O-Level Additional Math

[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

[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

[Jtutor]

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

Hi,

p should be 2^3 x 3^4 = 648.

p/2 will give 2^2 x 3^4 which is a perfect square with powers that are multiples of 2.
p/3 will give 2^3 x 3^3 which is a perfect cube with powers that are multiples of 3.

Cheers!
Jtutor

[lost boy]

Thanks Jtutor

[Rhyll]

Hi jtutor,

I was looking at the math question ,
Do you mind explain how to know the power for 2 and 3.
is it by testing eg. 2^2 x 3^2 is a perfect square as well as perfect cube, then follow by guessing the power.

[Jtutor]

Rhyll:

Hi jtutor,

I was looking at the math question ,
Do you mind explain how to know the power for 2 and 3.
is it by testing eg. 2^2 x 3^2 is a perfect square as well as perfect cube, then follow by guessing the power.

Hi Rhyll,

Yes this question involves some \"guess & check\" technique.

To have a perfect cube, the power for 2 and 3 must be either 3, 6, 9, etc (multiples of 3). To have a perfect square, the power must be either 2, 4, 6, etc (multiples of 2).

Examples of perfect squares: 2^2 x 3^2, 2^2 x 3^4
Examples of perfect cubes: 2^3 x 3^3, 2^3 x 3^6
(Pls note that the powers for 2 and 3 need not be the same.)

Cheers!
Jtutor