#$&*
course Mth 163
June 1, 6:00pm
Question: `q003. If you are earning 8 dollars / hour, how long will it take you to earn $72? The answer may well be obvious, but explain as best you can how you reasoned out your result.YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: (type in your solution starting in the next line)
It will take 9 hours because 72 divided by 8 is 9.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: OK
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Self-critique rating: 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.
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Your solution: The answer is 55 because (8+3) must be done first, which is 11. Then 11 multiplied by 5 is 55. The next problem is 23 because 3x5 must be done first which is 15. Then 8 is added which equals 23.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: OK
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Self-critique rating: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
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Your solution: The first problem is equal to 48 because 2^4 is equal to 16 and 16 times 3 is 48. The second problem is equal to 4096 because the operation in the parenthesis must be done first, so 4 times 3 equals 12. Then 2 raised to the 12th power is 4096.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: OK
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Self-critique rating: 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.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The answer to the first problem is -21 because the exponent must be taken care of first, which equals 9. 3 times 5 equals 15. 15 - 36 equals -21. The answer to the second problem is -129 because 4 times 3 must be done first, which makes it 3 * 5 - (12)^2. Then the exponent operation must be performed so it equals 3 * 5 - 144. 15- 144 equals -129.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critique: OK
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Self-critique rating: OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When x = -2, y is -1 because 2 times -2 is -4 and -4 plus 3 is -1.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 -1
-1 1
0 3
1 5
2 7
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did. The graph would be in a straight line, passing through the points (-2, -1), (-1, 1) etc. This would resemble the linear graph.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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.
Y for x= -2 would be 7 because -2 times itself is 4 and 4 plus 3 is 7.
• 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 7
-1 4
0 3
1 4
2 7
• 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.
Your solution: The graph that these points make curves upward and the graph that it most resembles is that of a parabola because it curves upward symmetrically.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique Rating: OK
*********************************************
Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
The result is 5 because 2 raised to the first power is 2 and 2 plus 3 is 5.
• Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1 5
2 7
3 11
4 19
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Your solution: These points form a graph that starts at point (1, 5) and then continues to rise. The graph that matches this is the exponential graph because it rises from left to right as well.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be the original number because if you divide a number by 1 it is always the same positive number.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result will always be less than the original number because it is breaking it up into smaller parts.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
*********************************************
Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
*********************************************
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
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When x = -2, y is -1 because 2 times -2 is -4 and -4 plus 3 is -1.
• 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
-1 1
0 3
1 5
2 7
• 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. The graph would be in a straight line, passing through the points (-2, -1), (-1, 1) etc. This would resemble the linear graph.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
Y for x= -2 would be 7 because -2 times itself is 4 and 4 plus 3 is 7.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 7
-1 4
0 3
1 4
2 7
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Your solution: The graph that these points make curves upward and the graph that it most resembles is that of a parabola because it curves upward symmetrically.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique Rating: OK
*********************************************
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.
The result is 5 because 2 raised to the first power is 2 and 2 plus 3 is 5.
• 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 5
2 7
3 11
4 19
• 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.
Your solution: These points form a graph that starts at point (1, 5) and then continues to rise. The graph that matches this is the exponential graph because it rises from left to right as well.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be the original number because if you divide a number by 1 it is always the same positive number.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result will always be less than the original number because it is breaking it up into smaller parts.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
*********************************************
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.
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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!
*********************************************
Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When x = -2, y is -1 because 2 times -2 is -4 and -4 plus 3 is -1.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 -1
-1 1
0 3
1 5
2 7
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did. The graph would be in a straight line, passing through the points (-2, -1), (-1, 1) etc. This would resemble the linear graph.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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.
Y for x= -2 would be 7 because -2 times itself is 4 and 4 plus 3 is 7.
• 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 7
-1 4
0 3
1 4
2 7
• 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.
Your solution: The graph that these points make curves upward and the graph that it most resembles is that of a parabola because it curves upward symmetrically.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique Rating: OK
*********************************************
Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
The result is 5 because 2 raised to the first power is 2 and 2 plus 3 is 5.
• Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1 5
2 7
3 11
4 19
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Your solution: These points form a graph that starts at point (1, 5) and then continues to rise. The graph that matches this is the exponential graph because it rises from left to right as well.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be the original number because if you divide a number by 1 it is always the same positive number.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result will always be less than the original number because it is breaking it up into smaller parts.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
*********************************************
Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!#*&!
*********************************************
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
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When x = -2, y is -1 because 2 times -2 is -4 and -4 plus 3 is -1.
• 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
-1 1
0 3
1 5
2 7
• 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. The graph would be in a straight line, passing through the points (-2, -1), (-1, 1) etc. This would resemble the linear graph.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q008. Let y = x^2 + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
Y for x= -2 would be 7 because -2 times itself is 4 and 4 plus 3 is 7.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 7
-1 4
0 3
1 4
2 7
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Your solution: The graph that these points make curves upward and the graph that it most resembles is that of a parabola because it curves upward symmetrically.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique Rating: OK
*********************************************
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.
The result is 5 because 2 raised to the first power is 2 and 2 plus 3 is 5.
• 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 5
2 7
3 11
4 19
• 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.
Your solution: These points form a graph that starts at point (1, 5) and then continues to rise. The graph that matches this is the exponential graph because it rises from left to right as well.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q010. If you divide a certain positive number by 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be the original number because if you divide a number by 1 it is always the same positive number.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result will always be less than the original number because it is breaking it up into smaller parts.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
*********************************************
Question: `q012. If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
*********************************************
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.
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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!#*&!#*&!
*********************************************
Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When x = -2, y is -1 because 2 times -2 is -4 and -4 plus 3 is -1.
• Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2 -1
-1 1
0 3
1 5
2 7
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did. The graph would be in a straight line, passing through the points (-2, -1), (-1, 1) etc. This would resemble the linear graph.
confidence rating #$&*:
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Self- Critique: OK
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.
Y for x= -2 would be 7 because -2 times itself is 4 and 4 plus 3 is 7.
• 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 7
-1 4
0 3
1 4
2 7
• 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.
Your solution: The graph that these points make curves upward and the graph that it most resembles is that of a parabola because it curves upward symmetrically.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique Rating: OK
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
• Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
The result is 5 because 2 raised to the first power is 2 and 2 plus 3 is 5.
• Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1 5
2 7
3 11
4 19
• In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
Your solution: These points form a graph that starts at point (1, 5) and then continues to rise. The graph that matches this is the exponential graph because it rises from left to right as well.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be the original number because if you divide a number by 1 it is always the same positive number.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
Self- Critique rating: OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result will always be less than the original number because it is breaking it up into smaller parts.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self- Critique: OK
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?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
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Question: `q013. Students often get the basic answers to nearly all, or even all these questions, correct. Your instructor has however never seen anyone who addressed all the subtleties in the given solutions in their self-critiques, and it is very common for a student to have given no self-critiques. It is very likely that there is something in the given solutions that is not expressed in your solution.
Your response should be inserted at the appropriate place in this document, and should be indicated by preceding it with ####.
As an answer to this question, include a copy of whatever you inserted above, or an indication that you can't find anything.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
If you divide a certain positive number by a positive number less than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: The result would be larger than the original number because it is the opposite of dividing it by a number greater than one (where the result is smaller than the original number)
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
####Self- Critique: My solution states that it is simply because it is the opposite of dividing by a number greater than one. The given solution states that it is also because it has to be larger than the original number because you are dividing it by smaller portions. I was confused because it seemed like dividing by any number would give you a smaller number just because you are “dividing.”
Self- Critique rating: 3
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Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
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