Q&A - PSLE Math

[Dreamerz]

Hi I need help for these questions:


1) Tap A can fill up an empty tank in 20 minutes and Tap B can empty it the full tank completely in 12 minutes. Both taps were turned on at the same when the tank is 1/2 filled. how long does it take for the tank to be completely emptied?

2)Mrs Lim’s son helped her to type the page numbers of her new book. He noticed that different pages required different numbers of digits. He counted that there were a total of 675 digits. How many pages were there in the book?

thank you in advance!!

[stary]

Dreamerz:

Hi I need help for these questions:


1) Tap A can fill up an empty tank in 20 minutes and Tap B can empty it the full tank completely in 12 minutes. Both taps were turned on at the same when the tank is 1/2 filled. how long does it take for the tank to be completely emptied?

thank you in advance!!

Hi!

F1RST Question:

Difference->1/12 - 1/20 = 1/30 tank per min
Time -> 1/2 (Divide by) 1/30 = 15 min

Best regards!

[stary]

Dreamerz:

Hi I need help for these questions:


2)Mrs Lim's son helped her to type the page numbers of her new book. He noticed that different pages required different numbers of digits. He counted that there were a total of 675 digits. How many pages were there in the book?

thank you in advance!!

Hi!

2ECOND question:

1 - 9 -> 9 digits
10 - 99 -> 90 numbers -> 180 digits
Total -> 189 digits
Left -> 675 - 189 = 486 digits
Division -> 486/3 = 162
Pages -> 162 + 99 = 261

Best wishes!

[Alchemist]

vidhyalog:

tianzhu:

[quote=\"vidhyalog\"]Hi - Could somebody help me with this sum. From Punggol Primay Prelim 2011.


An egg seller had chicken eggs, duck eggs and quail eggs. He had 225 more quail eggs than duck eggs. After he had sold 60% of the chicken eggs, 2/3 of the duck eggs and 3 times as many quail eggs as duck eggs sold, he found that he had 25% of his quail eggs and a total of 205 eggs left. Find the total number of eggs he had first.

Hi

I’ll just provide some pointers for you to draw the MD.

Draw 3 boxes to show duck.
2 units of duck sold, left 1 unit.
For quail eggs, sold ------- 6 units (3 times), left ------2 units (25% left).

Draw a 5 smaller boxes or circles to show chicken.

From MD, we can see
5 units ----- 225
1 unit ----- 45

Number of eggs left ------ 2 boxes for chickens + 1 unit(duck) + 2 units (quail) ------205

Hence 2 boxes for chicken -----205 – (3*45)
1 box of chicken ------ 35

Total number of eggs he had first. ------ (11*45) + (5*35) -----670

Best wishes

[/quote]
Sorry Tianzhu - I am afraid I do not understand how to get 5 circles for chickens.
Thanks

[Tang]

tianzhu:

ck123:

Hi tianzhu


How to teach the kid hexagonal packing? Any formula or pattern ?

Thanks for your enlightenment.

Hi

You may use 50 cents coins to form the pattern as demonstration. If you pack the coins in hexagonal format, you’ll be able to pack them more densely.

Hope this helps.

Best wishes

http://farm7.static.flickr.com/6176/6146554898_54f4db9088_z.jpg\">

Hi,

Sorry, I tried packing in hexagonal pattern, but only got 35 coins.

7 x 3 = 21
7 x 2 = 14
21 + 14 = 35

So it looks like 36 is the answer (12 x 3).

Someone may like to double-check and confirm what is the correct answer?

[tianzhu]

vidhyalog:

Sorry Tianzhu - I am afraid I do not understand how to get 5 circles for chickens.

Hi

In answering this question, a student needs to recognise that the box's size showing chickens is different from those of ducks and quails.

To differentiate them we may use other shapes such as circle or even star.

In this slide presentation, I used boxes of different sizes.

The four stars in my slide symbolises a bright and successful PSLE 2011 for PSLE kids. Needless to say, four A* for four subjects.

Best wishes

http://farm7.static.flickr.com/6192/6146804950_c011b6a6d6_z.jpg\">

[smileplease]

Please help with these 3 Qs:


1) John takes part in a race in which he needs to walk, run and cycle. He walks for 1km, runs for the next 2km and cycles for the last 3km of the race. He cycles thrice as fast as he runs and runs thrice as fast as he walks. The total time he takes to complete the 3 activities is 42 minutes more than if he has cycled for the whole journey. How much more time does he take to walk than run?

2) Jason has some cups. 10% of the cups are red. The number of red cups is 20% of the number of the blue cups. The rest of the cups are green. If there are 760 green cups, how many cups are there altogether?

3)The average cost of a few cups was $8. After another cup that cost $32 was added, the average cost became $12. How many cups were there in the end?

[nanosphere]

Anyone can give me the answer for this question:

A car left town A for town B. At the same time, a lorry left town B for town A. The average speed of the car was 90 km/h while the speed of the lorry was 70 km/h. The two vehicles passed each other at a point 36 km away from the mid-point between town A and town B. What was the distance between town A and town B?
:thankyou:

[tianzhu]

nanosphere:

Anyone can give me the answer for this question:

A car left town A for town B. At the same time, a lorry left town B for town A. The average speed of the car was 90 km/h while the speed of the lorry was 70 km/h. The two vehicles passed each other at a point 36 km away from the mid-point between town A and town B. What was the distance between town A and town B?

Hi

As in any speed question, it’s useful to translate words into picture. Draw a line diagram.

In 1h the car travelled 20km faster than the lorry. This means the vehicles meet or pass one another at 10km away from the midpoint.

10km ------- 1h
36km ------- 3.6

Distance between A and B ------- combined speed*time ------ 160*3.6 -------576

Best wishes

[tianzhu]

smileplease:

Please help with these 3 Qs:


1) John takes part in a race in which he needs to walk, run and cycle. He walks for 1km, runs for the next 2km and cycles for the last 3km of the race. He cycles thrice as fast as he runs and runs thrice as fast as he walks. The total time he takes to complete the 3 activities is 42 minutes more than if he has cycled for the whole journey. How much more time does he take to walk than run?

2) Jason has some cups. 10% of the cups are red. The number of red cups is 20% of the number of the blue cups. The rest of the cups are green. If there are 760 green cups, how many cups are there altogether?

3)The average cost of a few cups was $8. After another cup that cost $32 was added, the average cost became $12. How many cups were there in the end?

Hi

Sorry I am rushing out the solutions because you may need them urgently as your exam is near. Please bear with me if there are errors.

Q1

Time taken for
Walk ----- 9 units
Run ----- 3 units
Cycle ------- 1 unit

9 units + 6 units + 3 units -------- 6 units +42
12 units -----42
1 unit ------3.5

Walk ------ 31.5 mins
Run ------ 21 mins

Difference ------ 10.5 mins

Q2

1 unit ------ red
5 units------blue
4 units -----green

4 units -------760
1 unit -------190

Total number ------10 units -------1900


Q3

12-8 -----4

32-12 ------20

The extra $20 is distributed to the original or existing number of cups.

20/4 -----5

5+1 -------6

Best wishes