is increasing it has a positive slope. Explain which of the following descriptions is correct for each graph:

As we move from left to right the graph increases as its slope increases.

As we move from left to right the graph decreases as its slope increases.

As we move from left to right the graph increases as its slope decreases.

As we move from left to right the graph decreases as its slope decreases.

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RESPONSE -->

y= x^2 not sure of the slope

y = 1/x not sure of slope

y = sq. rt of x has a positive slope

self critique assessment: 1

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12:14:20

For x = 1, 2, 3, 4:

The function y = x^2 takes values 1, 4, 9 and 16, increasing more and more for each unit increase in x. This graph therefore increases, as you say, but at an increasing rate.

The function y = 1/x takes values 1, 1/2, 1/3 and 1/4, with decimal equivalents 1, .5, .33..., and .25. These values are decreasing, but less and less each time. The decreasing values ensure that the slopes are negative. However, the more gradual the decrease the closer the slope is to zero. The slopes are therefore negative numbers which approach zero.

Negative numbers which approach zero are increasing. So the slopes are increasing, and we say that the graph decreases as the slope increases.

We could also say that the graph decreases but by less and less each time. So the graph is decreasing at a decreasing rate.

For y = `sqrt(x) we get approximate values 1, 1.414, 1.732 and 2. This graph increases but at a decreasing rate.

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RESPONSE -->

did not make a table

self critique assessment: 0

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The programs don't skip questions. They do sometimes end ungracefully. There are some (rare) problems with sequencing of questions, but that doesn't happen on the q_a_initial_problems. Sometimes the explanations could be improved.

However this and other programs otherwise have run flawlessly for students literally thousands of times. It's not impossible that some computer glitch has occurred, but based on numerous responses I've gotten from students over several years it seems unlikely.

The sequencing of the necessary clicks and entries is defined in the typewriter notation exercises, which you appear to have run correctly. This is nevertheless sometimes a point of confusion early in the course. See if the following helps:

&#To run the program correctly you click on the Next Question/Solution button (top left), enter your response in the Answer box (the box at top right), click on the Enter Response button (above the top right box), then again on the Next Question/Solution botton (top left) to see the solution, and finally enter your response or self-critique in the Answer box and click on Enter Response.

You then start the process over with the next question, clicking on the Next Question/Solution button at top left, etc.

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