IGCSE/GCSE/O & A Level/IB/University Student Forum
Qualification => Subject Doubts => IGCSE/ GCSE => Math => Topic started by: shan2391 on May 17, 2009, 05:18:05 pm
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Q 7c(i) June 2002 can someone explain the method.
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reflection in y=-x
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how did u get it
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these are few very good notes provided by priceless in a post..
hope it helps u
Lol ya sure np. umm ok here v go.
Reflection:
1. reflection in ml y=x it's (0 1)
(1 0)
2. refelction in ml y=-x itz (0 -1)
(-1 0)
3. refelction in x-axis itz (1 0)
(0 -1)
4. reflection in y-axis itz (-1 0)
(0 1)
Rotation
1. rotation +90 degrees(anticlockwise) around centre(0,0) itz (0 -1)
(1 0)
2. rotation -90 degrees(clockwise) around centre (0,0) itz (0 1)
(-1 0)
3. rotation 180 degrees around centre (0,0) itz (-1 0)
(0 -1)
Enlargement
1. centre (0,0) wer k=scale factor, itz (k 0)
(0 k)
Shear
1. x invariant with x-axis wer k=scale factor (1 k)
(0 1)
2. y invariant with y-axis wer k=scale factor (1 0)
(k 1)
Stretch
1. x invariant with y-axis wer k=scale factor (1 0)
(0 k)
2. y invariant with x-axis wer k=scale factor (k 0)
(0 1)
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i was told to byheart them...and thus i remembered...
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A question that is asked by many!
How is shear applied?
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Shear is the transformation that keeps one line fixed, moves all the other points paralled to this line.
A transformation in which all points along a given line remain fixed while other points are shifted parallel to by a distance proportional to their perpendicular distance from . Shearing a plane figure does not change its area.
the formula => shear factor = distance a point moves/ distance of the point from the invariant line
any past paper question on shear
may be i can help
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The stretch thing on Q4) f)i)
http://freeexampapers.com/FreeExamPapers.com_.php?__lo=SUdDU0UvTWF0aHMvQ0lFLzIwMDQgTm92LzA1ODBfdzA0X3FwXzQucGRm
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@eddie_adi619
can u plz also tll the formula for stretch factor ???
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sure..
its SF = distance of the image of a point from the invariant line / distance of the point from the invariant line
thank you
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thank you!! :)
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whoa adi u mite b taking ur xam in nov but ur sum smart guy....u wud hv no probs wid da pprs hopefully n i ll pray 4 u. gud luck 4 ur upcoming xams though n thnkz 4 all da help. Take care
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thank u :)
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E7m e7m...ummm...
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ur welcum adi n sweetsh wats dat supposed 2 mean? sory i didnt get u?
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I asked eddie a question he didnt reply.
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ohh hell!!..
i'm so sorry..
i just 4got..
plz give me some time..
after finishing eating..
i'll surely answer it
it requires a graph paper..
veryyy sorry
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LOL oh ok can i b of any help? if u hv any probs sk me n i ll glad 2 help. but prob adi wud want 2 reply cuz he told u he wud ryt after eating....so LOL if u hv any other ques pls ask....n gud luck!!!
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soo sweetsh heres your answer..
first plot the triangle in a graph paper
this will make it easy for you
now lets start with the first point - A (2,2)
remember: the invariant line is the y-axis
the formula says :SF = distance of image from invariant / distance of object
therefore 1.5 = x/2 ("2" because the perpendicular distance of the point from the invariant line is 2units)
implies that x = 2*1.5 = 3
soo the co-ordinates of this point is (3,2)
repeat this method for the other points
sry for the delay once again
if any problem plz inform me
i'll try to help
thank you
good luck
byee
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the answers for the other points of the triangle...
point B (5,2) will be mapped to (7.5,2)
point C (5,4) will be mapped to (7.4/4)
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hope u have seen the answer :) :)
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ummm adi can u pls tell me wat ques this is n 4rm wat ppr? n very gud xplanation pretty clear n thnkz in advance.
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Thank you alot. It was my huge problem in math. God bless you!
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yeah sure..
it is 2004 oct/nov paper 4 math...Q 4.)f)i
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thnkz once again adi n yes as sweetsh u said..u solved a huge prob in math dat ate my head up LOL thnku heapz..Take care..n best of luck again adi.
:D
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plz help me in q7 part (c) oct/nov 2001 .....dunno hw to do it ???
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Another question, if they asked you to write the transformation matrix (- -
- -) what would you put it?
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@zara...cud u plz upload the paper...
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actually m hvin the hard copy n no soft copy....its nt der on FEP as well.. :-\
so ne1 hvin a soft copy plz plzzz upload it hea....
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@sweetsh..
i guess u r talking abt the next question
okk...heres how u do it
let the transformation matrix (2by2) be (a b)
(c d)
take 2 sets of co-ordinates from the object and arrange it vertically to form a 2 by 2 matrix
multiply it with the transformation matrix (abcd) and equate it to the corresponding sets of co-ordinates in the image
(again arranged vertically to form a 2 by 2 matrix)
lets take the points A and B
point A - (2,2) gets mapped to (3,2)
point B - (5,2) gets mapped to (7.5,2)
heres the equation desribed above
(2 5) * (a b) = (3 7.5)
(2 2) (c d) (2 2)
find the values of a,b,c,d by multiplying (3 7.5) with the inverse of (2 5)
(2 2) (2 2)
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these are few very good notes provided by priceless in a post..
hope it helps u
Lol ya sure np. umm ok here v go.
Reflection:
1. reflection in ml y=x it's (0 1)
(1 0)
2. refelction in ml y=-x itz (0 -1)
(-1 0)
3. refelction in x-axis itz (1 0)
(0 -1)
4. reflection in y-axis itz (-1 0)
(0 1)
Rotation
1. rotation +90 degrees(anticlockwise) around centre(0,0) itz (0 -1)
(1 0)
2. rotation -90 degrees(clockwise) around centre (0,0) itz (0 1)
(-1 0)
3. rotation 180 degrees around centre (0,0) itz (-1 0)
(0 -1)
Enlargement
1. centre (0,0) wer k=scale factor, itz (k 0)
(0 k)
Shear
1. x invariant with x-axis wer k=scale factor (1 k)
(0 1)
2. y invariant with y-axis wer k=scale factor (1 0)
(k 1)
Stretch
1. x invariant with y-axis wer k=scale factor (1 0)
(0 k)
2. y invariant with x-axis wer k=scale factor (k 0)
(0 1)
he/she got this points from Mathematics for IGCSE book by Cambridge i have it :D
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@sweetsh ...the answer is (1.5 0)
( 0 1)
@zara...i cudn't find the oct/nov 2001 paper in FEP...
sry
maybe u can type in the question
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@fahadali..
i got these points from "priceless"
maybe she has taken it from the book ..
anyway.
good luck for your exams
hope u do extremely well!!
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@ zara n adi umm i wud hv but evn i hv da hard copy. i cud hv scanned it but da scanner is in parents room n dey r sleeping LOL so im not sure wat 2 du. is it posible 2 explain da ques 2 adi cuz evn im not sure bout da ques n prob adi wud no how 2 solve it LOL
n bout da base vestors lol i dnt hv dat bk i thnk dat has da base vectors in it but ya dese were given 2 us by our teachers @ skul so i told u guyz. hope dey helped sweetsh. ;)
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Q 2) of which paper???
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@adi
its ques 7......By the way rnt u hvin this ppr....i thought u do.. :-\
@priceless
if u think u can den sure go ahead....
cz its realli big....wonder if adi gets it
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sorry i don't have the paper...
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oct/nov 2001 q7 (c)....i posted this earlier also...
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@adi lol no i didnt mean any ques 2 but i ment is it posible to explain da ques to adi as he wud prob no it...LOL :D
@zara i seriously wud hv if i cud cuz env i hv dat prob but as i said un4tunately da scanner is in parents rum n i cnt disturb dem cuz dey r sleeping. sorry but i du agree da ques is kinda long.hmmm any1 pls if posible upload da ppr. thnkz n sory once again zara
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i heard that the paper is during the afternoon (tomorrow in india)...
so maybe till morning if i can get the paper...or zara cud scan only that page...
anyone else or maybe even i wud be able to help u ..
if i get it somewhere hidden in my hard disk i may surely attempt it and try to explain..
thank u
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LOL thnkz n as u said da ppr is in da afternoon but un4tunately i ll b in da xam hall writing da busi ppr :D so but i prob ll ask my teacher n mayb zara cud du dat 2 if posible 4 her. n adi y r u saying thnk u LOL i shud say thnku 4 ur help n efforts dey helped alot specially da stretch thng-thnkz once again..gud luck wid evrythng!!!!
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@priceless...its k..
@adi...my bad...my stupid scanner is nt wrking :(...n ill be goin to m skool in the morning cz its impossible in aftrnoon due to transport problem :'(
ill be hea till or cum bak again maybe by 1 00 am accrding to gmt+4....
n if i don't get the answer ill see if teachers or frnds cn help....
Thanks a loads adi!!!!
u r so damn helpful!!!
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ur welcome..
i found the paper 4 2001 november in scribd..
but it is taking hell lot of time to load as it ihas 1988 -2005 papers too
moreover the print is extremely bad...
i can't view the questions properly..
if something works out ..
i'll try n help..
and ya...my GMT is (GMT + 5:30)
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ALL DA BEST ZARA!!!!! ;) :D
@adi ur a lyf saver ur rely gud n very helpful n not 2 mention u go 2 such xtreme lengths 2 help ppl. thnkz alot n best of luck 4 evrythng u du in lyf!!!! :D
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welcome..
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acutually...i complete my revision too by answering the doubts..its fun
lol
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hmmm da same reason y im nline da b4 my xams LOL ur completely ryt itz fun n i get my revision don't 2..thnkz ;) :D ;D :P
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da day b4***
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well ya dats true....
k guys m goin now ....cum bak later...tll den plz adi or ne1 try to get an answer to m doubt...
All the best to priceless n adi n rest of the members!!!!
God plz save us tom!!!!
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well! all d best to u guys and i save my luck till nov 2009..
lol
the paper has almost loaded
but still its gonna tak tym
will try my best
try contacting astar..
hes a genius and may also hav d paper...
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okk...guys got the answer for 7.a and 7.b
i found the paper too lol
will take time to explain it clealry...
will post all the answers within 15 mins..
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doesnt ur b___ (oops) back pain for sitting in one place from 2.5 hours, that too 15 mins for instructions, so 2.75 hours?
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K so its all most 12:00pm n im lost
err year 2004 Q3b and c november
if i cud get help
god bless yall!!
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hi coco
heres ur answer
b) part => first find the volume of water coming out from the pipe every secind..to do this u need to multiply 14 * 1.6 = 22.4
so this means that it fills 22.4 cm(3) in - 1 second
so wat about 552920 (your answer to (a) part)
that will be 552920/22.4 = 6.85 hours or 6 hours 51 min
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now your answer to the (c) part ..
the logic says this : after adding all the water in the tank to the pond the volume of the water in the pond will become equal to the volume of water in the tank = 552920
u need to also convert the 70m(2) to cm(2) ...i.e = 70 * 10(2)
soo u put it into equation
the volume of water in pond will be the surface area * the height of water
let the heigt be x
therefore 700000x=552920
therefore x = 552920/700000 = 0.789 cm = 7.89 mm
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@eddie_adi619
can you please help me with the sequence questions for question (9)(b) i have attached the file
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yeah sure..
heres your answer..
but before that use this formula for all sequences question - a+(n-1)d + 1/2(n-1)(n-2)c
where a is the 1st term
d is the difference between the 1st and the second term
and c is the final difference (find the difference of the difference until u get a constant value)
i) if there is a constant difference use a+(n-1)d => 7 - 2n +2 = 9-2n
ii) if u clearly see its the cube of the term...like the 2nd term has 8..the third term has 27...therefore - n cube
iii) if u see properly you will notice that the numerator = to the term and denominator is +1 of the numerator
therefore it is n/(n+1)
iv) (n+1) the whole square
v) 3 raise to (n-1)
vi) it is the sequence of (iv) - (v)
therefore (n+1) the whole squared - 3 raise to (n-1)
good luck
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okk now for the big one...Q7.c) from paper 4 2001 oct/nov
asked by "zara" and "priceless"
sry for the delay
heres your answer
7.c.) i hope you have already found the volume of the cylinder, the hemisphere and the cone in the previous question
taking the radius as 5cm, height of the cylinder as 5cm, and the perpendicular height of the cone also 5 cm..
you get the volume of the hemisphere as - 523.5987
the volume of the cylinder as - 392.699
the volume of the cone as - 130.899
as we are unaware of the mases..v take their volumes previously found out to get the ratio
first..relate the volume of the hemisphere, the cylinder and the cone to the volume of the cone as it is the least ...
the ratio of the volume of the hemisphere to the volume of the cone
i.e 523.5987/130.899 = 4
the ratio of the volume of the cylinder to the volume of the cone
i.e 392.699/130.899 = 3
the ratio of the volume of the cone to the volume of the cone is obviously 1
therefore the answer is 4:3:1
hope my method is correct
if anyone has a better method...plz suggest
good luck
thank You
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okk guys..i'm signing off now...i'll get back tomorrow morning now..
i gotta see the spanish premier league
la liga
k..everyone
night
hope all my answers are correct!!
happy to have helped u all!
Good bye
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nite adi....
n m happy dat ur a member hea!!!
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tanks man are you a genius or what ?
hey but i didnt understand questions 9 vi, v and iv.
what did u use? can anyone help
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hey zara did u understand???
i guess not
check my recent posts..
i have explained it
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yea i got it adi....or i must say the genius guy<mashallah>keep it up :)
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hey madikay.
ok lemme explain to u how i got (iv), (v) and (vi)
as itold u before use the formula
a+(n-1)d + 1/2(n-1)(n-2)c
a- 1st term
d - difference between 1st and 2nd term
c final difference(find the difference of the difference until u get a constant value)
the sequence
4 9 16 25
+5 +7 +9
+2 +2
you get 2 as the final difference
now substitute
4 + 5n -5 + ((n-1)(n-2) * 2)/2
= 4 + 5n -5 +n^2 -3n +2
= n^2 + 2n + 1
= (n+1)^2
use the same method for (v)
or if not possible try and observing the sequence very carefully and get the rule
the answer for (vi) is sequence for (iv) - sequence for (v)
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thanks man your are the best.
i understand now. increased your rep
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ur welcome...madikay :)
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Hey adi thnkz 4 ur help n as evry1 is saying U R A GENIUS u no evrythng n im glad ur a member of this forum. By the way i jst gave my maths n busi st. xams n wow mathz was gr8. cudnt hv been b8r!!!! da ques were sooo easy n gud thnkfully, i was doubting if da mathz ppr is paper 4 or not? LOL neway thnkz once again 4 ur help. sory 2 reply late cuz my comp shut down automatically. hope evry1's xam went well n best of luck 4 tom's xams!!!! ;) :D
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hey in the question where the graphs of the functions had to sketched,do we hve to label the axes too?no1 in class nor our teacher did so.
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no dont worry bout it!! ;)
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Thanx alot buh Didnt get to see how u work it out cuz i slept!
nyhow ma exam was an A >Hopefully
buh thanx nyway!! :)
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WELCOME BRO..
ANYTIME :) :)
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haha im a GIRL!
buh its all gud if da was meant to be slang!
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lol...