O-Level Additional Math

[SKT]

Hi,


Find the equations of the tangents from (2, -3) to the curve y = x + x².

TIA

[iFruit]

SKT:

Hi,


Find the equations of the tangents from (2, -3) to the curve y = x + x².

TIA

let's say the point at which the line and curve meet is (x, y) = (x, x+x²).

Then, Slope of tangent = (x+x²+3)/(x-2)

but slope of tangent = dy/dx of curve = d( x + x² )/dx = 1+2x

so (x+x²+3)/(x-2) = 1+2x--> x+x²+3 = 2x² -3x -2-->x²-4x-5 = 0 -> (x+1)(x-5) = 0---> x = -1 or 5

when x =-1, y = x + x² = 0, m = 1+2x = -1
when x = 5, y = 30, m = 11

The lines of the equation

y = -x + C1, y = 11x +C2,

Solving for point ( 2,-3), we get the tangents of curves

y = -x-1,

y = 11x -25


HTH

[SKT]

Hi,


A man 1.5 m tall is walking at a speed of 2 m/s away from a lamppost which has a lamp 5 m above the ground. Find the speed of the top of his shadow.

TIA

[iFruit]

SKT:

Hi,


A man 1.5 m tall is walking at a speed of 2 m/s away from a lamppost which has a lamp 5 m above the ground. Find the speed of the top of his shadow.

TIA

distance of man from lamp post at time t = 2t
Let distance of top of shadow from lamp post = s

tan x = 5/s = 1.5/(s-2t)--->5s -10t = 1.5s

3.5s = 10t

ds/dt = 10/3.5 = 20/7 m/s

[mramk]

Guan Hui:

Hi parents, just wondering why is there not a thread for secondary school maths questions and decided to start on one.(inspired by mathsguru contribution to this community)


So... yup this is for Q&A for secondary school maths questions.

Please state the level of the question when posting the question for the convenience of knowing which method should be used to explain the answers.(e.g. Sec 1)

Hope it helps!

Hi Guan Hui, thanks for your service. Could you please help with below question:

prove the identity: cos(x).cot(x) + sin(x) = cosec(x). (O level A-Math)

Thank alot.

[wmd]

mramk:

prove the identity: cos(x).cot(x) + sin(x) = cosec(x). (O level A-Math)

Thank alot.

cos(x).cot(x) + sin(x)
=cos(x)*(cos(x)/sin(x))+sin(x)
=(cos(x))^2/sin(x) + sin(x)
=((cos(x))^2+(sin(x))^2)/sin(x)
=1/sin(x)
=cosec(x)

[YLH88]

Hi achemtutor,


Thank you!

[mathqa]

Bounty:

I am back again. Thank you for your all your help.

I have spoken to my daughter’s school Prinicpal. I have the option of doing the subject privately as an additional subject and the school will register her for the O Level exam through the school. This is what MOE also told me.
So now, could anyone recommend me a good teacher who can teach her the complete school curriculum on a one-to-one tuition at home (or any other suggestions)? And the rates of course. I live in Woodlands.

Hi Bounty,

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Feel free to send your daughter in for a FREE workshop & an assessment test.

http://mathqa.blogspot.com/2010/11/free-revision-workshops-for-gce-o-level.html

http://mathqa.blogspot.com/2010/11/test-question-for-senior-olympiad.html

http://mathqa.blogspot.com/2010/11/sat-i-math-collection-of-medium-to-hard.html

[jackaljaysen]

Whoa so cheem! :shock:

[Muffins]

iFruit:

Muffins:

woah..... these questions making my head spin already :faint: :faint:

Welcome to the real world mate ! We have no Mohammads and Alis exchanging marbles or silly old mothers trying to pick up their daughters from the schools at constant speed every day here.

How, I wish, school would get easier as we advance in age.....

iFruit:

We just have beautiful x's and y's and before you blink sin As, cos Bs and Sec Cs.

I thought there was sine, cosine, and a tangent???? what's a Sec???