Q&A - PSLE Math

[verykiasu2010]

Dharma:

tianzhu:

[quote]At the end of Month 1 you have 2 pairs,

Hi Dharma

I am fine,Thank you.

I think there is only one pair at the end of month 1.(takes one month to mature)

Maybe,the error starts from the second month onwards.At the beginning of the second month, the first pair gives birth to the second pair.So the second pair will start to give birth from the beginning of the third month.

Thanks for pointing out the mistake.

Best wishes

After reading your reasoning I don't think you made a mistake. It is just that we made different assumptions. I assumed that the 1st pair was an adult pair and therefore already mature and was able to give birth to twins at the end of the 1st month.[/quote]just hijack the topic for one post : if only the singaporean population multiplies like the hamster!

[Tang]

Dharma:

tianzhu:

[quote] pair of hamsters can give birth to a pair of baby hamsters every month. Each pair of baby hamsters needs 1 month to mature and then this pair of hamsters will in turn give birth to a pair of baby hamsters every month. How many pairs of hamsters are there after 6 months? (4 marks)

Hi

I used a taulated list and got an answer of 13.

Dear fellow members, please help to check if my interpretation is correct.

Dharma,I'll appreciate if you could help to spot any mistakes in my table.

Best wishes

http://farm5.static.flickr.com/4102/4928674198_53b63b7647_b.jpg\">

Hi Tianzhu,
How are you doing friend?

At the beginning of Month 1, there will be only 1 pair of hamsters. At the end of Month 1 you have 2 pairs, end of Month 2, you have 3 pairs, end of Month 3 you have 5 pairs, end of Month 4 you have 8 pairs, end of Month 5 you have 13 pairs and finally at the end of Month 6 you will have 21 pairs.

Just shift the circles you have drawn in the boxes to the left so that they intersect with the vertical line. You will then have to insert the circles on the rightmost vertical line to show the number of pairs on the end of Month 6.

Thanks[/quote]
Hi,


The starting point should be Month 0 instead.

[tianzhu]

Dharma:

After reading your reasoning I don't think you made a mistake. It is just that we made different assumptions. I assumed that the 1st pair was an adult pair and therefore already mature and was able to give birth to twins at the end of the 1st month.

Hi Dharma

Thank you for your reply.

Looks like we need the predictive power of Paul the Octopus to know what the exam setter is looking for.

Best wishes

[kancheongmum]

Hi Dharma and James Ang


About the speed question, I don’t understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.

speed ratio UH: DH : GL ---- 4 : 12 : 6

time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)

total time 2h 20min—7/3 h

11u — 7/3h 1u — 7/33 h
UH distance ---- 6 x 7/33 x 4 — 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km

total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km

[tianzhu]

Hi kancheongmum


I think this question is from a Sec One textbook by Shinglee publishing.

There are three types of terrains, uphill, downhill and level ground.
The point to note is if the cyclist moves uphill in one direction, on the way back he moves downhill. So what is the average speed for this part of the road?

Use common multiple to find the average speed.

uphill ----4, downhill ----12, multiple-----12 (use 12 as the distance)

Distance/Speed ----Time

12/12 ----1h
12/4 ------3h
Average speed ------24/4 ------6 (distance two ways ----(12*2) --24)

Average speed for level ground -------6

Given time ------2h 20mins ------ 7/3h
Applying Distance -----S*T which is taught in P6 Maths

Distance ----7/3*6 -----14km

Best wishes

[James Ang]

I like this method, but Dharma has rightly pointed out that the correct answer should be independent of the distance travelled uphill/downhill.

kancheongmum:

Hi Dharma and James Ang

About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.

speed ratio UH: DH : GL ---- 4 : 12 : 6

time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)

total time 2h 20min---7/3 h

11u --- 7/3h 1u --- 7/33 h
UH distance ---- 6 x 7/33 x 4 --- 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km

total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km

[kancheongmum]

Hi tianzhu


Thank you for your reply and clear explanation. Now I fully understand the problem. Don’t know why this average thing did not cross my mind. Mental block. Actually this time inversely proportional to speed concept is from the book Conquer Problem Sums for Pri 6 thinking Maths onSponge which my ds use in his school as supplementary material.

[tianzhu]

Hi kancheongmum


You’re welcome.

Best wishes

[Dharma]

kancheongmum:

Hi Dharma and James Ang


About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.

speed ratio UH: DH : GL ---- 4 : 12 : 6

time ratio
(inversely proportional) UH : DH : GL ---- 12 : 4 : 6 ---- 6:2:3 (11u)

total time 2h 20min---7/3 h

11u --- 7/3h 1u --- 7/33 h
UH distance ---- 6 x 7/33 x 4 --- 168/33 km
DH distance ---- 2 x 7/33 x 12 ---- 168/33 km
GL distance ---- 3 x 7/33 x 6 ----126/33 km

total distance ----- 168/33 + 168/33 + 126/33 ---- 14 km

Hi kancheongmum,

Sorry for the late reply. Your method gives the correct answer but the approach in my opinion does not seem to be very correct . If you look at your working, you had worked out the individual distances for uphill , downhill and on level ground. Your workings suggest the distance uphill and downhill are the same but the question is silent about the ratio of individual distances. Since total time is given, it is possible to get the correct answer.

Pls correct me if I am wrong.

[Dharma]

kancheongmum:

Hi Dharma and James Ang


About the speed question, I don't understand why there must be a relationship between the speed of uphill, downhill and ground level. This is how I teach my ds how to solve the problem. Please let me know if I am wrong. Thanks.

Hi kancheongmum,

What I meant abt the relationship betw Uphill, downhill Level speeds is that as Tianzhu has shown the average speed of the 3 portions is the same 6km/h and thus the average speed of the whole journey can be taken as 6km/h too. Thus makes life easy as we just need to multiply with the total time taken to find the total distance.

If the average speed on the slope (up and down) and the level ground are different, we have a problem....