O-Level Additional Math

[ChiefKiasu]

insanePaPa:

Sec1 maths Question:

Two race cars, Car X and Car Y, are at the starting point of a 2km track at the same time. Car X and Car Y make one lap every 60s and 80s respectively.
How long, in minutes, will it take for the faster car to be 5 laps ahead of the slower car?

Thanks all Gurus in advance.

5 laps = 5 x 2km = 10km

Car A's speed = 2/60 = 1/30 kps
Car B's speed = 2/80 = 1/40 kps

Let T be time taken for Car A to be 10km ahead of Car B. Hence
(1/30)*T - (1/40)*T = 10
=> T(1/30 - 1/40) = 10
=> T(4-3/120) = 10
=> T(1/120) = 10
=> T = 1200s = 20mins

[insanePaPa]

ChiefKiasu:

insanePaPa:

Sec1 maths Question:

Two race cars, Car X and Car Y, are at the starting point of a 2km track at the same time. Car X and Car Y make one lap every 60s and 80s respectively.
How long, in minutes, will it take for the faster car to be 5 laps ahead of the slower car?

Thanks all Gurus in advance.

5 laps = 5 x 2km = 10km

Car A's speed = 2/60 = 1/30 kps
Car B's speed = 2/80 = 1/40 kps

Let T be time taken for Car A to be 10km ahead of Car B. Hence
(1/30)*T - (1/40)*T = 10
=> T(1/30 - 1/40) = 10
=> T(4-3/120) = 10
=> T(1/120) = 10
=> T = 1200s = 20mins

Thanks a million chief.

[ChiefKiasu]

chrisu:

Can ignore this, I already got the workings and answer. Thank you.

chrisu:

Please help A Sec.2 Maths question of Proportion.

Q) The scale of map P is 1:p and the scale of map Q is 1:q. If the same area is represented as 32sq.cm. on map P and 50sq.cm. on map Q, calculate the ratio p:q.

Kindly show workings as well.

Thank you.

1/p = sqrt(x/32) => p = sqrt(32/x)
1/q = sqrt(x/50) => q = sqrt(50/x)

=> p/q = sqrt(32/50) = sqrt(16/25)
=> p:q = sqrt(16) : sqrt(25) = 4 : 5

[ChiefKiasu]

YumYum:

Hi, need help with this sec1 Qn:


The key to a code is given by three whole numbers. The key is transmitted from the headquarters by 3 agents, who were given the product of 2 of the 3 numbers. Suppose that the numbers transmitted are 432, 540 and 720. What is the key code?

thanks.

The hard part to the question is trying to understand what the heck it is saying.

The code is A, B, C

Agent X has A*B = 432
Agent Y has B*C = 540
Agent Z has A*C = 720

X/Y => A/C = 432/540 => A = C*432/540
Since A*C =720
=> C*C*432/540 = 720
=> C*C = 720 * 540/432 = 900
=> C = 30
A = 720/C = 720/30 = 24
B = 432/A = 432/24 = 18

So the 3 numbers are 18, 24 and 30.

[ChiefKiasu]

YumYum:

Hi, 1 more Qn:


Given that S =. 1
___________________________________________________
1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 +...1/30

Find the largest whole number smaller than S.

Thanks

Sorry... don't understand what you typed. Can you scan the question and post it as an image?

[YumYum]

Dear chief,


Thank you for your help.

For the 2nd Qn, never mind, it was covered in school.

Thanks 

[insanePaPa]

Sec1 Qn:


A class has between 30 to 40 students. Each boy in the class brings 15 chocolates for a class party. The chocolates are shared equally among 20 girls and a teacher with no leftovers.
i) How many students are there in the class?
ii) How many chocolates does their teacher receive?
:thankyou:

[Jtutor]

insanePaPa:

Sec1 Qn:


A class has between 30 to 40 students. Each boy in the class brings 15 chocolates for a class party. The chocolates are shared equally among 20 girls and a teacher with no leftovers.
i) How many students are there in the class?
ii) How many chocolates does their teacher receive?
:thankyou:

Hi insanePapa,

Since there are between 30-40 students in the class, there should be between 10-20 boys (after deducting 20 girls).

If each boy brings 15 chocolates for the party, and the total chocolates are shared among 20 girls + 1 teacher = 21 people, we must find the number of boys such that when it is multiplied by 15 chocolates, the total number of chocolates can be divided equally among 21 people.

15 = 3 x 5
21= 3 x 7
Hence, possible values for the number of boys will be 7, 14, 21, etc.
Since we know that the value should be between 10-20, the number of boys should be 14.

i) Number of students in the class = 20 girls + 14 boys = 34.

ii) Each of the 20 girls & 1 teacher will receive 15 x 14 / 21 = 10 chocolates. Hence, answer is 10.

Cheers!
Jtutor

[chrisu]

Thank you for your working and answer.

But my daughter's teacher gave the answer a p:q = 5:4 instead of 4:5.

I also got 4:5 as answer initially.

ChiefKiasu:

chrisu:

Can ignore this, I already got the workings and answer. Thank you.
[quote=\"chrisu\"]Please help A Sec.2 Maths question of Proportion.

Q) The scale of map P is 1:p and the scale of map Q is 1:q. If the same area is represented as 32sq.cm. on map P and 50sq.cm. on map Q, calculate the ratio p:q.

Kindly show workings as well.

Thank you.

1/p = sqrt(x/32) => p = sqrt(32/x)
1/q = sqrt(x/50) => q = sqrt(50/x)

=> p/q = sqrt(32/50) = sqrt(16/25)
=> p:q = sqrt(16) : sqrt(25) = 4 : 5[/quote]

[lost boy]

Please help me answer this question.


Find the smallest number,p,such that p/2 is a perfect square and p/3 is a perfect cube