O-Level Additional Math

[TheOliveTree]

Hi chrisu,


Determine the scale for area first from the given linear scale.

Map P
1 cm : p cm
1 cm^2 : p^2 cm^2
32 cm^2 : 32p^2 cm^2

Map Q
1 cm : q cm
1 cm^2: q^2 cm^2
50 cm^2 : 50q^2 cm^2

Since the actual areas represented on Map P and Map Q are the same,

50q^2=32p^2
p^2/q^2=32/50
p/q = sqrt (32/50)
p/q= 8/10 = 4/5

Ratio of p:q = 4:5

Hope this helps.

The Olive Tree Learning Hub

[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.

[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

[chrisu]

Thank you very much TheOliveTree, especially the detailed workings.


Now I know how to explain to my daughter. But I think there is a slight mistake;
50q^2=32p^2
p^2/q^2=50/32 instead of 32/50.
Thus p/q = 5/4
The answer p:q = 5:4

Thanks once again.

TheOliveTree:

Hi chrisu,

Determine the scale for area first from the given linear scale.

Map P
1 cm : p cm
1 cm^2 : p^2 cm^2
32 cm^2 : 32p^2 cm^2

Map Q
1 cm : q cm
1 cm^2: q^2 cm^2
50 cm^2 : 50q^2 cm^2

Since the actual areas represented on Map P and Map Q are the same,

50q^2=32p^2
p^2/q^2=32/50
p/q = sqrt (32/50)
p/q= 8/10 = 4/5

Ratio of p:q = 4:5

Hope this helps.

The Olive Tree Learning Hub

[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.

[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.

[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.