Tutor MathsGuru: Ask me for your burning Maths questions!

[YLH88]

Hi Brenda10,


Thank you so much!! Now I understand liao ..

Hi VC,

Thank you so much for the solution!! You are right, the options given in the questions are in 1, 2, 3, 4 Just that I wrote in (a, b, c, d) to easy differentiate between the question and options You are so well-informed of where the answers to all the related questions are !!
[quote]I believe the answer options given in the actual Maths exam script is in numerical option (1,2,3,4) and not alphabetical option (a,b,c,d). Pls clarify.[/quote]

[Herbie]

Hi, I have one qn which needs help?




Paya Lebar MGS, Paper 2, Q15


5x5 = 25
5x5x5=125
5x5x5x5=625
5x5x5x5x5=3125

(a) What is the sum of the last three digits in 5 to the power of 15?
(b) What is the sum of the last four digits in 5 to the power of 210?

Can someone provide us with the solution?

Many thanks!

[Maths Monster]

delete

[CoffeeCat]

Herbie:

Hi, I have one qn which needs help?




Paya Lebar MGS, Paper 2, Q15


5x5 = 25
5x5x5=125
5x5x5x5=625
5x5x5x5x5=3125

(a) What is the sum of the last three digits in 5 to the power of 15?
(b) What is the sum of the last four digits in 5 to the power of 210?

Notice that the last 3 digits of 3125 is 125, which corresponds to the 125 from two lines before. The cycle will repeat itself 125, 625, 125,625...
As for the pattern of the last 4 digits more calculations is needed
just remember to work with the last 4 digits and discard the rest and u will find the pattern.

[corneyAmber]

Herbie:

Hi, I have one qn which needs help?

Paya Lebar MGS, Paper 2, Q15
5x5 = 25
5x5x5=125
5x5x5x5=625
5x5x5x5x5=3125

(a) What is the sum of the last three digits in 5 to the power of 15?
(b) What is the sum of the last four digits in 5 to the power of 210?

Can someone provide us with the solution?

Many thanks!

(a) odd number power => it ends with 125
so power of 15 is odd number => it will end with 125,
Hence sum of last 3 digits = 1+2+5 = 8

I need to mull over how to present (b).

[Muffins]

Brenda10:

Muffins:

Hi Brenda10, your daughter just managed to summarise my workings into a few steps! :shock: How old is your DD???

Thank you Muffins.

She is 11 years old.

:shock: :shock: Very young and VERY BRIGHT!!!

[ruyu]

Vanilla Cake:

YLH88:

6) Mark can climb uphill at an average speed of 2km/h and go downhill at an average speed of 6km/h. Going first uphill and then downhill, without stopping and using the same route, what will his average speed be for the entire trip ?

Assume the distance of the route be unit.
Total time taken = unit/2 + unit/6 = 4units/6 = 2units/3
Distance = unit
Average speed = unit÷2 units/3 = unitx3/2units = 3/2 = 1.5 km/h

This is similar to NMOS 2009 Prelim round Q3. Where is this question taken from?

dont understand :? care to explain?

[Brenda10]

Muffins:

Brenda10:

[quote=\"Muffins\"]Hi Brenda10, your daughter just managed to summarise my workings into a few steps! :shock: How old is your DD???

Thank you Muffins.

She is 11 years old.

:shock: :shock: Very young and VERY BRIGHT!!! :)[/quote]Hi Muffins,

Thank you for thinking highly upon her. :oops:


In fact, DD is just average. She has done more than 50 ratio/percentage questions during the school holiday and may be the numerous practices really help. The questions in this forum really provide her the good opportunity on trial and error. The more important thing is that she could also learn from all of you as well.

[Vanilla Cake]

ruyu:

dont understand :? care to explain?

Thks for pointing out, I have amended the workings.
Average speed should be 3 km/h

LCM of 2 and 6 is 12

Time taken to climb uphill @ 2 km/h = 12/2 = 6h
Time taken to go downhill @ 6 km/h = 12/6 = 2h
Total time taken = 8h
Total distance covered = 12x2 = 24 km
Average speed for the entire trip = 24km/8h = 3 km/h

[Dharma]

Vanilla Cake:

ruyu:

dont understand :? care to explain?

Thks for pointing out, I have amended the workings.
Average speed should be 3 km/h

LCM of 2 and 6 is 12

Time taken to climb uphill @ 2 km/h = 12/2 = 6h
Time taken to go downhill @ 6 km/h = 12/6 = 2h
Total time taken = 8h
Total distance covered = 12x2 = 24 km
Average speed for the entire trip = 24km/8h = 3 km/h

Time ratio: Uphill : Downhill = 3 : 1
Ave speed = ((2 x 3) + (6 x 1))km/(3 +1)h = 12km/4hr = 3km/h