Q&A - PSLE Math

[tianzhu]

Hi


Another similar question to your Q3.

There are two bag of stones labeled A and B. In bag A ,there are 350 black stones and 500 white stones. In bag B , there are 400 black stone and 100 white stones. How many black and white should be transfer from bag B to bag A so that 50% of the stones in bag A and 75%of those in bag B are black?

There are different approaches; you may solve it pictorially, by units and parts or letters of the alphabet.

Number of black stones ------ 350 + 400 ------ 750

Number of white stones ------- 500 + 100 ------ 600

Bag A

Black: White ------ 1u:1u (50% black, 50% white)

Bag B

Black: White ------ 3p:1p (75% black, 25% white)

2p -------- 750 – 600 ------150

1p ------- 75

3p ------- 225

1p -------- 75

Number of black stones transferred out ------ 400 – 225 ------- 175

Number of white stones transferred out ------ 100 – 75 ------- 25

Best wishes

[tianzhu]

Winx5015:

(2). Mrs Tan bought 3kg of strawberries and 8kg of grapes. Mrs Chin bought 3kg of grapes and 8kg of strawberries. Mrs Chin spent $35 more than Mrs Tan. If 1kg of grapes cost $8, how much would 1kg of strawberries cost?

Hi

You may use MD.

5 kg of strawberries ------- 35 more than 5 kg of grapes

Hence, 1kg of strawberries is $7 more expensive than 1kg of grapes.

1 kg of strawberries -------- 8+7 ------15

Best wishes

[jewelbox]

Hi, how do I solve this qn? Thanks. http://i47.tinypic.com/2j1si1k.jpg\">

[nounou]

This Q comes from Pei Chun Prelim 2012 Q18.

I would like to know if there is another method to find answer for b and c.
One that is easier to understand and remember. Please help. :?: :imdrowning:
:thankyou: :thankyou: :thankyou:


quote=\"charsen\"]

ms_lim:

Can help to explain how to solve this question?

http://i47.tinypic.com/v4ov3b.jpg\">

C)
I try to find the general rule and i found it for how to find the total no.of tiles.It is (pattern no.x2-1)x(pattern no.x2-1)+4.
I subtracted 4 from the total no. of tiles in each question.For example,29-4=25.
You know that 25 is a square root of 5,which is a odd no.So,if you subtract 4 from all the total no. of tiles,you get the square root of odd no.Next,you should find the odd no. of the square root you found.
take pattern 3 as an example.
29-4=25
5x5=25
i need to find the relation ship between the pattern no. and the odd no.So,I used the formula to find odd numbers which is 2n-1-->(3+3)-1=5
And there,i found the formula.
Cheers[/quote]

[Winx5015]

thanks tianzhu

[tianzhu]

Treelodge:

This Q comes from Pei Chun Prelim 2012 Q18.

I would like to know if there is another method to find answer for b and c.

Hi

This question is difficult as compared to the other pattern questions in previous papers.

I don't have much time to prepare slide, so just give you some pointers.

Please bear with it if you find it disorganised.

For the white tiles, notice that the number of white tiles in the odd pattern number is always 4 more than the number of white tiles in the even pattern number. That is to say when the number of white tiles in the even section changes, the number of white tiles in the next odd section increases by 4.

Take for example 8 to 12, 32 to 36.

So we focus on the even pattern number.

8 -------- 4*2 ------- 2*2*2

32 ------- 16*2 -------4*4*2

72 -------- 36*2 -------6*6*2

So we can see that the it follow a pattern of (n*n*2) where n is the pattern number.

For the odd pattern number, simply add 4 to the number tiles before it.

For pattern 30, we have 30*30*2 -------- 1800.

For the total number of tiles, take note that he difference between 2 numbers are 8, 16,32,24,32,40,48 …….

Hence, we have 8(1+2+3+4+5+6……..)

Students should be familiar with calculating the sum of numbers from 1 to 100.

We follow a pattern of 5 + 8 * (sum of numbers from 1 to n-1) , where n is the pattern number.

In this case, pattern 86.

So we have n ------ 86 and (n-1) ------ 85

Therefore, we need 5 + 8 * ( sum of numbers from 1 to 85)

The total number ------- 5 + 8( 85*86)/2 -------- 29245

Best wishes

[kuts]

What is the missing number in the box?

60*300 = ____*300 +300

[kwcllf]

kuts:

What is the missing number in the box?

60*300 = ____*300 +300

59 is the number.

[zanen]

hello can help me with this qns 10 workers can complete a painting job. If there are 2 more workers, the painting job will be completed 6 days sooner. If the same painting job were to be done 21 days earlier, how many additional workers are needed?

[zeemimi]

jewelbox:

Hi, how do I solve this qn? Thanks. http://i47.tinypic.com/2j1si1k.jpg\">

(a) ¼ x 2 π 3 + ¼ x 2 π 2 + 3/4x2 π 1 = 4 π

(b)

(A) Area of big quad = ¼ π3x3 = 9/4 π
(B) Area of white space under medium quad = 2x2 – ¼ π2x2 = 4 – π
(C) Area of white space in rect under smallest quad = 2x1 – ¼ π1x1= 2 – ¼ π
(D) Area of semi circle = ½ π 1x1= ½ π
Area of shaded region = (A) – (B) – (C) + (D) = 6.57 cm2