Thursday, 8/23/2018: We reviewed Algebra II concepts with two worksheets:
Fun With Lines
Completing the Square Review Answers
Friday, 8/24/2018: We derived the standard form equation of the parabola. 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. The derivation we did in class is close to this video, except we moved the 4p to the side with the linear term to avoid dealing with fractions. https://www.youtube.com/watch?v=NDh57N7U2BU http://www.purplemath.com/modules/parabola3.htm gives an example for finding the equation given the focus and directrix.
Monday, 8/27/2018: 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 video https://www.youtube.com/watch?v=5TQMJ09MLWM 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
Tuesday, 8/28/2018: Students had a worksheet to complete in class that summarized concepts of lines, circles, parabolas and ellipses. Tomorrow students should have all homework on conics ready to produce for a check as we look at all concepts about hyperbolas.
Wednesday, 8/29/2018: We looked at all things hyperbolic. 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 Students completed squares to write hyperbolas in standard form. The assignment is from the auxiliary text: Page 687: 1 - 4 all, 7-39 odd and Pg. 689: 49 - 58.
Thursday, 8/30/2018: 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 too much. Concentrate on the algebra and solving for y.
FRIDAY - 8/31/2018: WE DID LOOK AT ECCENTRICITY! Here is an idea of what eccentricity is when viewed from the cone: www.youtube.com/watch?v=Xabs4jkFEnY Here is an idea of how the eccentricity changes the conic on the plane. www.mathsisfun.com/geometry/eccentricity.html And here are the answers to quiz review
Tuesday, 9/4/2018 - Quiz and a Hyperbola Review and more questions/explanations about eccentricity.
Wednesday, 9/5/2018 - Today we answered questions about problems so far, including a problem about the double focus property of the hyperbola. Then we started an activity to look at the focus properties of the ellipse and parabola. The assignment tonight is application problems and the answers are on the back of the review.
Here are answers to the "try these" problems you got Tuesday except #10 shoul .
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://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.
Fun With Lines
Completing the Square Review Answers
Friday, 8/24/2018: We derived the standard form equation of the parabola. 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. The derivation we did in class is close to this video, except we moved the 4p to the side with the linear term to avoid dealing with fractions. https://www.youtube.com/watch?v=NDh57N7U2BU http://www.purplemath.com/modules/parabola3.htm gives an example for finding the equation given the focus and directrix.
Monday, 8/27/2018: 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 video https://www.youtube.com/watch?v=5TQMJ09MLWM 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
Tuesday, 8/28/2018: Students had a worksheet to complete in class that summarized concepts of lines, circles, parabolas and ellipses. Tomorrow students should have all homework on conics ready to produce for a check as we look at all concepts about hyperbolas.
Wednesday, 8/29/2018: We looked at all things hyperbolic. 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 Students completed squares to write hyperbolas in standard form. The assignment is from the auxiliary text: Page 687: 1 - 4 all, 7-39 odd and Pg. 689: 49 - 58.
Thursday, 8/30/2018: 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 too much. Concentrate on the algebra and solving for y.
FRIDAY - 8/31/2018: WE DID LOOK AT ECCENTRICITY! Here is an idea of what eccentricity is when viewed from the cone: www.youtube.com/watch?v=Xabs4jkFEnY Here is an idea of how the eccentricity changes the conic on the plane. www.mathsisfun.com/geometry/eccentricity.html And here are the answers to quiz review
Tuesday, 9/4/2018 - Quiz and a Hyperbola Review and more questions/explanations about eccentricity.
Wednesday, 9/5/2018 - Today we answered questions about problems so far, including a problem about the double focus property of the hyperbola. Then we started an activity to look at the focus properties of the ellipse and parabola. The assignment tonight is application problems and the answers are on the back of the review.
Here are answers to the "try these" problems you got Tuesday except #10 shoul .
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://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.