Help with O Level Math 4024 Exam Questions

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Discussion Overview

The discussion revolves around specific questions from the Cambridge University O Level Math 4024 past paper, particularly focusing on questions 9bi, 10, 11, and 12. Participants are seeking help with problem-solving strategies and understanding the questions presented in the exam paper.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in understanding how to find the length MN in relation to the variable x, given that OB, OA, and OP are all equal to 8 cm.
  • Another participant suggests that if MQ and OQ are equal, then MQ can be assumed to be x, leading to the conclusion that MN is 2x, as MQ is half of MN.
  • A participant confirms the reasoning about the congruence of triangles MOQ and NOQ, stating that the lengths MQ and QN are both x, thus supporting the calculation of MN as 2x.
  • Further mathematical hints are provided regarding the calculation of areas, including the area of a circular sector and the area of a triangle, with formulas shared for participants to apply in their problem-solving.

Areas of Agreement / Disagreement

Participants generally agree on the relationships between the lengths discussed (e.g., MQ, QN, and MN) and the use of congruent triangles to support their reasoning. However, there remains uncertainty about the overall understanding of the questions and how to proceed with the calculations, indicating that the discussion is not fully resolved.

Contextual Notes

Some participants express limitations in their understanding of the questions and the necessary steps to solve them, indicating potential gaps in their grasp of the underlying concepts or the specific requirements of the exam questions.

Who May Find This Useful

Students preparing for the Cambridge O Level Math 4024 exam, particularly those struggling with problem-solving techniques and understanding exam questions.

leylamew
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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/Cambridge%20International%20O%20Level/Mathematics%20D%20(Calculator%20Version)%20(4024)/4024_s10_qp_21.pdf

It's questions 9bi, 10, 11 and 12 that are bothering me greatly.
Help? :D
 
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leylamew said:
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/Cambridge%20International%20O%20Level/Mathematics%20D%20(Calculator%20Version)%20(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 ?
 
ZaidAlyafey said:
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 - - -

leylamew said:
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 said:
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?
 
leylamew said:
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:

$$\overline{MQ}=x$$

$$\overline{QN}=x$$

and so adding, we have:

$$\overline{MQ}+\overline{QN}=2x$$

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

$$\overline{MN}=2x$$

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?
 
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MarkFL said:
$$\bar{MQ}=x$$
@MarkFL: Just a comment about the LaTeX coding: \overline{AB} gives \overline{AB}. I think that looks like a better operation here than \bar.

-Dan
 
Last edited by a moderator:
Thank you, that does look better! (Happy)
 
MarkFL said:
...
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:

$$A_S=\frac{1}{2}r^2\theta$$

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

The area $A_T$ of a triangle is:

$$A_T=\frac{1}{2}bh$$

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

$$A=A_S-A_T=?$$