Some math questions, wont take much time.

• davidche

  12 Oct 08, 23:18

   Is there a good method to tackle questions regarding : find an expression, in terms of n, for the nth term of the sequence.

  Eg: The first 5 of the sequence are: 3,5,9,17,33 ....

   This possibility question.

  Amy bought a box of buns. Each box contains 5 red bean buns, 3 blueberry buns and 2 coconut buns.  If Amy picks 2 buns at random, Find the probability that the 2 buns are same flavour.

  Whats a real number whats an integer?

• ^tamago^

  12 Oct 08, 23:24

  Find a pattern between the differences of the terms?
• davidche

  12 Oct 08, 23:26

  it always takes me a long time to do it. Most of the times i never get the answer. XD

• iamapebble

  12 Oct 08, 23:29

  Is there a good method to tackle questions regarding : find an expression, in terms of n, for the nth term of the sequence.

  Eg: The first 5 of the sequence are: 3,5,9,17,33 ....

  There is actually a formula to find simple number pattern questions for addition and multiplication which we do not learn at the stage. But then for me, since it's usually only 1 mark, I would straightaway skip this question and grab the other guaranteed marks I can first then see my luck. :D

   

  Amy bought a box of buns. Each box contains 5 red bean buns, 3 blueberry buns and 2 coconut buns.  If Amy picks 2 buns at random, Find the probability that the 2 buns are same flavour.

  P (2 buns are same flavour)
  = P (2 red bean) + P (2 blueberry) + P (2 coconut)
  = (5/10)(4/9) + (3/10)(2/9) + (2/10)(1/9)
  = 14/45

  P/S: Oops, I don't know what the hell I was doing, sorry!

  Whats a real number whats an integer?

  An integer is a number that can be written without decimal or fraction ie. -2, -1, 0 , 1 , 2. A real number is basically any number actually, be it fraction or decimal, which means even your pi is a real number. =)

   

   

• BaByBoY

  12 Oct 08, 23:47

  for the 1st qn the answer is For the Nth Term. N=2^(n-1)x3-(2^(n-1)-1) with N1=3 you`ll get the rest naturally quite simple acutally
• BaByBoY

  12 Oct 08, 23:48

  if u don mind, i can explain the methods to you.
• davidche

  12 Oct 08, 23:51

  Originally posted by BaByBoY:

  if u don mind, i can explain the methods to you.

  
  dont mind? i would love to know your method! XD

• BaByBoY

  12 Oct 08, 23:54

  usually it`s easy to find out one pattern like tt and many are able to name the next few in the pattern.. as such, maybe u`ll notice the next running number is actually, N=2n-1 so u list down the pattern with the N1 as the base number. So u get: N1=3 N2=2N1-1 N3=2N2-1 N4=2N3-1 and so forth.. then u express everything in terms of N1.. N1=3 N2=2N1-1 N3=2N2-1=2(2N1-1)-1=4N1-3 and so on.. By cont that,we get N1=3 N2=2N1-1 N3=4N1-3 N4=8N1-7 and so forth.. then u see the relations.. by now it`ll be easier to see that Nn=2x3-(2(N1-1)-1) easy???
• Garrick_3658

  12 Oct 08, 23:55

  Amy bought a box of buns. Each box contains 5 red bean buns, 3 blueberry buns and 2 coconut buns.  If Amy picks 2 buns at random, Find the probability that the 2 buns are same flavour.

  P (2 buns are same flavour)
  = P (1 red bean, 1 blueberry) + P (1 blueberry, 1 coconut) + P (1 red bean, 1 coconut)
    + P( 1 blueberry, 1 red bean) + P(1 coconut, 1 blueberry) + P(1 coconut, 1 red bean)
  = 2(5/10)(3/9) + 2(3/10)(2/9) + 2(5/10)(2/9)
  = 31/45

  HMM?

  P (2 same-flavoured buns)= 5/10 x 4/9 + 3/10 x 2/9 + 2/10 x 1/9 = 14/45

  Is there a good method to tackle questions regarding : find an expression, in terms of n, for the nth term of the sequence.

  Eg: The first 5 of the sequence are: 3,5,9,17,33 ....

  Have to think hard, and really, try to see SIMPLE patterns.

  If can't, just skip and attempt the other more worthy questions.

   

• Ahm97sic

  12 Oct 08, 23:55

  Hi iamapebble,

  There are 6 common number patterns that are set in the "O" level E.Maths exam.

  Pattern 1

  5, 7, 9, 11, 13, .....

  Since the pattern is +2, + 2, the nth term formula will be 2n + a

  n = 1, 2(1) + 3 = 5

  n = 2, 2(2) + 3 = 7

  So, the nth  term forrmula is 2n + 3

  Pattern 2

  3, 5, 9, 17, 33, .....

  Since the pattern is +2, + 4, + 8, ......,

                            ie +2, +2^2, +2^3

  so the nth term formula will be 2^n + a

  n = 1, 2^1 + 1 = 3

  n = 2, 2^2 + 1 = 5

  n = 3, 2^3 + 1 = 9

  So, the nth term formula for the first question asked by davidche will be

  2^n + 1

  Pattern 3

  4, 7, 12, 19, .....

  Since the pattern is +3, +5, +7, the nth term formula will be n^2 + a

  n = 1, 1^2 + 3 = 4

  n = 2, 2^2 + 3 = 7

  n = 3, 3^2 + 3 = 12,

  So, the nth term formula is n^2 +3.

  Hope this will be of help to you.

  Thank you for your kind attention.

  Regards,

  ahm97sic

   

   

   

• BaByBoY

  12 Oct 08, 23:55

  anyway wat level of maths are u at? o levels?
• davidche

  13 Oct 08, 00:01

  Originally posted by BaByBoY:

  usually it`s easy to find out one pattern like tt and many are able to name the next few in the pattern..

  as such, maybe u`ll notice the next running number is actually,

  N=2n-1

  so u list down the pattern with the N1 as the base number.
  So u get:
  N1=3
  N2=2N1-1
  N3=2N2-1
  N4=2N3-1 and so forth..

  then u express everything in terms of N1..

  N1=3
  N2=2N1-1
  N3=2N2-1=2(2N1-1)-1=4N1-3 and so on..

  By cont that,we get

  N1=3
  N2=2N1-1
  N3=4N1-3
  N4=8N1-7 and so forth..

  then u see the relations..
  by now it`ll be easier to see that
  Nn=2×3-(2(N1-1)-1)

  easy???

  HOLY CRAP SERIOUSLY THAT HELPED A TON THANKS MAN!

  We should be taught this in school. Totally reasonable compared to the conventional ''try your luck'' method.

  I am O lvl. XD

• davidche

  13 Oct 08, 00:03

  Originally posted by Ahm97sic:

  Hi iamapebble,

  There are 6 common number patterns that are set in the "O" level E.Maths exam.

  Pattern 1

  5, 7, 9, 11, 13, .....

  Since the pattern is +2, + 2, the nth term formula will be 2n + a

  n = 1, 2(1) + 3 = 5

  n = 2, 2(2) + 3 = 7

  So, the nth  term forrmula is 2n + 3

  Pattern 2

  3, 5, 9, 17, 33, .....

  Since the pattern is +2, + 4, + 8, ......,

                            ie +2, +2^2, +2^3

  so the nth term formula will be 2^n + a

  n = 1, 2^1 + 1 = 3

  n = 2, 2^2 + 1 = 5

  n = 3, 2^3 + 1 = 9

  So, the nth term formula for the first question asked by davidche will be

  2^n + 1

  Pattern 3

  4, 7, 12, 19, .....

  Since the pattern is +3, +5, +7, the nth term formula will be n^2 + a

  n = 1, 1^2 + 3 = 4

  n = 2, 2^2 + 3 = 7

  n = 3, 3^2 + 3 = 12,

  So, the nth term formula is n^2 +3.

  Hope this will be of help to you.

  Thank you for your kind attention.

  Regards,

  ahm97sic

   

   

   

  OMG THIS IS SOME SICK INSIDE INFO TOO. THANKS! XD

• BaByBoY

  13 Oct 08, 00:03

  well, the general method, is to present N in terms of N-1, then u re-express everything in terms of N1, it aint tt hard.. comes w practice thou.. most can come up with the next few terms in the pattern but will be dumbfolded when asked for the Nth term.. and tt`s what u need to set urself apart.
• hiphop2009

  13 Oct 08, 00:04

  tamago! check your mailbox!

• eagle

  13 Oct 08, 00:06

  sigh... last time my sec school gave a series of number patterns question... had 25 of them...

  I used it to teach tuition, but left it with a tuition student very long ago, and it's gone :(

   

• iamapebble

  13 Oct 08, 10:15

  Originally posted by Ahm97sic:

  Hi iamapebble,

  There are 6 common number patterns that are set in the "O" level E.Maths exam.

  Pattern 1

  5, 7, 9, 11, 13, .....

  Since the pattern is +2, + 2, the nth term formula will be 2n + a

  n = 1, 2(1) + 3 = 5

  n = 2, 2(2) + 3 = 7

  So, the nth  term forrmula is 2n + 3

  Pattern 2

  3, 5, 9, 17, 33, .....

  Since the pattern is +2, + 4, + 8, ......,

                            ie +2, +2^2, +2^3

  so the nth term formula will be 2^n + a

  n = 1, 2^1 + 1 = 3

  n = 2, 2^2 + 1 = 5

  n = 3, 2^3 + 1 = 9

  So, the nth term formula for the first question asked by davidche will be

  2^n + 1

  Pattern 3

  4, 7, 12, 19, .....

  Since the pattern is +3, +5, +7, the nth term formula will be n^2 + a

  n = 1, 1^2 + 3 = 4

  n = 2, 2^2 + 3 = 7

  n = 3, 3^2 + 3 = 12,

  So, the nth term formula is n^2 +3.

  Hope this will be of help to you.

  Thank you for your kind attention.

  Regards,

  ahm97sic

   

  Hey, thanks for the formulas, I'm sure many of us has gained something from it =) Now let's hope for O'levels it come out patterns like these. xD

• davidche

  13 Oct 08, 12:35

  Originally posted by iamapebble:

  Amy bought a box of buns. Each box contains 5 red bean buns, 3 blueberry buns and 2 coconut buns.  If Amy picks 2 buns at random, Find the probability that the 2 buns are same flavour.

  P (2 buns are same flavour)
  = P (1 red bean, 1 blueberry) + P (1 blueberry, 1 coconut) + P (1 red bean, 1 coconut)
    + P( 1 blueberry, 1 red bean) + P(1 coconut, 1 blueberry) + P(1 coconut, 1 red bean)
  = 2(5/10)(3/9) + 2(3/10)(2/9) + 2(5/10)(2/9)
  = 31/45

  Answer is 14/45 nia.

  Anyways its just a careless mistake

• maurizio13

  13 Oct 08, 12:55

   

  [ (5 x 4) + (3 x 2) + (2 x 1) ] / (10 x 9) = 28 / 90 = 14 / 45

   

   

• Mikethm

  13 Oct 08, 17:41

  Originally posted by ^tamago^:

  Find a pattern between the differences of the terms?

  Gah... I am not the only one who know this...

  Anyways, differences of terms is so damned useful with the new calculators who can solve 3 unknowns. Used to have problem with students "seeing" the patterns, now with the new calculators... they can no need to understand the question and still get the solution haha. Nice free 5 marks advantage hohoho. Of coz this blind method should be used for exams only and regular teaching should focus on patten observation as is the intent of the syllabus.

• kenzoshin

  13 Oct 08, 23:19

  Davidche

  Are you a tutor trying to solve questions for your students through this means and still earn your bucks the easy way? Just start cracking your own head if you are.  Nothing comes easy.

• kenzoshin

  13 Oct 08, 23:21

  BTW, if it is really your homework, go back to school and approach your teacher.  They are not paid for nothing by MOE using taxpayers' monies.  All the best to you in your studies (if you are a student).

• maurizio13

  13 Oct 08, 23:24

   

  i have this feeling that quite alot of the questions could be posted by tutors.

   

   

• kenzoshin

  13 Oct 08, 23:26

  Originally posted by maurizio13:

   

  i have this feeling that quite alot of the questions could be posted by tutors.

   

   Yeah, me too.  And others solved their problems and they pocket the money. Now that is crap!

   

• eagle

  13 Oct 08, 23:27

  Originally posted by maurizio13:

   

  i have this feeling that quite alot of the questions could be posted by tutors.

   

   

  And I just sit around copy questions for ExamWorld?