Comments on: Maxima & Minima – A Semi-Circular Triangular Rectangular Affair http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-1208 Miss Loi Sat, 29 Sep 2007 10:03:27 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-1208 Thanks so much TYS, for pointing out this typo all the way back from the pioneering days of this blog! At the same time, Miss Loi has taken the liberty to 'enhance' the readability of the said working (just a little). She's feeling so noob now looking at her early posts :P Thanks so much TYS, for pointing out this typo all the way back from the pioneering days of this blog!

At the same time, Miss Loi has taken the liberty to 'enhance' the readability of the said working (just a little). She's feeling so noob now looking at her early posts :P

]]> By: TYS http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-1206 TYS Sat, 29 Sep 2007 09:22:16 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-1206 Anyway, I find that one of the steps in part 2 is wrong. GF/ AB = GD / h instead, it should be GF/ AB = (h - GD)/h Other than that, I agree with you that this is a gd qn. In fact, there are a lot of concepts tested in this qn. Anyway, I find that one of the steps in part 2 is wrong.

GF/ AB = GD / h

instead, it should be

GF/ AB = (h - GD)/h

Other than that, I agree with you that this is a gd qn. In fact, there are a lot of concepts tested in this qn.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-18 Miss Loi Sun, 01 Apr 2007 03:14:13 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-18 Ok answer time *drum roll*! <strong>Part 1:</strong> AB = √(8<sup>2</sup> + 6<sup>2</sup>) = 10 cm ∴ Area of ABC = (1/2)(8)(6) = 24 cm<sup>2</sup> <var>h</var> being height of triangle ABC, so solving this equation: (1/2)(<var>h</var>)(AB) = 24 cm<sup>2</sup> You should get <var>h</var> = 4.8 cm! :) (shihui where u want Miss Loi to treat u???) <strong>Part 2:</strong> Using similar triangles, (GF)/(AB) = (<var>h</var>-GD)/<var>h</var> GF = AB(1 - GD/<var>h</var>) = (10)(1 - <var>x</var>/<var>h</var>) = 10 - 10<var>x</var>/<var>h</var> Now using the value of <var>h</var> from part 1, 10/<var>h</var> = 10/4.8 = 25/12. GF = 10 - (25/12)<var>x</var> ∴ <var>A</var> = GD x GF = <var>x</var>( 10 - (25/12)<var>x</var> ) = 10<var>x</var> - (25/12)<var>x</var><sup>2</sup> :) <strong>Part 3:</strong> [pmath]dA/dx=10-{25/6}x=0[/pmath] [pmath]{25/6}x=10[/pmath] [pmath]x=2.4[/pmath] [pmath]{d^2A}/{dx^2} = -{25/6} < 0[/pmath] ∴ A is max when x = 2.4 cm :) Wah type until fingers also numb liao! Actually managed to get all these maths symbols out! BTW thanks to all of you who tried and responded but why all only do part 1???? Next time don't 半途而废喔! Ok answer time *drum roll*!

Part 1:

AB = √(82 + 62) = 10 cm
∴ Area of ABC = (1/2)(8)(6) = 24 cm2

h being height of triangle ABC, so solving this equation:
(1/2)(h)(AB) = 24 cm2

You should get h = 4.8 cm! :) (shihui where u want Miss Loi to treat u???)

Part 2:

Using similar triangles,

(GF)/(AB) = (h-GD)/h
GF = AB(1 - GD/h)
= (10)(1 - x/h)
= 10 - 10x/h

Now using the value of h from part 1, 10/h = 10/4.8 = 25/12.

GF = 10 - (25/12)x
∴ A = GD x GF
= x( 10 - (25/12)x )
= 10x - (25/12)x2 :)

Part 3:

dA/dx=10-{25/6}x=0
{25/6}x=10
x=2.4
{d^2A}/{dx^2} = -{25/6} < 0

∴ A is max when x = 2.4 cm :)

Wah type until fingers also numb liao! Actually managed to get all these maths symbols out!

BTW thanks to all of you who tried and responded but why all only do part 1???? Next time don't 半途而废喔!

]]> By: shihui http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-16 shihui Fri, 30 Mar 2007 11:10:23 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-16 haha... i got h=4.8cm, the rest dunno how to do. =P haha... i got h=4.8cm, the rest dunno how to do. =P

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-13 Miss Loi Thu, 29 Mar 2007 02:52:53 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-13 Wah Level 10 guru here to comment! *Kneels down and bow* John: someone's trying to pwn u! I should put the answers up soon but some of my students still haven't try yet - slackers! (Just joking here la - actually they're also very busy with school at the moment :)) Wah Level 10 guru here to comment! *Kneels down and bow*

John: someone's trying to pwn u!

I should put the answers up soon but some of my students still haven't try yet - slackers! (Just joking here la - actually they're also very busy with school at the moment :) )

]]> By: bruce http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-12 bruce Wed, 28 Mar 2007 22:31:00 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-12 As a geometry teacher, I like this problem. It touches on properties of semicircles, area of triangles, coordinate geometry, and a little derivative at the end. Oh yes, and the height is NOT 4.25 (I don't want to spoil the answer, but it's a little taller). As a geometry teacher, I like this problem. It touches on properties of semicircles, area of triangles, coordinate geometry, and a little derivative at the end. Oh yes, and the height is NOT 4.25 (I don't want to spoil the answer, but it's a little taller).

]]> By: maple http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-11 maple Mon, 26 Mar 2007 14:34:12 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-11 EEW! EEW! EEEEEEEWWW!!! EEW! EEW! EEEEEEEWWW!!!

]]> By: john http://www.exampaper.com.sg/questions/a-maths/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-10 john Fri, 23 Mar 2007 15:07:24 +0000 http://www.exampaper.com.sg/questions/maxima-minima-a-semi-circular-triangular-rectangular-affair#comment-10 1) h=4.25 the rest dunno so difficult maybe too tired ... 1) h=4.25
the rest dunno so difficult maybe too tired ...

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