IGCSE MATHS Doubts

[Vin]

ans. should be 3 ..

the eqn f(x) + x – 1 = 0 means how many solutions are there for the eqn wen y=0 ..

[diva_sparkles]

Hey guys im preparing for P4 maths which to come in a few days and Ive been solving p4  oct/nov and there is a question I dont quite understand and I'd really appreciate your help.
It is question 2 on page 5 (iv) part, its about transformations and tells me to describe triangle U onto triangle X and I know its shear , y axis invariant, but the shear factor is -1, not 1 as I though, can someone please describe me how to know when the shear value is negative? thanks for your help in advance

it is negative whn the image is toward da left!!

[Baladya]

ans. should be 3 ..

the eqn f(x) + x – 1 = 0 means how many solutions are there for the eqn wen y=0 ..

Ya but how did you know it was y=0?

[mdwael]

w09, paper 4, 2)iv

ok this negative shear factor thingy is horrible..i cant figure it out y the move upwards is considered negative.

anyhow, its always wiser to use the matrix method

take two object and correspoding image co-ordinates..

(-4,1) --> (-4,5)

(-1,1) --> (-1,2)

check the image attached

a shear transformation matrix with y-axis is invariant is = (1  0)
                                                                            (k   1)

here k = -1

Great thanks A LOT i never knew that a matrix gets inversed when its shifted to the other side of the equation

[Vin]

u might wanna know this too ..

https://studentforums.biz/index.php/topic,5575.msg167872.html#msg167872

[Vin]

Ya but how did you know it was y=0?

same way like u found 4 b) i)

[mdwael]

Can anyone explain me how to do question 7 the C part page 15 in paper 4 maths year oct/nov 2009
I tried and I couldnt figure out anything the MS answer says its 27W and 4W 

[Baladya]

for (i) u already have the lenght from a)i) this is the cirumference. Use C=pie(r^2) to find it.
(ii) Now u have the radius. Imagine the line h(height of cone). It makes a right angle triangle with the radius and AO. Use Pathegeroth rule to find the height.
 

[Ghost Of Highbury]

ci ) 1/3 * pi * (3x)^2 * 3y = 9x^2y*pi

      W = 1/3 * x^2 * y * pi = (x^2ypi)/3

W * 27 = 9x^2ypi

27W

cii) 1/3 * pi * (2x)^2 * y = (4x^2ypi)/3

W = 1/3 * x^2 * y * pi = (x^2ypi)/3

W * 4 = (4x^2ypi)/3

4W

[mdwael]

ci ) 1/3 * pi * (3x)^2 * 3y = 9x^2y*pi

      W = 1/3 * x^2 * y * pi = (x^2ypi)/3

W * 27 = 9x^2ypi

27W

cii) 1/3 * pi * (2x)^2 * y = (4x^2ypi)/3

W = 1/3 * x^2 * y * pi = (x^2ypi)/3

W * 4 = (4x^2ypi)/3

4W

I didnt understand  can you make it simpler please?

[Ghost Of Highbury]

Radius = X
Height = y

Volume or W = 1/3 * x^2 * y * pi = (x^2ypi)/3

3 times --> Radius = 3x
Height = 3y

VOlume = 1/3 * pi * (3x)^2 * 3y = 9x^2y*pi

W = (x^2ypi)/3
Vol. =  9x^2y*pi

W * 27 = Vol.

27W
----------

cii) Radius = 2x

      Height = y

Vol. = 1/3 * pi * (2x)^2 * y = (4x^2ypi)/3

W = (x^2ypi)/3

W * 4 = Vol.

Therefore, 4W

PS : Volume of a cone = 1/3*pi*r^2*h

[mdwael]

Radius = X
Height = y

Volume or W = 1/3 * x^2 * y * pi = (x^2ypi)/3

3 times --> Radius = 3x
Height = 3y

VOlume = 1/3 * pi * (3x)^2 * 3y = 9x^2y*pi

W = (x^2ypi)/3
Vol. =  9x^2y*pi

W * 27 = Vol.

27W
----------

cii) Radius = 2x

      Height = y

Vol. = 1/3 * pi * (2x)^2 * y = (4x^2ypi)/3

W = (x^2ypi)/3

W * 4 = Vol.

Therefore, 4W

PS : Volume of a cone = 1/3*pi*r^2*h

I think I got it now but why all this working and it only carries 1 mark so shouldnt there be a quicker way maybe like 3^3=27?

[Ghost Of Highbury]

I had to show all the working for ur explanation. u just have to know wat to multiply to W to get the new volume.

[ankitd_1994]

n also b) ii)

theres a great method my teacher taught me...
  (y)      x      U         =       X         
(a  b)     (-1  -4  -4 )        (  -1   -4  -4)
(c  d)     (1     1    3 )  =   (   2     5   7 )

multiply a b c d in matrix y to matrix U (they are the positions of the image, row 1 is x axis  row 2 is y )

( (-a + b) (-4a+b)  (-4a + 7b)  )
( (-c+d )   (-4c +d)  (-4c+ 7d)  )

now solve any two equation my simultaneous method...

so,  -a +b   = -1 (because the position of this equation is corresponding to matrix "X", look for the colours)

      -4a + b = -4

by solving u get a = 1 , b = 0
same for 'c' and 'd' ..u get  d= 1 and c = -1

i dont expect u to understand but this method is really good n its really difficult for me to teach online..
read it n try to follow the steps while solving the paper u might get it...

     

ya got the method bt u dont need to use it for all 3 pts only 2 will do fine

[mdwael]

in May/June paper 4 2009 page 19 d(ii) part (its the last question in the paper) how do you get 1711 and 1770 I got 58 and 59 can someone please explain?