O-Level Additional Math

PSLE marks the graduation of Primary school students and their entry into Secondary schools as teenagers. Discuss all issues about Secondary schooling here.
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archie2
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Re: Secondary School Mathematics

Post by archie2 » Sun Apr 07, 2013 9:38 pm

can someone help with this question
Q>> a bag contains 200 marbles. there are 60 red, 60 blue, 60 green and the remaining 20 consists of some yellow and white. If marbles are chosen from the bag without looking, what is the smallest number of marbles one must pick in order to ensure that, among the chosen marbles, at least 20 are of the same colour?

S-H
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Re: Secondary School Mathematics

Post by S-H » Sun Apr 07, 2013 10:34 pm

quekcc wrote:
S-H wrote:Hi Jieheng, I have one more question to ask:-

A woman invested an amount of money in a firm and earned a simple interest of $54 each year. In a certain year when the company was not performing well, the interest rate was decreased by 0.25%, and the annual interest received dropped to $47.20. How much money did she invest?

Thanks in advance!

The drop in interest received is $54-$47.2 = $6.8

which is equal to the amount invested $y x drop in interest rate

So 0.25% y = $6.8 ------> y = $2720



Thanks quekcc!

kelvinsoh
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Re: Secondary School Mathematics

Post by kelvinsoh » Mon Apr 08, 2013 12:39 am

archie2 wrote:can someone help with this question
Q>> a bag contains 200 marbles. there are 60 red, 60 blue, 60 green and the remaining 20 consists of some yellow and white. If marbles are chosen from the bag without looking, what is the smallest number of marbles one must pick in order to ensure that, among the chosen marbles, at least 20 are of the same colour?

To answer this question, we must understand that we want to be SURE that, even without looking, we will get at least 20 or the same colour. To be sure, we must account for if we are unlucky; in fact, we want to consider the unluckiest case possible to get the answer. So, assuming we have the worst luck ever, which marbles will we be picking up such that we don't get at least 20 of the same colour?
Hint 1 (Highlight to reveal) wrote: We might have picked the yellow and white ones, which will not give us 20 of the same. Thus, the answer is bigger than 20 because we could have picked those up and not get what we want.

Hint 2 (Highlight to reveal) wrote: If we are really unlucky, we will not get 20 red/blue/green quickly. We could have picked 19 red and then start drawing blue and greens and not get what we want. Thus, the answer is bigger than 20 (from hint 1) + 19. Try to continue from this way of thinking and see if you can arrive at the answer such that we surely will get 20 of a kind.

Answer (Hightlight to reveal) wrote: 78.
We could have picked 20 white/yellow, 19 reds, 19 blues and 19 greens and STILL not satisfy the criteria. After that, the next marble we pick would surely given us 20 red/green/blue marbles. Hence 20+19+19+19+1=78.
Last edited by kelvinsoh on Thu Apr 11, 2013 11:15 pm, edited 1 time in total.

pinkapple
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Re: Secondary School Mathematics

Post by pinkapple » Mon Apr 08, 2013 7:10 am

lost boy wrote:Q3. Write down three integers in A.P whose produce is a prime number


1(-1)(-3)

LOL123
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Re: Secondary School Mathematics

Post by LOL123 » Fri Apr 12, 2013 11:12 pm

hello, i would appreciate if someone can help me with these questions thanks in advance

1. Express the equation 100^x-10^(x+1)=11 as a quadratic equation in 10^x. Hence, find the value of x,correct to 2 decimal places.

2. (lgx)^2-lgx=0

3. Given y=e^(-1/2x), find the equation of the straight line in order to obtain the solution to the equation x+2lg(3x-1)=0

Thank You!


archie2
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Re: Secondary School Mathematics

Post by archie2 » Sat Apr 13, 2013 2:43 pm

can someone help with this question
John went to a stationery shop to buy some pens. A fountain pen cost $6, a roller ball pen cost $3 while a ballpoint pen costs $0.10. John spent $100, buying 100 pens in total. How many roller ball pen did he buy?

paperaeroplanes
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Re: Secondary School Mathematics

Post by paperaeroplanes » Sun Apr 14, 2013 2:08 am

can someone help with this question
John went to a stationery shop to buy some pens. A fountain pen cost $6, a roller ball pen cost $3 while a ballpoint pen costs $0.10. John spent $100, buying 100 pens in total. How many roller ball pen did he buy?


let the number of fountain pen be a, roller ball pen be b and ballpoint pen be c.

a+b+c = 100. 6a+3b+0.1c = 100
3b + 5.9c = 500
possible values of b = 147, 88, 29
a = 1, b = 29, c = 70

1. Express the equation 100^x-10^(x+1)=11 as a quadratic equation in 10^x. Hence, find the value of x,correct to 2 decimal places.

2. (lgx)^2-lgx=0

3. Given y=e^(-1/2x), find the equation of the straight line in order to obtain the solution to the equation x+2lg(3x-1)=0


1. 100^x-10^(x+1)=11
(10^x)^2 - 10(10^x) = 11
(10^x - 11)(10^x+1) = 0
10^x = 11 or 10^x = -1

2. (lgx)^2-lgx=0
(lgx)(lgx-1) = 0
lgx = 0 or lgx = 1

pinkapple
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Re: Secondary School Mathematics

Post by pinkapple » Sun Apr 14, 2013 8:27 am

LOL123 wrote:
3. Given y=e^(-1/2x), find the equation of the straight line in order to obtain the solution to the equation x+2lg(3x-1)=0



her u go
http://www.facebook.com/photo.php?fbid= ... =3&theater

lost boy
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Re: Secondary School Mathematics

Post by lost boy » Mon Apr 15, 2013 10:05 pm

Solve xy= -5
3x-2y= -11

Thanks :-)

jieheng
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Re: Secondary School Mathematics

Post by jieheng » Mon Apr 15, 2013 11:30 pm

lost boy wrote:Solve xy= -5
3x-2y= -11

Thanks :-)


3x - 2y = -11
=> y = (3x + 11) / 2

xy = -5
x [ (3x + 11) / 2 ] = -5
3x^2 + 11x + 10 = 0
(3x+5)(x+2) = 0
(3x+5) = 0 or (x+2) = 0
=> x = - 5/3 or x = -2

when x = - 5/3 , y = 3

when x = -2 , y = 5/2

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