O-Level Additional Math

[Eddow]

carebear:

How to do 3+4+5+6.....+200


and 10+12+14+16+.....+400?

TIA.
:oops:

First, find how many number are there from 3 to 200 (both inclusive)
(200-3) + 1 = 198 numbers.

flip the sentence to become 200+199+198+...+4+3
Add this new sentence to the question, you'll get 203+203+203+...+203

198 x 203 = 40194
40194 /2 = 20097 (have to divide cos you've made a duplicate)

For the next question , same way of doing, try it.
but to find how many numbers there are :
(400-10)/2 + 1 = 196 numbers
(reason why divide by 2 is you are skipping 1 number in between)

[JadeDry]

Eddow:

mum_sugoku:

[quote=\"JadeDry\"]@ Eddow & Pinkapple


I checked the question, it still is: 9(x to the power of ab) - ((xy) to the power of ab) - 9(y to the power of ab) - 81

I would appreciate more help if you do not mind.

Which is the simplest form?:

(4X- 8Y) or 4(X-2Y)

And why?

Thanks in advance.

If question is .... \"+\" ((xy) to the power of ab).... instead of \"-\", then solution is (x^ab -9) (y^ab +9)..

I suspect printing error in the question. If it's ....+81, then answer should be (x^ab +9) (9 - y^ab)

For question like this...Which is the simplest form?:
(4X- 8Y) or 4(X-2Y) .
If the question is asking you to FACTORISE, then correct ans is 4(x-2y).[/quote]If I am asked to simplify is the correct answer also 4(X-2y)?

[Eddow]

JadeDry:

If I am asked to simplify is the correct answer also 4(X-2y)?

This is factorise form already. Can I have the question ? If the question has brackets and ask you to simplfy, then you have to expand all and the ans should be 4x-8y.

[pinkapple]

yup.

[mum_sugoku]

Eddow:

oh.. you're assuming +9(x^ab) - 81. And I'm assuming -9(x^ab) +81, that's why ans diff.


It's just printing error in the original question.

Agree with you - I also tried a few \"+\" & \"-\" combinations, but none can give answer that matches the question exactly :scratchhead:

[wkong]

Hi I have two questions from my son:


1. Find the smallest whole number that is not a factor of 12345…31

2. Find the largest prime number that divides this number

123…59+123*4…*60

Thank you in advance.

[FrekiWang]

wkong:

Hi I have two questions from my son:


1. Find the smallest whole number that is not a factor of 1*2*3*4*5......*31

2. Find the largest prime number that divides this number

1*2*3....*59+1*2*3*4.....*60

Thank you in advance.

1. 37
2. 61

I have to say that your son's trainer (most probably maths olympiad) is a failure >_< as these are very simple questions at competition level.

[wkong]

FrekiWang:

wkong:

Hi I have two questions from my son:


1. Find the smallest whole number that is not a factor of 1*2*3*4*5......*31

2. Find the largest prime number that divides this number

1*2*3....*59+1*2*3*4.....*60

Thank you in advance.

1. 37
2. 61

I have to say that your son's trainer (most probably maths olympiad) is a failure >_< as these are very simple questions at competition level.

Thanks Freki for your help. My DS wasn't trained for maths olympiad. This is part of his sch maths homework given by his sch teacher.

[Herbie]

I hv 2Qn.


1 factorise 3x^2+26x+51.
HENCE OR OTHERWISE FIND TWO FACTORS OF 32651.

2. If (a+b)^2=73 and ab=6.5, CALCULATE THE VALUE OF a^2+b^2

Can help to show the working? Tq

[mum_sugoku]

Herbie:

I hv 2Qn.


1 factorise 3x^2+26x+51.
HENCE OR OTHERWISE FIND TWO FACTORS OF 32651.

2. If (a+b)^2=73 and ab=6.5, CALCULATE THE VALUE OF a^2+b^2

Can help to show the working? Tq

1. (3x^2+26x+51) = (3x+17)(x+3)

32651=3*100^2 +26*100 +51 ==> x=100

Hence factors are (3*100+17) ie 317, and (100+3) ie 103.

2. (a+b)^2=a^2+2ab+b^2

==> 73 = a^2 + 2(6.5) +b^2
hence a^2 + b^2 =73 - 2(6.5) = 60