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course Phy 232
Question: `q001. If you are earning money at the rate of 8 dollars / hour and work for 4 hours, how much money do you make during this time? Answer in such a way as to explain your reasoning as fully as possible. A solution to this problem appears several lines below, but enter your own solution before you look at the given solution.4*8=32
32 dollars
confidence rating #$&*: 3
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Self-critique: OK
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Question: `q002. If you work 12 hours and earn $168, then at what rate, in dollars / hour, were you making money?
168/12=14
$14 an hour
confidence rating #$&*: 3
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Self-critique: OK
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Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.
72/8=9
9 hours
Confidence:3
Self-critique: OK
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Question: `q004. Calculate (8 + 3) * 5 and 8 + 3 * 5, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
(8+3)=11
11*5=55
(8+3)*5=55
3*5=15
15+8=22
8+3*5=22
Confidence:3
Self-critique=OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution: 2^4=16
16*3=48
(2^4)*3=48
4*3=12
2^12=4096
2^(4*3)=4096
confidence rating #$&*:
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Self-critique (if necessary):OK
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Question: `q006. Calculate 3 * 5 - 4 * 3 ^ 2 and 3 * 5 - (4 * 3)^2 according to the standard order of operations, indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results.
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Your solution: 3^2=9
4*9=36
3*5=15
15-36=-21
3*5-4*3^2=-21
3*5=15
(4*3)^2=144
15-144=-129
confidence rating #$&*:
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Self-critique (if necessary):OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2
-1
0
1
2
Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
x y
-2 -1 2(-2)+3=-1
-1 1 2(-1)+3=1
0 3 2(0)+3=3
1 5 2(1)+3=5
2 7 2(2)+3=7
This graph is a linear graph.
confidence rating #$&*:
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Self-critique Rating:OK
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Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2
-1
0
1
2
Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
x y
-2 7 (-2)^2+3=7
-1 4 (-1)^2+3=4
0 3 (0)^2+3=4
1 4 (1)^2+3=4
2 7 (2)^2+3=7
This graph is a quadratic function
confidence rating #$&*:
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Self-critique Rating:OK
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1
2
3
4
Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
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Your solution:
x y
1 5 2^1+3=5
2 7 2^2+3=7
3 11 2^3+3=11
4 19 2^4+3=19
This graph is a exponential function.
confidence rating #$&*:
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Self-critique Rating:OK
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Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution:
The number is the same. Anything divided by one is itself much like anything multiplied by one is itself.
confidence rating #$&*:
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Self-critique Rating:OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution: The number is smaller than it was before. 2/4 is one half and 3/9 is three.
####: More detail in my answer examples
36/2 = 18. Now 3 is bigger than 2, and
36 / 3 = 12. The quotient got smaller. Now 4 is bigger than 3, and
36 / 4 = 9. The quotient got smaller again. Let's skip 5 because it doesn't divide evenly into 36.
36 / 6 = 4. Again we divided by a larger number and the quotient was smaller.
confidence rating #$&*:
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Self-critique Rating:OK
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Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
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Your solution: The result is greater than the original. 2/.5 is 4 and 6/.1 is 60
confidence rating #$&*:
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Self-critique Rating:OK
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Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
This doesn't mean that you did a bad job. If you got most of the 'answers' right, you did fine.
However, in order to better understand the process, you are asked here to go back and find something in one of the given solutions that you did not address in your solution, and insert a self-critique. You should choose something that isn't trivial to you--something you're not 100% sure you understand.
If you can't find anything, you can indicate this below, and the instructor will point out something and request a response (the instructor will select something reasonable, but will then expect a very good and complete response). However it will probably be less work for you if you find something yourself.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
####: More detail in my answer examples
36/2 = 18. Now 3 is bigger than 2, and
36 / 3 = 12. The quotient got smaller. Now 4 is bigger than 3, and
36 / 4 = 9. The quotient got smaller again. Let's skip 5 because it doesn't divide evenly into 36.
36 / 6 = 4. Again we divided by a larger number and the quotient was smaller.
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I won't ask you to resubmit this file, but in the future you need to submit a complete version of the document, with nothing deleted. Insert your answers in the appropriate place, but delete nothing.
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