Monday, April 10



Pre-Calculus Lesson Plans Unit 13 4th term

April 4th to April 17th 2012

Conics and Parametric Equations

|Date |Topic |Homework |Did it |

|Wednesday |Intro to Circles, Semicircles, Ellipses and |Worksheets pages 1 & 2 | |

|4/4 |Hyperbolas | | |

|Thursday |Parabolas |Worksheet page 3 | |

|4/5 | | | |

|Monday |Circles and Ellipses |Worksheet page 4 | |

|4/9 | | | |

|Tuesday |Conics Word Problems |Worksheet pages 5 & 6 | |

|4/10 |Quiz: Conics | | |

|Wednesday |Parametric Equations |Worksheet page 7 | |

|4/11 | | | |

|Thursday |Parametric Word |Worksheet page 8 | |

|4/12 | | | |

|Friday |Parametric Word |Review Worksheet pages 9, 10, 11 | |

|4/13 |Quiz: Word Problems | | |

|Monday |Review |Study for test | |

|4/16 | | | |

|Tuesday |TEST |Print out unit 14 | |

|4/17 | | | |

Wednesday, April 4 Circles, Semicircles, Ellipses, and Hyperbolas

I. Identify each equation as a circle, semicircle, ellipse or hyperbola.

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

II. Complete the square and write in standard form.

13) [pic] 14) [pic] 15) [pic]

page 1

II. Complete the square and write in standard form.

16) [pic] 17) [pic] 18) [pic]

III. Identify each graph as a circle, semicircle, ellipse or hyperbola.

19) 20) 21) 22)

23) 24) 25) 26)

IV. Write an equation for each ellipse.

27) 28)

page 2

Thursday, April 5th Parabolas

I. Complete the square for each parabola and write in standard form.

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

II. Graph each parabola.

7) [pic] 8) [pic] 9) [pic] 10) [pic]

III. Write an equation for each parabola.

11) the vertex is (0, 12) and a 12) the vertex is (0, 10) and 13) the vertex is the origin and

point on the graph is (10, 20) a point on the graph is (4,0) a point on the graph is (15, 4)

14) 15) 16)

IV. Write the following in standard form. Find the vertex, focus and Focal length. DO NOT GRAPH.

17.[pic] 18. [pic] *19. [pic]

page 3

Monday, April 9th Conic Sections: Circles and Ellipses

I. Identify each equation as a Circle, Semi-Circle, Ellipse, or Parabola.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

II. Complete the Square and get into Standard Form. Do Not Graph.

7. [pic] 8. [pic]

9. [pic] 10. [pic]

III. Graph the following.

11. [pic] 12. [pic] 13. [pic]

14. [pic] 15. [pic] 16. [pic]

IV. Write an Equation for each of the following.

27) 28) 29) A circle centered at (-3, 4) with a radius of 7.

30. A circle centered at (5, -2) with a radius of [pic].

page 4

Tuesday, April 10th Parabola and Ellipse Word Problems

1) The main cables of a suspension bridge are 20 meters above the road at the towers and 4 meters above the road at the center. The road is 80 meters long. Vertical cables are spaced every 10 meters. The main cables hang in the shape of a parabola. Find the equation of the parabola.

2) The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet across and 90 feet high. Find an equation describing the door's shape.

3) An engineer designs a satellite dish with a parabolic cross-section. The dish is 15 ft. wide at the opening and the depth is 4 feet. Find the position of the light source (the focus).

4) A car headlight mirror has a parabolic cross section with diameter of 6 in, and a depth of 5 in. How far from the vertex should the bulb be positioned if it is to be placed at the focus?

5) The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 400 feet apart and 100 feet high. If the cables are at a height of 10 feet midway between the towers, what is the height of the cable at a point 50 feet from the center of the bridge?

6) A doorway in a castle is shaped like a parabola. Find an equation describing the door given that is 4 feet across and 8 feet high in the center.

7) The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cable are 600 feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point 150 feet from the center of the bridge?

page 5

8) A searchlight is shaped like a parabola of revolution. If the light source is located 2 feet from the base along the axis of symmetry and depth of the searchlight is 4 feet, what should the width of the opening be?

9) According to Kepler’s Laws, planets have elliptical orbits, with the sun at one of the foci. The farthest Pluto gets from the sun is 7.4 billion kilometers. The closest it gets to the sun is 4.4 billion kilometers. Find the equation Pluto’s orbit.

10) An arch in the shape of the upper half of an ellipse is used to support a bridge that is to span a river 20 meters wide. The center of the arch is 6 meters above the center of the river (see figure). Write an equation for the ellipse in the x-axis coincides with the water level and the y-axis passes through the center of the arch.

11) An elliptically shaped garden is surrounded by a wood walkway. The garden is 15 meters long and 8 meters wide. The walkway is 2 meters wide. Find the equation describing the garden and walkway.

12) The Statuary Hall in the United States Capitol is elliptical. It measures 46 feet wide and 96 feet long. If a person is standing at one focus, her whisper can be heard by a person standing at the other focus. How far apart are the two people?

13) A narrow arch supporting a stone bridge is in the shape of half of an ellipse and 24 meters long and 8 meters high. A person standing at one location throws a rubber ball against the arch. No matter what direction the ball is thrown, it always bounces off the arch once and strikes the same point on the ground. How far apart are the person throwing the ball and point on the ground at which the ball first strikes?

14) An arch of a bridge over a highway is semi-elliptical in shape and 42 ft. across. The highest point of the arch is 14 feet above the highway. What is the maximum height, to the nearest inch, of a truck 8 ft. wide that can fit under the arch?

page 6

Wednesday, April 13 Parametric Equations

Convert the rectangular equations below to parametric equations. Use the given parameters.

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

Convert the rectangular equations below to parametric equations:

6. [pic] 7. [pic] 8. [pic]

9. [pic] 10. [pic] 11. Circle: center: (2, -1), r = 9

Convert the rectangular equations below to parametric equations: First, complete the square first.

11. [pic] 12. [pic] 13. [pic]

Eliminate the Parameter and write the corresponding Rectangular Equation. Identify the shape.

14. [pic] 15. [pic] 16. [pic]

17. [pic] 18. [pic] 19. [pic]

page 7

Parametric Word Problems

1. Kevin hits a baseball at 3 ft. above the ground with an initial airspeed of 150 ft/sec at an angle of [pic] with the

horizontal. Will the ball clear a 20-foot fence that is 400 feet away?

2. During a Baseball game, Mr. Wernau swings as hard as he can at a ball 3.5 feet off the ground. He hits the ball with an initial velocity of 75 ft/sec at an angle of 36[pic] with the horizontal. Confident of hitting another home run, Mr. Wernau walks the bases. The outfield fence is 250 feet from home plate and is 20 feet tall, did Mr. Wernau hit a home run or should he start running?

3. A dart is thrown upward with an initial velocity of 58 ft/sec at an angle of elevation of [pic]. Find the parametric equations that model the problem situation. When will the dart hit the ground? Find the maximum height of the dart. When will this occur?

4. Kevin hits a baseball at 3 ft. above the ground with an initial airspeed of 150 ft/sec at an angle of [pic] with the horizontal. Will the ball clear a 20-foot fence that 400 feet away?

5. Find the maximum height and range of: a) [pic] feet per second b) [pic] feet per second

6 A baseball leaves the bat of a baseball player 3 feet above the ground with an initial velocity of 120 ft/sec at an angle of elevation of [pic]. If the wind is still, will the ball clear a 20 ft. fence 400 ft. from home plate?

page 8

7. A golfer hits a ball with an initial velocity of 133 ft/sec at an angle of elevation of [pic]. When does the ball hit the ground? Where does the ball hit the ground?

8. In celebration of the end of the school year, Mr. Wernau was firing his 45-calibur gun in the air at an angle of 75[pic]. If the muzzle velocity of a 45-calibur bullet is 825 ft/sec, find the following: The maximum height of the bullet and the maximum distance the bullet will travel.

9) A dart is thrown upward with an initial velocity of 58 ft/sec at an angle of elevation of [pic]. Find the parametric

equations that model the problem situation. When will the dart hit the ground? Find the maximum height of the dart.

When will this occur?

10) Kirby hits a ball when it is 4 ft. above the ground with an initial velocity of 125 ft/sec. The ball leaves the bat at a [pic] angle with the horizontal and heads toward a 30 ft. fence 350 ft from home plate. Does the ball clear the fence? If so, by how much? If not, could the ball be caught?

11)A golfer hits a ball with an initial velocity of 133 ft/sec at an angle of elevation of [pic]. When does the ball hit the ground? Where does the ball hit the ground?

12) A baseball leaves the bat of a baseball player 3 feet above the ground with an initial velocity of 120 ft/sec at an angle of elevation of [pic]. If the wind is still, will the ball clear a 20 ft. fence 400 ft. from home plate? If there is a 9 mph tailwind, will the ball clear the fence?

page 9

Conics and Parametrics Review

I. Identify the equation or graph as a parabola, circle, ellipse, hyperbola or semicircle.

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) 8) 9) 10)

II. Complete the square and write in standard form.

11) [pic] 12) [pic] 13) [pic]

III. Write an equation for each ellipse or parabola.

14) 15) 16) an vertical ellipse with a = 6, c = 5, center (2, -3)

17) a parabola with the vertex at (0, 8) and

a point on the graph is (12, 0).

IV. Convert the rectangular equations to parametric equations. Use the given Parameters.

18) [pic] 19) [pic] 20) [pic]

V. Eliminate the parameter and identify the graph of the curve.

21) [pic] 22) [pic] 23) [pic]

page 10

VI. Solve each word problem.

24) A microphone is placed at the focus of a parabolic reflector to collect sounds for the television broadcast of a football game. The microphone is 6 inches away from the center of the reflector. The width of the reflector is 36 inches across. How deep is the reflector?

25) The whispering chamber at the Museum of Science and Industry in Chicago is shaped like an ellipse. A person standing at once focus can hear a person standing at the other focus. The two people are 43 feet apart and are each 2 feet from the closest wall. Write an equation describing the ellipse.

26) Spencer is kicking a field goal. The ball is placed on the ground 40 yards from the goal post which has a crossbar 10 feet high. He kicks the ball with an initial velocity of 70 ft/sec at an angle of elevation of 40°.

a) Write the parametric equations describing the kick. b) Will he make the field goal?

GRAPH:

27) [pic] 28) [pic]

29) [pic] 30) [pic]

page 11

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download