Assignments for Chapters 4 & 9:
Assignment #24
Sections 4.1-4.2/ p.283-284 / 67-68, 76-116(skip by 4's), 117-124
and p.292-293 / 77-116 (by 3's), 118-122,125
Assignment #25
Sections 4.3 / p.297-300 /19-58(3), 59-74(3), 78, 83, 84 (convert to miles per hour use #79), 85
Sections 4.4 / p.307-309 / 6, 9, 10, 57, 58, 61, 66, 70-73, 75
Assignment #26
Section 4.6 / pg. 324-325 / 54-90(3),99,100,102
Section 4.7 / pg. 330-331 / 2-6,17-24, 28-58(3)
Assignment #27
Section 4.8 / pg. 340-342 / 55-70(3), 78-87(3), 94, 99, 107-108, 112
Assignment #28
Section 9.1 / pg. 640-641 / 1-15, 19-61(3), 71, 72
Assignment #29
Section 9.2 / pg. 650-653 / 21-45 (skip by 3), 65, 70, 72, 74
Monday, December 03, 2007
Wednesday, October 31, 2007
Chapter 7 Homework
Assignment 19
Section 7.1 / pg.516-517 / 21-69(3), 78, 79 use graph paper
Assignment 20
Section 7.2 / pg.527-530 / 1-14, 17, 23-73(5), 74, 76, 77
Assignment 21
Section 7.3 / pg.536-539 / 17-77(5), 80-84, 89, 90
Assignment 22
Section 7.4 / pg. 549-553/ 3-10, 12-16, 18,20,21,23,24,28, 29, 30,
Assignment 23
Section 7.5/ pg.560-561 / 4-18, 19-46(3) use graph paper
STUDY GROUP ASSIGNMENT:
from the chapter review:
pg 566-569 / 4-6, 10-14, 17, 19-21, 25-34
This is 22 problems total. Do them, in your groups, in reverse order to maximize the time you spend on the more difficult concepts.
Assignment 19
Section 7.1 / pg.516-517 / 21-69(3), 78, 79 use graph paper
Assignment 20
Section 7.2 / pg.527-530 / 1-14, 17, 23-73(5), 74, 76, 77
Assignment 21
Section 7.3 / pg.536-539 / 17-77(5), 80-84, 89, 90
Assignment 22
Section 7.4 / pg. 549-553/ 3-10, 12-16, 18,20,21,23,24,28, 29, 30,
31, 33, 34, 36, 38, 40, 44, 46, 48, 55, 56
Assignment 23
Section 7.5/ pg.560-561 / 4-18, 19-46(3) use graph paper
STUDY GROUP ASSIGNMENT:
from the chapter review:
pg 566-569 / 4-6, 10-14, 17, 19-21, 25-34
This is 22 problems total. Do them, in your groups, in reverse order to maximize the time you spend on the more difficult concepts.
Friday, April 27, 2007
General outline of Final Exam
you may print this post and not the whole blog by linking here http://rosieworkinteralgebra.blogspot.com/2007/04/general-outline-of-final-exam-1-writing.html first and then printing
1) writing algebraic equations
2) operations with rational numbers
3) catergories of real numbers
4) writing variable expressions
5) graphing real numbers on the number line
6) writing algebraic expressions
7) solving percent problems (IS over OF = % over 100)
8) Simplifying algebraic expressions
9) "
10) "
11) "
12) evaluating using order of operations
(keep in mind that -5^2 does not have the same meaning as (-5)^2. The former means the opposite of the square of 5, the latter means the square of the opposite of five. For all even powers this distinction is significant.
13) more evaluating using order of operations
14) "
15) Solving equations containing combining like terms, distributive property, fractions, ect.
16) "
17)
18)
19)
20) solving an inequality. graphing its solution and writing its solution in interval notation.
21) solving a formula for a specified variable
22) Solving a mixture problem as in chapter 2.6 ex. 7 or 8
23) graphing linear equations including possibly vertical or horizontal lines
remember vertical lines have a undefined slope ( the change in x is zero), and have no y-intercept (because they are vertical). Vertical lines have equations that have only x's in them. No y variable.
horizontal lines have a zero slope ( no change in y as they travel from left to right), no x intercept (they don't cross the x-axis, they are parallel to it) and like the x axis have an equation that when simplified simply says y=__.
24) more graphing
25) finding slopes, watch out for your negatives, that you put the change in y over the change in x and distinguish between when a result is undefined and therefore vertical or zero and horizontal.
26) finding slope
27) putting an equation in slope- intercept form (equation must be written in y = mx + b form so basically solve the equation by moving stuff around until it basically says Y = something times x plus or minus something else. The something by x will be the slope and the somethingelse will be the y intercept. Solving the equation for y is not the same as saying find the value of y or find the y intercept. In the first case, solving the equation for y the result will still be an equation but with the y on one side and the x and someother stuff on the other. In the second and third case in order to find a particalar value of y. Whether it be a y-intercept of something else a specific value of x must be entered in the equation to complete the ordered pair.
28) Finding x and y intercepts
29) writing equations of lines given either the slope and the y-intercept, the slope and a random point that the line goes through, or two points that sit on the line. In the third case you will need to find the slope and then, having found it, just like the second case pick one of the points to use in conjuction with the slope to substitute into the formula for x,y and m after which you will be able to solve for b to figure out the equation.
30. more writing equations
31. "
32. "
33. determining if the graphs or two given equations are parallel perpendicular or neither
34. solving systems of linear equations by either graphing or substitution
35. "
36. "
I will probably add a few more problems but so far this is what I have. I definetely want to add one or two about completing a table of solutions for a given equation and graphing resulting ordered pairs. I also have in mind add one relating to geometry. something with perimeter or angles like 2.6 ex. 3
I might include a bonus either about related to Interest type problem or Distance = rate times time like 2.6 ex 5 and 6
Good luck with your studies for all your finals.
Kenneth Rosever
you may print this post and not the whole blog by linking here http://rosieworkinteralgebra.blogspot.com/2007/04/general-outline-of-final-exam-1-writing.html first and then printing
1) writing algebraic equations
2) operations with rational numbers
3) catergories of real numbers
4) writing variable expressions
5) graphing real numbers on the number line
6) writing algebraic expressions
7) solving percent problems (IS over OF = % over 100)
8) Simplifying algebraic expressions
9) "
10) "
11) "
12) evaluating using order of operations
(keep in mind that -5^2 does not have the same meaning as (-5)^2. The former means the opposite of the square of 5, the latter means the square of the opposite of five. For all even powers this distinction is significant.
13) more evaluating using order of operations
14) "
15) Solving equations containing combining like terms, distributive property, fractions, ect.
16) "
17)
18)
19)
20) solving an inequality. graphing its solution and writing its solution in interval notation.
21) solving a formula for a specified variable
22) Solving a mixture problem as in chapter 2.6 ex. 7 or 8
23) graphing linear equations including possibly vertical or horizontal lines
remember vertical lines have a undefined slope ( the change in x is zero), and have no y-intercept (because they are vertical). Vertical lines have equations that have only x's in them. No y variable.
horizontal lines have a zero slope ( no change in y as they travel from left to right), no x intercept (they don't cross the x-axis, they are parallel to it) and like the x axis have an equation that when simplified simply says y=__.
24) more graphing
25) finding slopes, watch out for your negatives, that you put the change in y over the change in x and distinguish between when a result is undefined and therefore vertical or zero and horizontal.
26) finding slope
27) putting an equation in slope- intercept form (equation must be written in y = mx + b form so basically solve the equation by moving stuff around until it basically says Y = something times x plus or minus something else. The something by x will be the slope and the somethingelse will be the y intercept. Solving the equation for y is not the same as saying find the value of y or find the y intercept. In the first case, solving the equation for y the result will still be an equation but with the y on one side and the x and someother stuff on the other. In the second and third case in order to find a particalar value of y. Whether it be a y-intercept of something else a specific value of x must be entered in the equation to complete the ordered pair.
28) Finding x and y intercepts
29) writing equations of lines given either the slope and the y-intercept, the slope and a random point that the line goes through, or two points that sit on the line. In the third case you will need to find the slope and then, having found it, just like the second case pick one of the points to use in conjuction with the slope to substitute into the formula for x,y and m after which you will be able to solve for b to figure out the equation.
30. more writing equations
31. "
32. "
33. determining if the graphs or two given equations are parallel perpendicular or neither
34. solving systems of linear equations by either graphing or substitution
35. "
36. "
I will probably add a few more problems but so far this is what I have. I definetely want to add one or two about completing a table of solutions for a given equation and graphing resulting ordered pairs. I also have in mind add one relating to geometry. something with perimeter or angles like 2.6 ex. 3
I might include a bonus either about related to Interest type problem or Distance = rate times time like 2.6 ex 5 and 6
Good luck with your studies for all your finals.
Kenneth Rosever
Monday, March 05, 2007
Chapter 3 Homework Assignments: 7 total
Assignment 12 / Section 3.1/ pg.189-194/8,27,29,36,37,38,41,43,44
Assignment 13 / Section 3.2/pg.202-206/1-11,14,17,22-66(4),68
Assignment 14 / Section 3.3/pg.214-217/3-23,25-65(4),68,70,79,80
Assignment 15 / Section 3.4/pg.224-229/2-15,23-32,38-62(4),70-72
and 3.5/pg.237-241/17,27,31
Assignment 16 / Section 3.5/pg.237-241/1-16,23-75(4), 77-86(graph them), 87-102
and pg.271/23,25
Assignment 17 / Section 3.6/pg.247-251/13-17,22-62(4),64,67,71,72,77-80
Assignment 18 / Section 3.7/pg.260-261/33-66(3),67,72, and 52,58,59 also
Study Group assignment for Chapter 3
Chapter Review / pg.264-267 / 3, 7-22, 26-32, 34-39, 41, 44
Assignment 12 / Section 3.1/ pg.189-194/8,27,29,36,37,38,41,43,44
Assignment 13 / Section 3.2/pg.202-206/1-11,14,17,22-66(4),68
Assignment 14 / Section 3.3/pg.214-217/3-23,25-65(4),68,70,79,80
Assignment 15 / Section 3.4/pg.224-229/2-15,23-32,38-62(4),70-72
and 3.5/pg.237-241/17,27,31
Assignment 16 / Section 3.5/pg.237-241/1-16,23-75(4), 77-86(graph them), 87-102
and pg.271/23,25
Assignment 17 / Section 3.6/pg.247-251/13-17,22-62(4),64,67,71,72,77-80
Assignment 18 / Section 3.7/pg.260-261/33-66(3),67,72, and 52,58,59 also
Study Group assignment for Chapter 3
Chapter Review / pg.264-267 / 3, 7-22, 26-32, 34-39, 41, 44
Wednesday, February 07, 2007
Penny Lab
In class you will prepare a chart that compares the number of pennies a bridge holds to how thick it is. Using this table you then make a graph on graph paper of Bridge's Thickness (in layers) verses Bridge's Strength measured in the Breaking Weight (in pennies). In order to make the table and the subsequent graph you must decide which variable in the experiment is the independant variable (x) and which is the dependant variable (y) .
1. What are the independant and dependant variables in this experiment and how do you know?
2. Make a chart of x and y values for bridges of the varous thickness assigned to your group. Make sure to fold your papers correctly and consistantly and avoid changes to the distance between your books. Also be sure to allow time for the bridge to collapse before adding another penny. Once you have done bridges of thicknesses assigned you may go back and repeat the trials if instructed. Do not use the same piece of paper twice. Make an uncompromised brand new layer for every layer of every trial.
3. On graph paper, after labeling your axis, begin plotting your data points from your various trials.
Answer all the following questions in paragraph form, show work for all relevant calculations organized neatly and in order.
4. Does the data on the resulting graph seem pretty-much linear? Does the data indicate an increasing, decreasing, or constant trend. Why does/doesn't this make sense in terms of what adding a layer of paper should do to the strength of the bridge?
5. Draw a straight line on your graph that approximates what the data seems to be doing fairly well and find the equation for it by using two points that lay on the line you drew. (Your line doesn't actually have to hit any of the points you plotted from your experiment. It just needs to be the straight line that you feel does the best job of approximating the results you got in your experiment. This is called the line of best fit.)
6. Tell me what is slope and y-intercept found in your equation specifically mean in terms of the experiment. Do you agree with their validity? Why/ Why not?
7. Use the equation from your eyeballed line of best fit result to predict the number of pennies a bridge of each of the thicknesses assigned to your group should hold. These results are called the predicted value because you are using your equation to predict how the thickness will determine the breaking weight.
8. Comparing the answer that the equation predicts to the average of the answers you actually found, find the percentage of error and tell me "Do you think the your eyeballed equation does a good job modeling the data?" Why/why not?
9. Now use the statistical method discussed in class to find the true line of best fit showing all your calculations.
10. Answer discussion questions 6,7 and 8 again but with respect to the equation you developed in #9 with the added question, which equation do you think does a better job (your eyeballed one or the stats derived one) and why (support you conclusion with comparisions of pertinent results).
11. Find the regression coeffecient for the data and explain what it means in terms of the experiment.
12. Describe some of the factors in the experiment that may have introd uced some error into your results and subsequently the two equations you developed.
13. Use your second equation to estimate how many layers would be needed to hold 100 pennies. Would it be correct to round your answer up or down? Why?
14. Use your equation to predict how many pennies a 5 layer bridge and 12 layer bridge would break at.
15. In reality you can experiment with only integer values for the x and y. You can only use complete layers and complete pennies. Your equation on the other hand allows you do much more. Use one non-integer value for x in your formula which would make sense if the layers weren't paper thin but which would be impossible to try to replicate in an experiment. Explain what your result means.
16.When you answered the previous three questions at what points were you interpolating and at what points were you extrapolating from your experimental model?
17. Finally Engineers and Statisticians, among others, both interpolate and extrapolate regularally by creating models from data to predict tendencies and possible outcomes. In terms of designing and building bridges, why does it make sense to use a scaled-down experimentation and mathematical modeling? Also in this context, why is it important to never throw out strange results from an experiment, until the cause of the deviation has been explained?
Self Check. Go on Rosiework and follow the link to the online linear regression tool. Input your x and y data and compare the resulting mathematically generated line of best fit to the one you created just to double check your results before you turn in the paper.
In class you will prepare a chart that compares the number of pennies a bridge holds to how thick it is. Using this table you then make a graph on graph paper of Bridge's Thickness (in layers) verses Bridge's Strength measured in the Breaking Weight (in pennies). In order to make the table and the subsequent graph you must decide which variable in the experiment is the independant variable (x) and which is the dependant variable (y) .
1. What are the independant and dependant variables in this experiment and how do you know?
2. Make a chart of x and y values for bridges of the varous thickness assigned to your group. Make sure to fold your papers correctly and consistantly and avoid changes to the distance between your books. Also be sure to allow time for the bridge to collapse before adding another penny. Once you have done bridges of thicknesses assigned you may go back and repeat the trials if instructed. Do not use the same piece of paper twice. Make an uncompromised brand new layer for every layer of every trial.
3. On graph paper, after labeling your axis, begin plotting your data points from your various trials.
Answer all the following questions in paragraph form, show work for all relevant calculations organized neatly and in order.
4. Does the data on the resulting graph seem pretty-much linear? Does the data indicate an increasing, decreasing, or constant trend. Why does/doesn't this make sense in terms of what adding a layer of paper should do to the strength of the bridge?
5. Draw a straight line on your graph that approximates what the data seems to be doing fairly well and find the equation for it by using two points that lay on the line you drew. (Your line doesn't actually have to hit any of the points you plotted from your experiment. It just needs to be the straight line that you feel does the best job of approximating the results you got in your experiment. This is called the line of best fit.)
6. Tell me what is slope and y-intercept found in your equation specifically mean in terms of the experiment. Do you agree with their validity? Why/ Why not?
7. Use the equation from your eyeballed line of best fit result to predict the number of pennies a bridge of each of the thicknesses assigned to your group should hold. These results are called the predicted value because you are using your equation to predict how the thickness will determine the breaking weight.
8. Comparing the answer that the equation predicts to the average of the answers you actually found, find the percentage of error and tell me "Do you think the your eyeballed equation does a good job modeling the data?" Why/why not?
9. Now use the statistical method discussed in class to find the true line of best fit showing all your calculations.
10. Answer discussion questions 6,7 and 8 again but with respect to the equation you developed in #9 with the added question, which equation do you think does a better job (your eyeballed one or the stats derived one) and why (support you conclusion with comparisions of pertinent results).
11. Find the regression coeffecient for the data and explain what it means in terms of the experiment.
12. Describe some of the factors in the experiment that may have introd uced some error into your results and subsequently the two equations you developed.
13. Use your second equation to estimate how many layers would be needed to hold 100 pennies. Would it be correct to round your answer up or down? Why?
14. Use your equation to predict how many pennies a 5 layer bridge and 12 layer bridge would break at.
15. In reality you can experiment with only integer values for the x and y. You can only use complete layers and complete pennies. Your equation on the other hand allows you do much more. Use one non-integer value for x in your formula which would make sense if the layers weren't paper thin but which would be impossible to try to replicate in an experiment. Explain what your result means.
16.When you answered the previous three questions at what points were you interpolating and at what points were you extrapolating from your experimental model?
17. Finally Engineers and Statisticians, among others, both interpolate and extrapolate regularally by creating models from data to predict tendencies and possible outcomes. In terms of designing and building bridges, why does it make sense to use a scaled-down experimentation and mathematical modeling? Also in this context, why is it important to never throw out strange results from an experiment, until the cause of the deviation has been explained?
Self Check. Go on Rosiework and follow the link to the online linear regression tool. Input your x and y data and compare the resulting mathematically generated line of best fit to the one you created just to double check your results before you turn in the paper.
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