Q&A - PSLE Math

[Dharma]

yeodo:

Hi Parents


Please help with this question :

Luke spent 45% of his monthly income. For the month of July, his income was 30% less than August. His expenses for July was $648 less than his expenses for August. What was his income in August?

0.45 (10u - 7u) = $648
1.35u = $648
Income in Aug = 10u = $6480/1.35 = $4800

[Kiasu Friend]

Hi all,


Could anyone provide the solution for this problem:

Robert cycles to his friend’s house and then returns home by the same route. He always cycles at constant sppeds of 5 km/h when going uphill, 15 km/h when going downhill, and 8 km/h when on level ground. If his total cycling time is 2 hrs 40 minutes, what is the distance he cycles in km?

Thanks a lot for your help.

[tianzhu]

James Ang:

Came across some thinking type questions in sec 1 textbooks that can be solved using model/primary methods.;


1. Jack cycles to his friend's house and then returns home by the same route. He always cycles at 4 km/h when going uphill and, 12 km/h when going downhill, and 6 km/h when on level ground. If his total cycling time is 2h 20mins, what is the distance he cycles in km?

Kiasu Friend:

Robert cycles to his friend's house and then returns home by the same route. He always cycles at constant sppeds of 5 km/h when going uphill, 15 km/h when going downhill, and 8 km/h when on level ground. If his total cycling time is 2 hrs 40 minutes, what is the distance he cycles in km?

Hi

Your question is almost similar to JA's earlier question in this thread except for changes in the name and speeds of cyclist.The duration is also slightly different.

You may wish to check if figures(5,8 and 15) are in order.

Best wishes

[kiasuparents_user]

Hi gurus!


I am unsure of the solutions provided for the above question.


Q15c) It is a question to detect patterns.
Any gurus can help me visualise the patterns? Most most most appreciated! Don’t have the diagram so please help if you can.

100 x 49 = 4900 -> how & why?
4900 + 50 - 4950 - how & why?

Thanks in advance!!

[James Ang]

not sure if my speed problem has been solved, the correct answer is 14km.


Kiasu friend's question may not be correct, the uphill speed is 5km/h, the downhill speed is 15km/h, the possible way to solve is when the level ground speed is 7.5km/h, then the total distance travelled is 20km. What is the source of this question, perhaps I can find out if the question is correct or not. Cheers.

tianzhu:

James Ang:

Came across some thinking type questions in sec 1 textbooks that can be solved using model/primary methods.;

1. Jack cycles to his friend's house and then returns home by the same route. He always cycles at 4 km/h when going uphill and, 12 km/h when going downhill, and 6 km/h when on level ground. If his total cycling time is 2h 20mins, what is the distance he cycles in km?

Kiasu Friend:

Robert cycles to his friend's house and then returns home by the same route. He always cycles at constant sppeds of 5 km/h when going uphill, 15 km/h when going downhill, and 8 km/h when on level ground. If his total cycling time is 2 hrs 40 minutes, what is the distance he cycles in km?

Hi

Your question is almost similar to JA's earlier question in this thread except for changes in the name and speeds of cyclist.The duration is also slightly different.

You may wish to check if figures(5,8 and 15) are in order.

Best wishes

[tianzhu]

kiasuparents_user:

Hi gurus!


I am unsure of the solutions provided for the above question.

Q15c) It is a question to detect patterns.
Any gurus can help me visualise the patterns? Most most most appreciated! Don't have the diagram so please help if you can.

100 x 49 = 4900 -> how & why?
4900 + 50 - 4950 - how & why?

Hi

First thing first, if you’re looking for gurus, then you’re in the wrong thread.

Many of us here are parents who are sharing from their experience as one who had gone through the PSLE journey.

As for your question, it’ll be helpful if you could let us know the source (school/P5/6/year) so that we could search for more information.

Best wishes

[Dharma]

James Ang:

not sure if my speed problem has been solved, the correct answer is 14km.


Kiasu friend's question may not be correct, the uphill speed is 5km/h, the downhill speed is 15km/h, the possible way to solve is when the level ground speed is 7.5km/h, then the total distance travelled is 20km. What is the source of this question, perhaps I can find out if the question is correct or not. Cheers.

tianzhu:

[quote=\"James Ang\"]Came across some thinking type questions in sec 1 textbooks that can be solved using model/primary methods.;

1. Jack cycles to his friend's house and then returns home by the same route. He always cycles at 4 km/h when going uphill and, 12 km/h when going downhill, and 6 km/h when on level ground. If his total cycling time is 2h 20mins, what is the distance he cycles in km?

Kiasu Friend:

Robert cycles to his friend's house and then returns home by the same route. He always cycles at constant sppeds of 5 km/h when going uphill, 15 km/h when going downhill, and 8 km/h when on level ground. If his total cycling time is 2 hrs 40 minutes, what is the distance he cycles in km?

Hi

Your question is almost similar to JA's earlier question in this thread except for changes in the name and speeds of cyclist.The duration is also slightly different.

You may wish to check if figures(5,8 and 15) are in order.

Best wishes

[/quote]Hi Kiasu Friend,

What JA is trying to say is that in order to solve this problem, there must be a certain relationship between the speeds that are given in the question for uphill, downhill and on level ground.

For JA’s Qn

(A/4 + B/6 + C/12) + (A/12 + B/6 + C/4) = 7/3
Solving
4(A+ B + C)/12 = 7/3
A + B + C = 7km

Total distance cycled by Jack = 7km x 2 = 14km

Take note :
1/6 = (1/4 + 1/12)/2

For Kiasu Friend’s question

If speed at level ground is X

1/X = (1/5 + 1/15)/2 =2/15
X = 7.5

If X = 7.5km/h

(A/5 + 2B/15 + C/15) + (A/15 + 2B/15 + C/5) = 8/3
4(A + B + C )/15 = 8/3

A + B + C = 10

Total distance travelled by Robert = 10km x 2 = 20km

[atutor2001]

kiasuparents_user:

Hi gurus!


I am unsure of the solutions provided for the above question.


Q15c) It is a question to detect patterns.
Any gurus can help me visualise the patterns? Most most most appreciated! Don't have the diagram so please help if you can.

100 x 49 = 4900 -> how & why?
4900 + 50 - 4950 - how & why?

Thanks in advance!!

Maybe the question is as follows :

Pattern No. 1 is \"1 square of area 50 cm sq\"
Pattern No. 2 is \"1 square of area 50 + 1 square of side 7cm\"
Pattern No. 3 is \"1 square of area 50 + 2 squares of side 7cm\"
Pattern No. 4 is \"1 square of area 50 + 3 squares of side 7cm\"
.....

Find the area of all the squares for pattern number 101.

You can break down the \"area\" of above pattern into :

Pattern No. 1 gives an area of 50 = 50 + (0 x 49)
Pattern No. 2 gives an area of 99 = 50 + (1 x 49)
Pattern No. 3 gives an area of 148 = 50 + (2 x 49)
Pattern No. 4 gives an area of 197 = 50 + (3 x 49)

Notice the \"multiple of 49\" is less than the pattern no. by 1.

Pattern No. 101 gives an area of 50 + (101-1)x49 = 4950

Hope my guess make sense.

[Kiasu Friend]

Dharma:

Hi Kiasu Friend,

What JA is trying to say is that in order to solve this problem, there must be a certain relationship between the speeds that are given in the question for uphill, downhill and on level ground......... [/quote]

--------------------------

Hi Dharma, Tianzhu and James Ang,

Thank you very much for providing the solution to the 'speed' question so quickly. The question was taken from a Maths Forum posted there by some member. So the speed on level ground could have been erroneously mentioned as 8 Km instead of 7.5 km. I am sorry for the error.

I thank you for your time and splendid effort in providing not only the solution, but also for promptly pointing out the error in data.

Thanks and best regards to each of you.

[tianzhu]

Kiasu Friend:

The question was taken from a Maths Forum posted there by some member. So the speed on level ground could have been erroneously mentioned as 8 Km instead of 7.5 km. I am sorry for the error.

Hi

Could you help to provide a link to the Maths forum you mentioned so that members can have another avenue to broaden their knowledge?

Best wishes