O-Level Additional Math

[tianzhu]

teddy7171:

The scale of map P is 1/p and the scale of map Q is 1/q. Suppose a street is represented by lines of 12cm long and 16cm long on maps P and Q respectively.
a) find p/q and express the answer in the simplest form.
b) if p=5000, find (i) the value of q, (ii) the actual length, in m, of the street.
c) if p=5000 and the actual area of a plot of land in 2812.5metre square, calculate its area on (i) map P and (ii) map Q.

Hi

I did some reading using my boy’s textbook and will attempt to answer your question.

a)A scale of 1:p means that 1cm represents pcm
Therefore 12cm represent 12pcm in map P
Likewise, 16cm represent 16qcm in map Q
12p=16q
Hence p/q = 4/3

b)q = 3750
The actual length of the street is 12*5000 = 600m

c)For map P
1cm represents 50m
1 cmsq represents 2500 cmsq
2812.5/2500 = 1.125 cmsq

For map Q
1cm represents 37.5m
1 cmsq represents 1406.25 cmsq
2812.5/1406.25 = 2 cmsq

Are my answers correct?

Best wishes

[teddy7171]

a)A scale of 1:p means that 1cm represents pcm

Therefore 12cm represent 12pcm in map P
Likewise, 16cm represent 16qcm in map Q
12p=16q
Hence p/q = 4/3

b)q = 3750
The actual length of the street is 12*5000 = 600m

c)For map P
1cm represents 50m
1 cmsq represents 2500 cmsq
2812.5/2500 = 1.125 cmsq

For map Q
1cm represents 37.5m
1 cmsq represents 1406.25 cmsq
2812.5/1406.25 = 2 cmsq

Are my answers correct?

Best wishes[/quote]


Hi Tianzhu,
My boy does not have the answers for the question and doesn’t know how to solve it.

His answer for (a) is 3/4 instead.

Please enlighten us how do u arrived at 4/3 and q = 3750.

Sorry for the trouble and thanks.

[tianzhu]

Hi teddy7171


In order to solve this question, students need to understand the concepts of Scales and Maps. You may refer to your son’s textbook for a more detailed explanation.

A scale of 1:p means that 1cm represents pcm
Therefore 12cm represent 12pcm in map P

Likewise, 16cm represent 16qcm in map Q

The same street is represented by different scales as in map P and Q
12p=16q
Hence p/q = 4/3

Here p is given as 5000
p/q = 4/3
5000/q = 4/3
Hence q = 15000/4 = 3750

Best wishes

[Sahimi]

Hi! pls help!!


If n is a number, show that for all values of n, (n3 + 11n) is divisible by 6. (sec Two maths)
Thks

[iFruit]

Sahimi:

Hi! pls help!!


If n is a number, show that for all values of n, (n3 + 11n) is divisible by 6. (sec Two maths)
Thks

n³ + 11n = n³ -n + 12n = n(n²-1)+12n = n(n-1)(n+1)+12n = (n-1)n(n+1)+12n


(n-1)n(n+1) is the product of 3 consecutive numbers which is always divisible by 6 ( you can use induction to prove if necessary) and 12n is divisible by 6.

So, n³ + 11n is divisible by 6

HTH

[Sahimi]

iFruit:

Sahimi:

Hi! pls help!!


If n is a number, show that for all values of n, (n3 + 11n) is divisible by 6. (sec Two maths)
Thks

n³ + 11n = n³ -n + 12n = n(n²-1)+12n = n(n-1)(n+1)+12n = (n-1)n(n+1)+12n


(n-1)n(n+1) is the product of 3 consecutive numbers which is always divisible by 6 ( you can use induction to prove if necessary) and 12n is divisible by 6.

So, n³ + 11n is divisible by 6

HTH

thks very much, iFruit.

[k1ndan]

E:{x:30<x<=100}

A:{x: Multiples of 3}
B:{x: unit digit is 10}

What is A’n B’?[/url]

[k1ndan]

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[k1ndan]

k1ndan:

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Sorry, typo error, the condition should be if a=b, what is the value of W?

[k1ndan]

€ = {x : x is an integer, 30 < x≤100}

A: {x : x is divisible by 3}
{x: units digits of x is 0}

List the elements of A’ n C’