O-Level Additional Math

[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

[Xiao Hu]

Hi FrekiWang,


Need help on this question, I think it’s 2010 O level Maths paper 1 question.
Part2 looks innocuously easy, but it trips me up. Difficult to put my reasonings in writings.

There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5

#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?

From #1, since 90=6x15, how can this be used to work out possible values of x?

The answers given for x are 9 and 45.

TIA,
Xiao Hu.

[FrekiWang]

Xiao Hu:

Hi FrekiWang,


Need help on this question, I think it's 2010 O level Maths paper 1 question.
Part2 looks innocuously easy, but it trips me up. Difficult to put my reasonings in writings.

There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5

#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?

From #1, since 90=6x15, how can this be used to work out possible values of x?

The answers given for x are 9 and 45.

TIA,
Xiao Hu.

90=2*3^2*5
6=2*3
15=3*5
Therefore, x=2^a * 3^2 * 5^b
where a=0 or 1(reject as odd) and b=0 or 1
when a=0,b=0: x=3^2=9
when a=0,b=1: x=3^2*5^1=45

[Xiao Hu]

FrekiWang:

Xiao Hu:

Hi FrekiWang,


Need help on this question, I think it's 2010 O level Maths paper 1 question.
Part2 looks innocuously easy, but it trips me up. Difficult to put my reasonings in writings.

There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5

#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?

From #1, since 90=6x15, how can this be used to work out possible values of x?

The answers given for x are 9 and 45.

TIA,
Xiao Hu.

90=2*3^2*5
6=2*3
15=3*5
Therefore, x=2^a * 3^2 * 5^b
where a=0 or 1(reject as odd) and b=0 or 1
when a=0,b=0: x=3^2=9
when a=0,b=1: x=3^2*5^1=45

Hi FrekiWang,
Good one!! I could't have expessed the solution this way, I would have them in English.
This is a bit tough for O level Maths, isn't it? It's only 1 mark. Crazy.

Thanks very much, appreciate it.
Xiao Hu.

[Bestmark]

Hi


Any recommendation for maths tuition centre? which is better mavis, mind stretcher or smartlab or ms loi?

[JadeDry]

Hello,


Can you please help me with the following question?

Make "t" the subject of the formula:

T= 2(pi) * (the square root of(( (t^2) + (k^2)) / 2gt))

I have checked the answer which is:
t = (+ or -) (1/ (2pi)) (The square root of((2gt(T2)) - ((4(pi squared))(k squared))

I do not understand how they have used the lower case "t" in the formula.

Is it correct?

Thanks in advance.

[Belle2011]

Hello,

May I ask where can I get books/resources on math olympiad questions suitable for lower sec?
Thank-you.

cheers,
Belle.

[mum_sugoku]

JadeDry:

Hello,


Can you please help me with the following question?

Make \"t\" the subject of the formula:

T= 2(pi) * (the square root of(( (t^2) + (k^2)) / 2gt))

I have checked the answer which is:
t = (+ or -) (1/ (2*pi)) *(The square root of((2gt(T*2)) - ((4*(pi squared))(k squared))

I do not understand how they have used the lower case \"t\" in the formula.

Is it correct?

Thanks in advance.

Ya by right \"t\" shouldn't be in there if it is the subject.. So I too think that answer is incorrect.

Anyway this is a seemingly tedious sum (I mean the working). You'll need to apply the standard formula x=[-b +- sq rt (b^2 -4ac) ]/2a to solve it.. Here's what I've got after working it out, not sure if it's correct though:

t ={ (T^2)g +- {sq rt[(T^4)(g^2) - 16(pi^4)(k^2)]} } / (4pi^2)