Q&A - PSLE Math

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Thanks for your time.


Question 1:
Theodore, Gareth and Linus ytook part in a 100-meter race. When Theodore completed the race, Gareth and Linus were 15m and 30m away from the finishing line respectively. How far Linus from the finishing line when Gareth finished the race? (note: all the boys were travelling at a comstant speed throughout the race)

Question2:

http://www.postimage.org/image.php?v=PqNdgtS

:?:

[tianzhu]

Hi, hope this helps.


Q1. Linus was 15m away. Difference between Gareth and Linus was (30-15).

Q2. Length of one side of equilateral triangle = 12
Area of triangle CYW = ½6.83 = 10.2 (XW=3, midpoint)
Area of triangle CXW = 25.8 – 10.2 = 15.6 cm2

[chengsmummy]

Hi,


Q1, the answer should not be 15m, because Linus and Gereth are travelling on the different speed, so the difference should not remain the same.
assume they took 1 unit of time to complete the first 85 and 70m respectively, then Gereth will take 15/85 unit time to finish the remaining 15m.
then Linus will travel 15/85 * 70 = 12.35m at the same time. so when Gereth at the finish line, Linus was 30-12.35 = 17.65m away.

tianzhu:

Hi, hope this helps.

Q1. Linus was 15m away. Difference between Gareth and Linus was (30-15).

Q2. Length of one side of equilateral triangle = 12
Area of triangle CYW = ½*6.8*3 = 10.2 (XW=3, midpoint)
Area of triangle CXW = 25.8 – 10.2 = 15.6 cm2

[tianzhu]

chengsmummy:

Hi,


Q1, the answer should not be 15m, because Linus and Gereth are travelling on the different speed, so the difference should not remain the same.
assume they took 1 unit of time to complete the first 85 and 70m respectively, then Gereth will take 15/85 unit time to finish the remaining 15m.
then Linus will travel 15/85 * 70 = 12.35m at the same time. so when Gereth at the finish line, Linus was 30-12.35 = 17.65m away.

Hi, Thank you for the correction.

[kiasiparent]

tianzhu:

Hi, hope this helps.


Q1. Linus was 15m away. Difference between Gareth and Linus was (30-15).

Q2. Length of one side of equilateral triangle = 12
Area of triangle CYW = ½*6.8*3 = 10.2 (XW=3, midpoint)
Area of triangle CXW = 25.8 – 10.2 = 15.6 cm2

Hi,

For Q2, the question is wrong.

By pythagoras theorem, we will know that CX =sqrt root(144 - 36) = sqrt 108 = 10.39 cm

By similar triangle, CX = 6.8 x 2 = 13.6 cm

[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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http://farm4.static.flickr.com/3393/3417332796_6a8904c6e1_o.jpg\">

[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: .