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Help in my O Levels~

leylamew

New member
Apr 10, 2013
3

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Hi, I'm leylamew.
So, I'm in the Cambridge University O Level board and I'm studying for my examinations, which will be in May. I'm taking the Math 4024 paper.
I was solving the past paper for 2010 and I hit a roadblock. (Shake)
Here's the link. http://papers.xtremepapers.com/CIE/...Calculator Version) (4024)/4024_s10_qp_21.pdf

It's questions 9bi, 10, 11 and 12 that are bothering me greatly.
Help? :D
You are supposed to at least show some effort and tell us where are you stuck ?
 

leylamew

New member
Apr 10, 2013
3
You are supposed to at least show some effort and tell us where are you stuck ?
I'd upload the sheet where I've scribbled the logic, but I don;t have a scanner.
Here's my thinking process:
OB=OA=OP=8 cm and as OQ is x cm, MN should be...something. But I can't understand for the life of me, how to find MN. I don't understand what I'm supposed to do with the x there.

- - - Updated - - -

I'd upload the sheet where I've scribbled the logic, but I don;t have a scanner.
Here's my thinking process:
OB=OA=OP=8 cm and as OQ is x cm, MN should be...something. But I can't understand for the life of me, how to find MN. I don't understand what I'm supposed to do with the x there.
And, I don't understand what the questions are asking of me in the others.
 

leylamew

New member
Apr 10, 2013
3
I'd upload the sheet where I've scribbled the logic, but I don;t have a scanner.
Here's my thinking process:
OB=OA=OP=8 cm and as OQ is x cm, MN should be...something. But I can't understand for the life of me, how to find MN. I don't understand what I'm supposed to do with the x there.

- - - Updated - - -



And, I don't understand what the questions are asking of me in the others.
All right, so I put my ruler to use and hoping that the diagram was to scale, I measured MQ and OQ. They're the same, so I safely assumed that MQ is x and so, therefore, MN is 2x, as MQ is 1/2MN. Did I do it right?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
All right, so I put my ruler to use and hoping that the diagram was to scale, I measured MQ and OQ. They're the same, so I safely assumed that MQ is x and so, therefore, MN is 2x, as MQ is 1/2MN. Did I do it right?
Yes, as triangles $MOQ$ and $NOQ$ are congruent, and are right isosceles triangles, we know that:

\(\displaystyle \overline{MQ}=x\)

\(\displaystyle \overline{QN}=x\)

and so adding, we have:

\(\displaystyle \overline{MQ}+\overline{QN}=2x\)

And we know that \(\displaystyle \overline{MQ}+\overline{QN}=\overline{MN}\), hence:

\(\displaystyle \overline{MN}=2x\)

Now, for the next part of the problem, find the total area of the cross-section using the formula for the area of a circular sector (or simply from the fact that it is a quarter circle) and then subtract away the area of triangle $MON$. What do you find?
 
Last edited:

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,123
\(\displaystyle \bar{MQ}=x\)
@MarkFL: Just a comment about the LaTeX coding: \overline{AB} gives [tex]\overline{AB}[/tex]. I think that looks like a better operation here than \bar.

-Dan
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Thank you, that does look better! (Happy)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
...
Now, for the next part of the problem, find the total area of the cross-section using the formula for the area of a circular sector (or simply from the fact that it is a quarter circle) and then subtract away the area of triangle $MON$. What do you find?
Hints:

The area $A_S$ of a circular sector is:

\(\displaystyle A_S=\frac{1}{2}r^2\theta\)

and you know $r$ and $\theta$.

The area $A_T$ of a triangle is:

\(\displaystyle A_T=\frac{1}{2}bh\)

and you know the base $b$ and the height $h$ in terms of $x$. So you now need to compute:

\(\displaystyle A=A_S-A_T=?\)