Q&A - PSLE Math

[fudgemum]

Thanks Ksmama. simplified way.


pattern 4 –> 4 * (4+3) = 47=28.
pattern 10 –> 10 * (10+3) = 1013 = 130.
pattern 438–> 438 (438+3) = 438441=193158.

To find out the number of diamonds without finding the number of toothpick

18th pattern –> 1+2+3+…+17+18 = 1819/2=171
500th pattern –> 1+2+…+499+500 = 500501/2 = 125250.

[fudgemum]

Another way of finding the number of toothpick


The pattern is
4,10,18,28,40 etc.

It can be written as
22, 22 + 32, 22 + 32 +42, 22 + 32 +42 +52, 22 + 32 +42 +52 +62 etc.

If you simply the above, nth pattern will be (n+1)(n+2) -2

So the 10th pattern will be 1112 - 2=130.

[ksmama]

Hi fudgemum, thanks, your 1st calculation for diamonds is straight forward and better. Yes, I remembered some years’ back a question in psle was 1+2+3…100 and was mentioned in the newspaper. After that the school taught the kids how to tackle such questions. Thanks for the reminder. 2nd method is more complicated for p6. Gee… its been such a long time since I saw that method. We did that in sec school right? Gee! I am just too old.

[fudgemum]

Hi Ksmama, I thought the second one was easier. Maybe I did not explain properly.


If the pattern is 4,10,18,28,40 then the difference between the n th and the n-1 th position is (n+1)2.

So the value of the nth position is =(n+1)2 + n2 + (n-1)2 +(n-2)2 +(n-3)2 + — + 22

Take the 2 out. So 2[2+3+4+5+…+(n-1) + n +(n+1)]
[Note: The sum of the sequence from 2 to n+1. The starting 1 is missing].

So it is 2 [ (n+1)(n+2)/2 -1].

Multiplying the 2 gives you (n+1)(n+2) -2.
Still if I have not put it properly, please ignore it.

[ksmama]

Hi, thank you. This formula was taught in sec sch in my days so I would not expect my kid in p5 to need to know this as yet but I noticed it is taught in Olympiad books and here I was trying to see the problem in old-fashioned primary- school- standard ways…Better look through my dust-gathering Olympiad books to catch up with what is expected…Still, it is fun to see the my favourite part of Maths: different ways to explore a problem

[tianzhu]

Maths questions from CNA forum ( http://www.channelnewsasia.com/discussion/forum.htm )


1. Jennifer bought some sugar and flour in the ratio 4:7. After baking some muffins, the ratio of the remaining sugar and flour became 5:6. 1/4 of the sugar and 1.7 kg of flour were used to bake the muffins. How much sugar did she buy?

2. Ahmad and Mei Ling saved $800 altogether.1/4 of Ahmad's savings was $65 more than 1/5 of Mei Ling's savings. How much money than Mei Ling did Ahmad save ?

[fudgemum]

[quote] Jennifer bought some sugar and flour in the ratio 4:7. After baking some muffins, the ratio of the remaining sugar and flour became 5:6. 1/4 of the sugar and 1.7 kg of flour were used to bake the muffins. How much sugar did she buy?[/quote]
4:7
20:35 (Mutiplying by 5)
1/4 of 20 is 5. So remaining is 20-5 =15.
15 ==> 5. So 6 units is 18.
So 35-18 = 17
17 units==>1.7kg
So 1 unit is 100 g.
20*100 = 2000.
The answer is 2 kg.

[quote]Ahmad and Mei Ling saved $800 altogether.1/4 of Ahmad's savings was $65 more than 1/5 of Mei Ling's savings. How much money than Mei Ling did Ahmad save ?[/quote]65*4=260.
800-260=540.
5+4=9
540/9 = 60.
Mei Ling ==>60*5 = 300
Ahmed ==>(60+65)*4 = 500
500-300=200
The answer is $200.

[tianzhu]

Thank you for your time.


Q1) During a warehouse book sale, Sally spent 62.5% of her money on 24 books and 18 pens. She also spent 25% of her remaining money on 18 files. Each pen costs 8/9 as much as the price of one book. The file costs $7.80 less than a book. Find the total cost of one book and one pen.

Q2) John and Sherry shared some sweets. John has 180 sweets less than Sherry. If Sherry gives 1/7 of her share to John, John will have 20 more sweets than Sherry How many sweets did Sherry have at first?Express the ratio of Sherry’s sweets to John’s sweets after the distribution?

[fudgemum]

Hi tianzhu,


For Q1 , I could solve only using algebra.

For Q2,
Sherry==>7units
John==>5units+20 [if you draw the model it will be easier]
The difference is 2units-20 =>180.
So 1 unit is 100.
So Sherry had 700 sweets at first.

After distribution Sherry has 6 units and John has 6units +20. Since each unit is 100, the ratio of Sherry’s sweet to John’s sweet after distribution is 600/620=30/31.

[suiyuan]

Thank you for your help.


1) 9 fewer students in the lower primary than upper primary competed in the story telling this year. 2/3 of all those who competed were boys. 3/7 of the lower primary participants were girls. 1/4 of the participants in the upper primary were girls. How many boys took part in the competition?

2) 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 rubber balls?

3) In Hall A, 30% of the 800 people were men. In Hall B, 40% of the 400 people were women and children. After some of the people in both halls had switched hall, 25% of the people in Hall A and 75% of those in Hall B were men. How many people were there in Hall B after the change?