Q&A - PSLE Math

[AnnT2009]

Both questions are from CHIJ 2008 SA1.


Q1 Cabrini had 2 squares, M and N. Square M and N have perimeter in the ration 7:5. The lenghts and bradths of both squares are whole numbers.
She cut square N into 5 equal strips and put 4 strips side by side with square M to form a new shape. Find the perimeter of the new shape.

Q2 There are some rubber balls and plastic balls in a bag. If 1 rubber ball were to be removed from the bag, then 1/7 of the remaining balls in the bag would be rubber balls. If 2 plastic balls were to be removed from the bag instead of 1 rubber ball. then 1/5 of the balls left behind would be rubber balls. If another 5 rubber balls were to be put into the bag, what fraction of all the balls would be runner balls?

[Dharma]

Hi,


Q1 is not very clear as to how the strips are arranged with square M …are they arranged vertically or horizontally on 1 side only …OR are they arranged on all sides?

Different arrangements will give different answers

[Dharma]

Hi,


As for Q2…u need to use ratios to solve

If u remove 1 rubber ball,

Original ratio of rubber : plastic = 1unit +1 : 6 units

If u remove 2 plastic balls,

Original ratio of rubber : platic = 1 unit + 1 : 4 units + 4 + 2

Therefore …6 units = 4 units + 6
2 units = 6
1 unit = 3

There were 4 rubber balls and 18 plastic balls originally.

If 5 more rubber balls are put into the bag,

The fraction of rubber balls = 4 +5 /4+18+5 = 9/27 = 1/3

[tianzhu]

Hi,hope this helps.


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[edanson]

HI,


Yes, TianZhu is correct for both questions.

Although I would like to add in a little. The question mentioned that the ratio of the perimeter M to perimeter N is 7 : 5 and not ratio of each side of the square is 7:5

If ratio is 7:5,
then you can expand it (by multiplying them by 2), you will get 14: 10 or (multiplying by 4 for this case for easy calculaion ) 28:20

With this expanded ratio 28:20 each side of the square M will be 7 units (28 units/4 sides) and each side of square N will be 5 units (20units / 4 sides ) and each breadth of the 5 strips wil be one unit ( 5units / 5 strips )

From here, one will be able to understand TianZhu's answer more eaeily.

Hope my part helps and not confuse you parents.


TianZhu - are you a school teacher or Maths tutor or a lover for :love: Maths too ? You are great and extremely clear in your explaination. You are also very IT savy to be able to put your explainatione in pictures.

Any hint how you do that, wanted to learn to help my kids too :oops: .

[AnnT2009]

Dharma, Tianzhu and edanson,


Thank U.

[Dharma]

Thanks for posting Fig 2 of Q1, tianzhu… makes it all the more obvious

[tianzhu]

edanson:

TianZhu - are you a school teacher or Maths tutor or a lover for :love: Maths too ? You are great and extremely clear in your explaination. You are also very IT savy to be able to put your explainatione in pictures.

Any hint how you do that, wanted to learn to help my kids too :oops: .

Hi edanson

All your guesses were wrong. I am a victim of circumstances. Private schools specialising in Maths are expensive and my pockets are not deep enough to send my son there. Realising that he needs help at certain times, I am forced to read up so as to be able to help him when he needs it.

I am glad you liked my solutions. I want to show my son that Maths is beautiful. It can be colourful and fun too.

I am definitely not IT savvy, just a one finger typist. I use PowerPoint 2007 to work out the answers.

[tianzhu]

Dharma:

Thanks for posting Fig 2 of Q1, tianzhu..... makes it all the more obvious

Hi
You may view the questions @ http://www.misskoh.com

[Dharma]

Hi Friends


Came across a question posted earlier …The Xmas Tree shape Qn …wish to share a different approach to solve this qn using patterns.

a)
If we notice the centre column of numbers …their difference are all in multiples of 4.

We can determine the middle column nos. as follows

Row 1 = 1 [1+0] = [1+4(0)]
Row 2 =5 [1+4] = [1+4(1)] [1+4(1)]
Row 3 =13 [1+4+8] = [1+4(1)+4(2)] [1+4(1+2)]
Row 4 = 25 [1+4+8+12] = [1+4(1)+4(2)+4(3)] [1+4(1+2+3)]
.
.
Row N [1+4(1)+4(2)+…4(N-1)] [1+4(1+2+…+(N-1)]

We can therefore determine the middle number of Row 6 by using the pattern above

Middle number of row 6 - [1+4(1+2+3+4+5)] = 61

We now need to find out how many numbers are there in each row…

Row Pattern
1 - 1
2 - 3 [(2x2)-1]
3 - 5 [(3x2)-1]
. .
. .
N 2N-1

There are 2(6)-1 = 11 numbers in Row 6[ 5 numbers on the left and 5 numbers on the right of the middle number]

3rd number of Row 6 = 61 - (5-2)x2
= 55

b) To find the sum of numbers in the 1st 5 rows (all odd numbers from 1 to 49)

Sum of all numbers from 1 to 49 = (49x50)/2
= 1225

Sum of all even numbers from 1 to 49 = 2(1+2+3+ …+22+24)
= 2 x (24x25)/2
= 600

Sum of all odd numbers from 1 to 49 = 1225 - 600
= 625

Hope that this explanation is useful …