Page 2 of 7 FirstFirst 1234 ... LastLast
Results 26 to 50 of 168
Like Tree16Likes

Thread: Cambridge HSC MX1 Textbook Marathon/Q&A

  1. #26
    Cadet
    Join Date
    Nov 2014
    HSC
    2016
    Gender
    Male
    Posts
    97
    Rep Power
    3

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Capture.PNG

    By the way, thanks for making this thread David

  2. #27
    Executive Member
    Join Date
    Jun 2014
    HSC
    N/A
    Gender
    Male
    Location
    Sydney, New South Wales
    Posts
    1,885
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by wu345 View Post
    Capture.PNG

    By the way, thanks for making this thread David
    Your question was

    13 (c) In how many ways can one yellow, two red and four green beads be placed on a bracelet if the beads are identical apart from colour? [Hint : This will require a listing of patterns to see if they are identical when turned over.]

    To arrange 1 yellow, 2 red, and 4 green objects in a line, the number of possible ways is:
    7! / (1! * 2! * 4!)
    = (7*6*5*4*3*2*1) / (1 * 2*1 * 4*3*2*1)
    = 105

    However, since the objects are not in a line but in a circlular way (e.g. on a bracelet), the circle can be rotated to that what appears to be 7 possibilities is actually just 1, i.e. ABCDEFG = BCDEFGA = CDEFGAB = DEFGABC = EFGABCD = FGABCDE = GABCDEF. So instead of 105 possibilities, there are actually 105 divide 7 = 15 ways.

    But since you can also FLIP the bracelet, not just rotate it, you'll find that of those 15 possibilities, 3 of them are symmetrical (so flipping them has no effect), and the other 12 are actually just 6 pairs of equivalent possibilities. So the actual answer is 15 - 6 = 3 + (12/2) = 3 + 6 = 9
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

  3. #28
    Executive Member
    Join Date
    Jun 2014
    HSC
    N/A
    Gender
    Male
    Location
    Sydney, New South Wales
    Posts
    1,885
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    I had a problem with this question tonight EX 3A, Q 5 (b)







    Here is my effort of drawing the displacement-time graph:



    What confused me was the answer should the graph distances being accumulated? Is this supposed to be? Im treating the base of the hill at its initial position, the top of the hill as its maximum, and returning back down the hill as back to where it initially started.
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

  4. #29
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by davidgoes4wce View Post
    I had a problem with this question tonight EX 3A, Q 5 (b)







    Here is my effort of drawing the displacement-time graph:



    What confused me was the answer should the graph distances being accumulated? Is this supposed to be? Im treating the base of the hill at its initial position, the top of the hill as its maximum, and returning back down the hill as back to where it initially started.
    It says that he goes down the other side of the hill, so he doesn't come back to where he starts; his final displacement should be 2 m.

  5. #30
    Executive Member
    Join Date
    Jun 2014
    HSC
    N/A
    Gender
    Male
    Location
    Sydney, New South Wales
    Posts
    1,885
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post
    It says that he goes down the other side of the hill, so he doesn't come back to where he starts; his final displacement should be 2 m.
    ok thanks, personally felt that question was pretty badly worded but maybe its just me. Could accept something along the lines of 'total distance-time' graph.
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

  6. #31
    Cadet
    Join Date
    Jul 2015
    HSC
    N/A
    Gender
    Undisclosed
    Posts
    39
    Rep Power
    3

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Can someone please help me with question 20


    Sent from my iPhone using Tapatalk

  7. #32
    Member jathu123's Avatar
    Join Date
    Apr 2015
    HSC
    2017
    Gender
    Male
    Location
    Sydney
    Posts
    339
    Rep Power
    3

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    http://imgur.com/uMddJgF

    That's part a. Not entirely sure about part b though
    2017
    4u99 - 3u98 - EngAdv88 - Phys94 - Chem94
    Atar : 99.55
    Course: AdvSci(Hons)/Engineering(Hons) @ UNSW

  8. #33
    Cadet
    Join Date
    Nov 2014
    HSC
    2016
    Gender
    Male
    Posts
    97
    Rep Power
    3

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    part b... I think...
    I'm not sure that you can just assume the altitudes meet at E
    http://i.imgur.com/9qgFLtr.jpg

  9. #34
    Cadet
    Join Date
    Jul 2015
    HSC
    N/A
    Gender
    Undisclosed
    Posts
    39
    Rep Power
    3

    Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by wu345 View Post
    part b... I think...
    I'm not sure that you can just assume the altitudes meet at E
    http://i.imgur.com/9qgFLtr.jpg
    But isn't AC 5x^2 not 4x^2 in part a
    Last edited by dlau; 15 Apr 2016 at 11:27 PM.

  10. #35
    -insert title here- Paradoxica's Avatar
    Join Date
    Jun 2014
    HSC
    2016
    Gender
    Male
    Location
    Outside reality
    Posts
    2,438
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    It is not obvious at all to me that the altitudes intersect on the edge.

    (If it did, I would have already used my signature phrase)
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  11. #36
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread





    I've forgotten how to binomial probability completely

  12. #37
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by leehuan View Post




    I've forgotten how to binomial probability completely
    Use standard binomial probability formulas with p = 18/30 if you want to define 'success' as a rainy day, or p = 1 – 18/30 = 12/30, if you want to define 'success' as a fine day.

  13. #38
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post
    Use standard binomial probability formulas with p = 18/30 if you want to define 'success' as a rainy day, or p = 1 – 18/30 = 12/30, if you want to define 'success' as a fine day.
    Didn't work when I tried because I forgot what nCr is

  14. #39
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by leehuan View Post
    Didn't work when I tried because I forgot what nCr is
    n!/(r!.(n-r)!)

    n will be 5 because we have 5 days total.

  15. #40
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Oops, my bad on the wording. I meant what to use as n and r.

    Basically, two clumsy attempts whilst being tired weren't correct.

    30C3.(3/5)^3.(2/5)^27
    +30C4.(3/5)^4.(2/5)^26
    +30C5.(3/5)^5.(2/5)^25 which I realised was obviously wrong but

    5C3(3/5)^3 (2/5)^2 + 5C4 (3/5)^4 (2/5)^1 + 5C5 (3/5)^5 (2/5)^0. still didn't work

  16. #41
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by leehuan View Post
    Oops, my bad on the wording. I meant what to use as n and r.

    Basically, two clumsy attempts whilst being tired weren't correct.

    30C3.(3/5)^3.(2/5)^27
    +30C4.(3/5)^4.(2/5)^26
    +30C5.(3/5)^5.(2/5)^25 which I realised was obviously wrong but

    5C3(3/5)^3 (2/5)^2 + 5C4 (3/5)^4 (2/5)^1 + 5C5 (3/5)^5 (2/5)^0. still didn't work
    For the first two days chosen to be fine, the probability is: (prob. a day is fine)^2 = (12/30)^2

    This Q. is like a coin toss Q. basically.

    (We are assuming for this Q. that the weather of the days are independent of each other (which is probably not a valid assumption, but oh well).)

  17. #42
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Oh right I was staring at part b) though I did get stuck on both

    The answers were a) 0.0124, b) 0.7102 (at 4d.p.)
    _______________________________

    But I'm feeling really dumb right now. I still can't see anything. Might need a more specific sketchout...

    For a) If I assume the same day can get chosen twice I used (2/5)^2(3/5)^3 but that just gives 0.03456.

    I don't know what I'm doing

  18. #43
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by leehuan View Post
    Oh right I was staring at part b) though I did get stuck on both

    The answers were a) 0.0124, b) 0.7102 (at 4d.p.)
    _______________________________

    But I'm feeling really dumb right now. I still can't see anything. Might need a more specific sketchout...

    For a) If I assume the same day can get chosen twice I used (2/5)^2(3/5)^3 but that just gives 0.03456.

    I don't know what I'm doing
    I found how they got their answer to part a): they did (12/30)^5 (but this should be the probability that all days are fine, not the probability that the first two days are fine).

  19. #44
    Executive Member
    Join Date
    Jun 2014
    HSC
    N/A
    Gender
    Male
    Location
    Sydney, New South Wales
    Posts
    1,885
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by leehuan View Post
    Oops, my bad on the wording. I meant what to use as n and r.

    Basically, two clumsy attempts whilst being tired weren't correct.

    30C3.(3/5)^3.(2/5)^27
    +30C4.(3/5)^4.(2/5)^26
    +30C5.(3/5)^5.(2/5)^25 which I realised was obviously wrong but

    5C3(3/5)^3 (2/5)^2 + 5C4 (3/5)^4 (2/5)^1 + 5C5 (3/5)^5 (2/5)^0. still didn't work












    Last edited by davidgoes4wce; 16 Apr 2016 at 11:28 AM.
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

  20. #45
    Executive Member
    Join Date
    Jun 2014
    HSC
    N/A
    Gender
    Male
    Location
    Sydney, New South Wales
    Posts
    1,885
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Reckon they did a mistake in the book for both parts a) and b)
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

  21. #46
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by davidgoes4wce View Post












    In leehuan's version of the question (the one he typed up some posts ago), part a) just asked for the probability that the first two days are wet, which is different to your part a), which also requires the remaining days to be fine. Is leehuan's edition of the textbook different to yours?

  22. #47
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Facepalm... I didn't type a bit of the question...
    davidgoes4wce likes this.

  23. #48
    Rambling Spirit
    Join Date
    Dec 2014
    HSC
    N/A
    Gender
    Male
    Posts
    6,043
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by leehuan View Post
    Facepalm... I didn't type a bit of the question...
    Ah OK, that would explain the difference. Though if davidgoes4wce's version of the Q. is correct, then yes, the answers had a mistake, they did the probability all days were fine. This mistake could be added to the textbook mistakes thread if anyone wants to add it in.
    davidgoes4wce likes this.

  24. #49
    Ancient Orator leehuan's Avatar
    Join Date
    May 2014
    HSC
    2015
    Gender
    Male
    Posts
    5,812
    Rep Power
    7

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread

    Quote Originally Posted by InteGrand View Post
    Ah OK, that would explain the difference. Though if davidgoes4wce's version of the Q. is correct, then yes, the answers had a mistake, they did the probability all days were fine. This mistake could be added to the textbook mistakes thread if anyone wants to add it in.
    @david Please.

    This disheartened my morning lol.

  25. #50
    Executive Member
    Join Date
    Jun 2014
    HSC
    N/A
    Gender
    Male
    Location
    Sydney, New South Wales
    Posts
    1,885
    Rep Power
    4

    Re: Year 12 Mathematics 3 Unit Cambridge Question & Answer Thread















    Just had a bit of trouble with part (a)
    | B Eng (Hons) | IB Mathematics SL | IB Mathematics HL | Australian Cricket | Casual University Statistics Tutor

Page 2 of 7 FirstFirst 1234 ... LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •