Outline for Integrated 3 Spring Final

May 2005

Questions

 

1.     Remember Height(time) = -9.8 meters/second2 * t2 + sin(angle)*velocity*t + init height and Distance(time) = cos(angle) * velocity * t If a goalie kicks a ball at 25 meters/sec at 10o from 0.5 meters high, how far will the ball travel before it hits the ground?

2.     You are playing Risk and are on the attack.  You roll three dice.  Using Pascal’s triangle, how would you calculate the probability of rolling at least two fives?  What would that probability be?

3.     You agree to meet a friend at the mall between 12:00 PM and 1:00 PM and each of you agree to wait 15 minutes before leaving.  What would be the probability that you would actually meet?

4.     You are running a lottery for your school.  You agree that there will be a grand prize of $800.00, two $500.00 prizes, three $100.00 prizes, and ten $20.00 prizes.  Each ticket costs $1.00.  If you want to make $4000.00 profit for your school, how many tickets would you need to sell?  What would be the actual fair price for each ticket?  How much profit will you make on each ticket sold?

5.     What are the differences between polar and compass coordinates (bearing)?

6.     What are the rectangular coordinates for the following Polar Coordinates?

a.  (110, 36o)     b. (87, 136o)

7.     Add the following two vectors:  (110, 36o) and (87, 136o)

8.     If you are rowing across a river that is 0.5 kilometers wide with a flow of 4 km/h and row at 5 km/h, at what angle upriver would you have to row to cross straight across the river?

9.     What is the Law of Cosines?  How is the law modified for a right triangle?  If you know that a = 5 cm, b = 8 cm, and m<C = 43o, what are the measures of c, m<B, and m<A?

10. What is the Law of Sines?  If at point A, you look at a mountain and it is at 240 West of North.  You go 23 miles at 370 south of east to point B.  At point B, you look at the same mountain and it is 360 West of North.  How far is the mountain away from both A and B?

11. On page 543, look at examples A. and B., describe each graph and give an example of something that would cause a graph of this type.

12. You get onto a ferris wheel at the bottom of its loop.  At this point, you are 6 feet above the ground.  The radius of the ferris wheel is 33 feet.  It makes 3 revolutions per minute.  Please create a formula (using A, B, C, and D) to describe the sine or cosine function.

13. Looking at page 578, create a pattern with a vertical reflection.

14. What is a tessellation?

15. Draw one tessellation.  Show how it can repeat.  What geometric shapes did you use?

16. What did you like best about this class during the year?

17. What did you learn, that you did not know previously, in this class?

18. Do you have any suggestions on how to make this class better?

19. What plans do you have for this summer?  Will you be doing anything in which you could do any mathematical calculations that you learned this year?

20. What are your plans for next year?