Wednesday, 9/6/2016: Today we reviewed equations of circles and parabolas. The assignment is from page 667 of the auxiliary text: 19, 24, 29, 31, 35, 37-42, 61, 63, 69, 71, 73, 79, 81, 91, 103-110. http://www.purplemath.com/modules/parabola3.htm gives an example for finding the equation given the focus and directrix.
Thursday, 9/7/2017: Here are the answers to the practice quiz. Thank Christian Scholar for this!!!
1. D 2. C 3. C 4. B 5. C 6. A 7. D 8. D 9. C 10. B 11. 66 12. 4 13. 200 14. 200/6 = 33.33..., 15. 185 16. 133
17. C 18. B 19. E 20. C 21. 1/5 22. 3/40 23. 3/100 24. 32% = .32 25. sqrt(.32*.68/300) = .027 26. moe = 1.96(.027) = .0528, so CI = (.32 - .053, .32 + .053) = (.267, .373) or from 26.7% to 37.3%. 27. moe = 1.96sqrt(.5(1-.5)/n) and solving for n, you get 2401. (Note that if you used 32%, you are assuming that the AJC knows the result of the survey before they complete the survey.) 28. 31.1%
29. C(12, 9)((.311)^9)(.689)^3) 30. Don't bother 31. The distribution of the means from the cartons is roughly normal. 32. The mean of the means from the cartons is approximately 65 grams (the population mean). 33. The standard deviation of the means from the cartons is approximately 5/sqrt(12).
Friday, 9/8/2017: Students took the probability/statistics quiz. The homework assignment is to be completely caught up with all the conic assignments (Except the Probability and Conics side of Thursday's assignment) and be ready to start looking at ellipses on Monday. 3rd period, bring in Pg. 634, Pg. 645, Testing Task and Normal Curve Task for a homework check on Monday.
Wednesday, 9/13/2017: Today students drew their own ellipse and found the major axis, the minor axis, the foci and found out that if a is the semimajor axis, b is the semiminor axis and c is the focal length, then a^2 = b^2 + c^2. Furthermore, the equation of a standard ellipse with major axis on the x axis is x^2/a^2 + y^2/b^2 = 1. This derivation is done on this webpage:
http://nebula.deanza.edu/~bloom/math43/ellipse-derivation.pdf and this
http://mathopenref.com/coordgeneralellipse.html shows the relationship between a, b and c and the shape of the ellipse. They also realized that the values of a and b can be thought of as radii in the x and y directions - and that the larger number is called a, so that the Pythagorean relationship holds.
The homework assignment is from the auxiliary text: Pg. 677: 1-6, 7, 9, 15-39 odd, 47-53 odd, 63, 65
Thursday, 9/14/2017: With a smaller class due to the Academic Letter Ceremony, we looked at the differences between the general forms of the conics and then looked at the differences between the ellipse and the hyperbola. The assignment is to either continue and complete the ellipse homework or else to start working on the hyperbola section: Page 687: 1-4, 7-47 odd
Friday, 9/15/2017: Today students learned the definition of a hyperbola and how to write the equation of one. Here is that derivation:
http://nebula.deanza.edu/~bloom/math43/hyperbola-derivation.pdf Today students completed squares to write hyperbolas in standard form. They also learned how to write hyperbolas given characteristics of them. The assignment is from the auxiliary text: Page 687: 1 - 4 all, 7-39 odd and Pg. 689: 49 - 58.
Monday, 9/18/2017: Today we looked at intersections of conics and how to solve for y in order to graph them on the calculator. The assignment is Page 697: 21 - 26, 27 - 51 odd, but don't worry about the discriminant part. It looks like you have lots of time to master conics!
Tuesday, 9/19/2017: Today we went over the Conic Faces Project, reviewed the new schedule, answered questions about the quiz tomorrow and/or homework questions. Remember to bring all conics homework tomorrow because I am checking to see if you've been working or not... Thank Mr. Slater for the answer key to the practice quiz you got today! But, AS I SAID IN CLASS, the quiz tomorrow will contain all 4 types of conics, while the practice quiz only focuses on 2.
Wednesday, 9/20/2017: Students took a quiz and got a serious review. I encourage students to work two or three problems a day over the break so they don't forget conic concepts.
Thursday, 9/21/2017: Today we looked at the alternate definition of the hyperbola: the set of points in a plane whose distances to two fixed points in the plane have a constant difference. The homework is to complete the back which contains more systems of equations and inequalities.
Friday, 9/22, 2017: Today first period asked many questions about various concepts and project requirements. Second and third periods looked at the 2 focus property of the ellipse with a group project.
More details:
Here are answers to the applications worksheet from Tuesday:
Here is the derivation for the equation of an ellipse
Here are the answers to the probability and conics worksheet.
Here are answers to the "try these" problems you got Friday.
Here are answers to the long review you got Wednesday.
Furthermore, here are links to other resources:
http://www3.ul.ie/~rynnet/swconics/applications_of_conic_sections.htm Real life application ideas.
http://platonicrealms.com/encyclopedia/conics Really good notes about conics.
http://www.shelovesmath.com/precal/conics Notes with applications that have solutions
http://ww2.d155.org/cls/tdirectory/KGreenfield/Shared%20Documents/Pre-Calculus/Chapter%2010/Applications%20of%20Conics%20Worksheet.pdf nice pdf with answers
http://rgoglesby.weebly.com/uploads/3/7/3/6/37367927/conic_word_problems_solutions_sheet.pdf another teacher's worksheet with solutions
And don't forget that Dr. Shildneck's website also has some good conics resources.
Thursday, 9/7/2017: Here are the answers to the practice quiz. Thank Christian Scholar for this!!!
1. D 2. C 3. C 4. B 5. C 6. A 7. D 8. D 9. C 10. B 11. 66 12. 4 13. 200 14. 200/6 = 33.33..., 15. 185 16. 133
17. C 18. B 19. E 20. C 21. 1/5 22. 3/40 23. 3/100 24. 32% = .32 25. sqrt(.32*.68/300) = .027 26. moe = 1.96(.027) = .0528, so CI = (.32 - .053, .32 + .053) = (.267, .373) or from 26.7% to 37.3%. 27. moe = 1.96sqrt(.5(1-.5)/n) and solving for n, you get 2401. (Note that if you used 32%, you are assuming that the AJC knows the result of the survey before they complete the survey.) 28. 31.1%
29. C(12, 9)((.311)^9)(.689)^3) 30. Don't bother 31. The distribution of the means from the cartons is roughly normal. 32. The mean of the means from the cartons is approximately 65 grams (the population mean). 33. The standard deviation of the means from the cartons is approximately 5/sqrt(12).
Friday, 9/8/2017: Students took the probability/statistics quiz. The homework assignment is to be completely caught up with all the conic assignments (Except the Probability and Conics side of Thursday's assignment) and be ready to start looking at ellipses on Monday. 3rd period, bring in Pg. 634, Pg. 645, Testing Task and Normal Curve Task for a homework check on Monday.
Wednesday, 9/13/2017: Today students drew their own ellipse and found the major axis, the minor axis, the foci and found out that if a is the semimajor axis, b is the semiminor axis and c is the focal length, then a^2 = b^2 + c^2. Furthermore, the equation of a standard ellipse with major axis on the x axis is x^2/a^2 + y^2/b^2 = 1. This derivation is done on this webpage:
http://nebula.deanza.edu/~bloom/math43/ellipse-derivation.pdf and this
http://mathopenref.com/coordgeneralellipse.html shows the relationship between a, b and c and the shape of the ellipse. They also realized that the values of a and b can be thought of as radii in the x and y directions - and that the larger number is called a, so that the Pythagorean relationship holds.
The homework assignment is from the auxiliary text: Pg. 677: 1-6, 7, 9, 15-39 odd, 47-53 odd, 63, 65
Thursday, 9/14/2017: With a smaller class due to the Academic Letter Ceremony, we looked at the differences between the general forms of the conics and then looked at the differences between the ellipse and the hyperbola. The assignment is to either continue and complete the ellipse homework or else to start working on the hyperbola section: Page 687: 1-4, 7-47 odd
Friday, 9/15/2017: Today students learned the definition of a hyperbola and how to write the equation of one. Here is that derivation:
http://nebula.deanza.edu/~bloom/math43/hyperbola-derivation.pdf Today students completed squares to write hyperbolas in standard form. They also learned how to write hyperbolas given characteristics of them. The assignment is from the auxiliary text: Page 687: 1 - 4 all, 7-39 odd and Pg. 689: 49 - 58.
Monday, 9/18/2017: Today we looked at intersections of conics and how to solve for y in order to graph them on the calculator. The assignment is Page 697: 21 - 26, 27 - 51 odd, but don't worry about the discriminant part. It looks like you have lots of time to master conics!
Tuesday, 9/19/2017: Today we went over the Conic Faces Project, reviewed the new schedule, answered questions about the quiz tomorrow and/or homework questions. Remember to bring all conics homework tomorrow because I am checking to see if you've been working or not... Thank Mr. Slater for the answer key to the practice quiz you got today! But, AS I SAID IN CLASS, the quiz tomorrow will contain all 4 types of conics, while the practice quiz only focuses on 2.
Wednesday, 9/20/2017: Students took a quiz and got a serious review. I encourage students to work two or three problems a day over the break so they don't forget conic concepts.
Thursday, 9/21/2017: Today we looked at the alternate definition of the hyperbola: the set of points in a plane whose distances to two fixed points in the plane have a constant difference. The homework is to complete the back which contains more systems of equations and inequalities.
Friday, 9/22, 2017: Today first period asked many questions about various concepts and project requirements. Second and third periods looked at the 2 focus property of the ellipse with a group project.
More details:
Here are answers to the applications worksheet from Tuesday:
Here is the derivation for the equation of an ellipse
Here are the answers to the probability and conics worksheet.
Here are answers to the "try these" problems you got Friday.
Here are answers to the long review you got Wednesday.
Furthermore, here are links to other resources:
http://www3.ul.ie/~rynnet/swconics/applications_of_conic_sections.htm Real life application ideas.
http://platonicrealms.com/encyclopedia/conics Really good notes about conics.
http://www.shelovesmath.com/precal/conics Notes with applications that have solutions
http://ww2.d155.org/cls/tdirectory/KGreenfield/Shared%20Documents/Pre-Calculus/Chapter%2010/Applications%20of%20Conics%20Worksheet.pdf nice pdf with answers
http://rgoglesby.weebly.com/uploads/3/7/3/6/37367927/conic_word_problems_solutions_sheet.pdf another teacher's worksheet with solutions
And don't forget that Dr. Shildneck's website also has some good conics resources.