your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv Every hour that I work I earn 8 dollars, if I divide my total earnings of $72 by 8 dollars, I will have worked for a total of 9 hours.
confidence rating #$&*:
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Self-critigue: 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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv In the problem (8 + 3) * 5, the first step is to work within the parentheses. 8 + 3 = 11. Then 11 * 5 = 55. Whereas in the problem 8 + 3 * 5, the first step is to times 3 by 5 to get 15, then add 8 + 15 to get a total of 23.
confidence rating #$&*:
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Self-critigue: OK
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Question: `q005. Calculate (2^4) * 3 and 2^(4 * 3), indicating the order of your steps. Explain, as best you can, the reasons for the difference in your results. Note that the symbol '^' indicates raising to a power. For example, 4^3 means 4 raised to the third power, which is the same as 4 * 4 * 4 = 64.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv In the problem (2^4) * 3, the first step is to work inside the parentheses and then times by 3 to get a total of 48; In 2^(4 * 3), the first step is to work inside the parentheses to get 2^(12) then times 2 by 2 twelve times. The answer would be 4,096.
confidence rating #$&*:
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Self-critigue: 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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv The differences between the first problem and the second is the placement of paratheses and the exponents. For the first problem 3 * 5 - 4 * 3^2 reduces down to 3 * 5 - 4 * 9 then it reduces to 15 - 36 and the total would be -21. The second problem, 3 * 5 - ( 4 * 3 )^ 2 reduces to 3 * 5 - (12)^2 this then reduces to 3 * 5 - 144 this reduces to 15 - 144 to equal -129.
confidence rating #$&*:
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Self-critigue: OK
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Question: `q007. Let y = 2 x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
Evaluate y for x = -2. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values -1, 0, 1 and 2. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
-2
-1
0
1
2
Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv In my solution for solving y for x = -2, I substituted -2 for x in the equation y = 2 x + 3. y = 2 * -2 + 3, which reduces to y = -4 + 3 and y is equal to -1.
In my table, the solutions for -1,0,1, and 2 include: y = 2 * -1 + 3, that reduces to y = -2 + 3, y = 1; y = 2 * 0 + 3, that reduces to y = 0 + 3, y = 3; y = 2 * 1 + 3 reduces to y = 2 + 3, y = 5; y = 2 * 2 + 3 reduces to y = 4 + 3, y = 7.
The graph is linear, and it is a straight line.
confidence rating #$&*:
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Self-critigue: 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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv In my solution for solving y for x = -2, I substituted -2 for x in the equation y = x^2 + 3, y = -2^2 + 3 this reduces to y = 4 + 3 which means y = 7.
For the remainder of the numbers listed I substituted -1, 0, 1, and 2 in the place of x. y = -1^2 + 3 this reduces to y = 1 + 3, y = 4; y = 0^2 + 3 reduces to y = 0 + 3 and y = 3; y = 1^2 + 3 reduces to y = 1 + 3, y = 4; y = 2^2 + 3 reduces to y = 4 + 3, y = 7
The graph that I sketched closely resembled the quadratic or parabolic graph. I chose this one because of the curve that is also present in the quadratic or parabolic graph.
confidence rating #$&*:
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Self-critigue: OK
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Question: `q009. Let y = 2 ^ x + 3. (Note: Liberal Arts Mathematics students are encouraged to do this problem, but are not required to do it).
Evaluate y for x = 1. What is your result? In your solution explain the steps you took to get this result.
Evaluate y for x values 2, 3 and 4. Write out a copy of the table below. In your solution give the y values you obtained in your table.
x y
1
2
3
4
Sketch a graph of y vs. x on a set of coordinate axes resembling the one shown below. You may of course adjust the scale of the x or the y axis to best depict the shape of your graph.
In your solution, describe your graph in words, and indicate which of the graphs depicted previously your graph most resembles. Explain why you chose the graph you did.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv In my solution for solving y for x = 1, I substituted 1 for x in the equation y = 2^x + 3, y = 2^1 +3 this reduces to y = 2 + 3, y = 5
For the remainder of the following table lists 2, 3, and 4 I substituted those in the place of x. y = 2^2 + 3 reduced to y = 4 + 3, y = 7; y = 2^3 + 3 reduces to y = 8 + 3, y = 11; y = 2^4 + 3 reduces to y = 16 + 3, y = 19
The graph that was sketched with these coordinates resembles the exponential graph. The points gradually increased higher and higher.
confidence rating #$&*:
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Self-critigue: 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?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv Equal to the original number
confidence rating #$&*:
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Self-critigue: OK
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Question: `q011. If you divide a certain positive number by a number greater than 1, is the result greater than the original number, less than the original number or equal to the original number, or does the answer to this question depend on the original number?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv The result would be less than the original number.
confidence rating #$&*:
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Self-critigue: 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?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv Depends on the Orginal number.
confidence rating #$&*:
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Self-critigue: I don't fully understand this question. I read the solution, but it still doesn't seem to click with me.####
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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.
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv ""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?
your answer: vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv Depends on the Orginal number.
confidence rating #$&*:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Self-critigue: I don't fully understand this question. I read the solution, but it still doesn't seem to click with me.####""
"
Self-critique (if necessary):
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Self-critique rating:
________________________________________
#$&*
@&
Very good.
Note, however, that you need to submit the entire document, without deleting anything.
In other words, copy the indicated part of the document, insert your answers in the specified places, and submit without removing anything.
The program I'm using to review these files relies on certain codes in the original document, so that I can very quickly locate your responses without having to visually scan the document. This speeds the process up greatly, giving me more time to give students the assistance they need.
No need to repeat this document, but be sure to follow this practice on future submissions.
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