Q&A - PSLE Math

[its888me]

its888me:

So sorry, another question from Nanyang prelim 2010 again, Q11:


Diagram A shows a closed rectangular tank of dimensions 20cm by 20cm by 40cm with a cube of edge 10cm glued to its bottom left corner. The tank contains 12 litres of water.

Diagram B shows the same rectangular tank lying on its side. Find the height of the water level, in cm, corrected to 2 decimal places.

http://i48.tinypic.com/302o09z.jpg\">

Again, TIA!

Can someone help with this question? My child assumed that in the Diagram B, the water level reached at the 1/2 point at the cube, thus, getting the answer 14.36cm. Given answer is 15.71.

Again, thanks a lot!

[speedmaths.012624com]

its888me:

its888me:

So sorry, another question from Nanyang prelim 2010 again, Q11:


Diagram A shows a closed rectangular tank of dimensions 20cm by 20cm by 40cm with a cube of edge 10cm glued to its bottom left corner. The tank contains 12 litres of water.

Diagram B shows the same rectangular tank lying on its side. Find the height of the water level, in cm, corrected to 2 decimal places.

http://i48.tinypic.com/302o09z.jpg\">

Again, TIA!

Can someone help with this question? My child assumed that in the Diagram B, the water level reached at the 1/2 point at the cube, thus, getting the answer 14.36cm. Given answer is 15.71.

Again, thanks a lot!

Hi,

Let's try this method:

First,
find the \"Volume of Air\" at top part of Diagram A.
(Vol of air) = (Vol of tank) - (Vol of water) - (Vol of cube).

Next,
find height (or depth) of air at top of Diagram B.
(Height of air) = (Vol of air) / (nett Base Area)
nett Base Area = (40 x 20) - (10 x 10)

Finally,
Height of water = 20 cm - (height of air)

Can you work from here?

Hope this helps.

Cheers

speedmaths.com


.

[tianzhu]

Essential:

Need help, please kindly assist. At 11am a car left town P for Town Q. Travelling at a speed of 80 km/h. At the same time , another car left town Q for town P at a speed of 100 km / h . The distance between the two towns was 720 km.at what time did the cars pass each other ?

Hi

Good Morning.

As usual for Speed questions, start with a simple diagram.

In 1h, the two cars covered 180 km (100 + 80).

When they pass each other or meet, they cover the entire distance between P and Q which is 720 km.

720/180 ------- 4 h

Hence, they passed each other at 3 pm.

Alternatively, if students are familiar with inverse proportion, they may also use it to calculate the distance travelled by the two cars.

Speed ratio

Car A: Car B ------- 80:100 ------ 4.5

The distance ratio remains the same as 4:5

9 units ------ 720

1 unit ------ 80

Distance covered by car A ------ 4*80 -------- 320 km

Time taken by car A ------- 320/80 -------- 4h

You may also use the distance covered by Car B and get the same answer of 4h.

In this case,(5*80)/100 ------ 4h

Best wishes

[Essential]

Good morning Tianzu, thank u very much for helping …

[Michaelia0816]

Pls help with this questions,


1) In a class, there are 4 more girls than boys. 1/3 of the boys and 7/11 of the girls take pubic buses to school. If 1/2 of the class takes pubic bus to school, how many pupils are there in the class?

My method:
Girls—1u+4
Boys—1u
In the class—2u+4
Half of the class—1u+2

1-1/3=2/3
1-7/11=4/11
(Take pubic bus) 1u+2-----1/3(boys)+7/11(girls)
(Do not take pubic bus) 1u+2-----2/3( boys)+4/11( girls)
Then, I dun know how to continue the next step, so help…

2) Isa had a total of 1464 orange, yellow and purple balloons for sale. The ratio o the orange balloons to the number of yellow balloons was 2:3. After Isa sold 3/4 of the yellow balloons, 1/2 half of the purple balloons and none of the orange balloons, he had 812 balloons left. How many yellow balloons did Isa have at first?

My answer for this is 960, but I do checking, I found out it is wrong so I really really dun know do this question.

[tianzhu]

Michaelia0816:

1) In a class, there are 4 more girls than boys. 1/3 of the boys and 7/11 of the girls take pubic buses to school. If 1/2 of the class takes pubic bus to school, how many pupils are there in the class?

Hi

You may use “Units and Parts”.

Boys

Total number ----- 3 units

1 unit ----- take public bus

Girls

Total number ----- 3 units + 4

1/2 of the class takes pubic bus to school

Total number of boys and girls in class ----- 6 units + 4

1/2 of the class ----- 3 units + 2

Hence, number of girls taking public transport ------ 2 units + 2 (3 units + 2 – 1 unit)

If you need a diagram at this stage, draw a simple one.

2 units + 2 ----- 7 parts (7/11)

1 unit + 2 ----- 4 parts (4/11)

Equalise the parts or cross multiply.

8 units + 8 ----- 7 units + 14

1 unit ----- 6

Number of girls ----- 3*6 + 4 ----- 22

Number of boys ----- 18

Total number ----- 40

Another possible way is to use logical reasoning with “SL”.

We know that the number of girls must be multiples of 11 and the average class size is about 30/40.

Work out a listing and see that the conditions are met.

Best wishes.

[tianzhu]

Michaelia0816:

My answer for this is 960, but I do checking, I found out it is wrong so I really really dun know do this question.

Hi

If you work based on the question, you would get an answer of 960.

However when you plugged back to check, it defied logic.

Please check your question.

Best wishes

[tech_nomax]

Pls help with these questions:

1) In March, the number of goldfish in an aquarium was 2/5 the number of angelfish. In April, some goldfish gave birth and its population increased by 80. In the same month, after 50 angelfish died, there were 80% as many goldfish as angelfish. What was the difference between the number of goldfish and the number of angelfish left in the aquarium?

2) At a farm, there were 360 more chickens than ducks. 3/5 of the chickens and 25% of the ducks were sold. In the end, there were 80 more ducks than chickens. How many chickens were there at the farm in the end?

[tianzhu]

tech_nomax:

2) At a farm, there were 360 more chickens than ducks. 3/5 of the chickens and 25% of the ducks were sold. In the end, there were 80 more ducks than chickens. How many chickens were there at the farm in the end?

Hi

You may use MD or work using units.

Chickens ------ 20 units + 360

Chickens@sold ----- 12 units + 216 (3/5)

Chickens@left ----- 8 units + 144

Ducks ------ 20 units

Ducks@sold ----- 5 units (25%)

Ducks@left ----- 15 units

15 units ----- 8 units + 144 + 80

1 unit ----- 32

Number of chickens in the end ------ 8 units + 144 ------ 400

Best wishes

[tianzhu]

tech_nomax:

Pls help with these questions:

1) In March, the number of goldfish in an aquarium was 2/5 the number of angelfish. In April, some goldfish gave birth and its population increased by 80. In the same month, after month, after 50 angelfish died, there were 80% as many goldfish as angelfish. What was the difference between the number of goldfish and the number of angelfish left in the aquarium?

Hi

Please check phrase highlighted in pink.

Best wishes