Mathematics: Post your doubts here!

[mominzahid]

for question 9(ii)

u have the found 2 roots = 1-√2i and 1+√2i
so the 2 factors of the polynomial that has been found are (u-(1-√2i)) and (u-(1+√2i)) if u multiply these factors together u will get a quadratic equation of u^2-2u+3 now u have the polynomial equation as u^4 + u^2 + 2u + 6....u or x it doesnt matter they are all letters after all anyway apply long division or whatever way u have learnt to find the other quadratic equation..then from that other equation u will find the other 2 roots then boom u have 4 roots found

Hey thanksss.... What about other questions? can u solve them please?

 

[MustafaMotani]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf

Q5ii) How do we do these type of questions ? There others like this.. eg find the value of y as x becomes very large..

from part i) u would have got
y = 70 e^(e^(-3t) -1)

p = mass at time t / initial mass x 100
p = 70 e^(e^(-3t) -1) / 70 x 100
p = e^(e^(-3t)-1)) x 100


now if yu see if t becomes very large the expression e^(-3t) would approach zero .
look at it this way
e^(-3t) = 1/e^(3t)
see if denominator becomes very large the fraction becomes too small i.e. it approaches zero.
thus if e^(-3t) aproaches zero then e^(-3t)-1 approaches -1
thus e^(e^(-3t)-1) approaches e^(-1)

so p = e^(-1) x 100

take yur time reading this post..

 

[studen12345]

from part i) u would have got
y = 70 e^(e^(-3t) -1)

p = mass at time t / initial mass x 100
p = 70 e^(e^(-3t) -1) / 70 x 100
p = e^(e^(-3t)-1)) x 100


now if yu see if t becomes very large the expression e^(-3t) would approach zero .
look at it this way
e^(-3t) = 1/e^(3t)
see if denominator becomes very large the fraction becomes too small i.e. it approaches zero.
thus if e^(-3t) aproaches zero then e^(-3t)-1 approaches -1
thus e^(e^(-3t)-1) approaches e^(-1)

so p = e^(-1) x 100

take yur time reading this post..

Plz Can U Help Me With q6 (i) Part And Q 9 First How To Solve Them Realy Confused Of This Paper..

 

[monoho]

can someone help me with q 10 part iii an iv http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_w08_qp_3.pdf

 

[Soldier313]

Aoa wr wb

Can someone please tell me, how do we know whether we have to use
5 rather than 4.5 etc for these sort of qns?



Thank you.

 

[D0cEngi]

Ashique Thank you so much.

 

[D0cEngi]

I'm not able to solve a single question of vectors and argand diagram..I'm screwed.i'm so messed up. I'm crying. Don't know what to do. Plz help me.

 

[MustafaMotani]

Plz Can U Help Me With q6 (i) Part And Q 9 First How To Solve Them Realy Confused Of This Paper..

bro i did Q6(i) but its too long and too complicated for me to type in the post ...

i shall give u little starting point

tan(2x+x) = (tan2x + tanx)/ (1 - tan(2x)tan(x)) = k tanx


i then substituted tan2x = (2tanx)/ (1-tan^2(x))

and after doing some algebraic i got the answer

 

[MustafaMotani]

Plz Can U Help Me With q6 (i) Part And Q 9 First How To Solve Them Realy Confused Of This Paper..

in Question
9i) just equate both the equations

equation of l : r1 = (3-λ)i + (-2+2λ)j + (1+λ)k
equation of m : r2 = (4 +µa)i + (4 +µb)j + (2-µ)k

since they intersect r1 = r2
(3-λ)i + (-2+2λ)j + (1+λ)k = (4 +µa)i + (4 +µb)j + (2-µ)k
compare the coeficients
and after some substitutions u shall get the desired result .

ii) since they are perpendicular ... dot the direction vector of both the lines and equate it to zero ..
u shall get another eqution with a and b . Solve them simultaneously to get values of a and b.

iii) easiest.. when you got values of a and b ... u would have got some equations in terms of a and b for λ and µ in part (i)
calculate either λ or µ and then substitute that value in either equation of l or m respectively ...

its difficult to understand by reading .. just do it to get it

 

[Esme]

I'm not able to solve a single question of vectors and argand diagram..I'm screwed.i'm so messed up. I'm crying. Don't know what to do. Plz help me.

These might help, but do as many past paper questions on these topics as you can.
And most importantly pray to Allah, insha'Allah you will get it.

 

[studen12345]

bro i did Q6(i) but its too long and too complicated for me to type in the post ...

i shall give u little starting point

tan(2x+x) = (tan2x + tanx)/ (1 - tan(2x)tan(x)) = k tanx


i then substituted tan2x = (2tanx)/ (1-tan^2(x))

and after doing some algebraic i got the answer

Oh I Also Did The Same But Might Have Done Smthng Wrong In Algebra Thanku Very Much

 

[studen12345]

in Question
9i) just equate both the equations

equation of l : r1 = (3-λ)i + (-2+2λ)j + (1+λ)k
equation of m : r2 = (4 +µa)i + (4 +µb)j + (2-µ)k

since they intersect r1 = r2
(3-λ)i + (-2+2λ)j + (1+λ)k = (4 +µa)i + (4 +µb)j + (2-µ)k
compare the coeficients
and after some substitutions u shall get the desired result .

ii) since they are perpendicular ... dot the direction vector of both the lines and equate it to zero ..
u shall get another eqution with a and b . Solve them simultaneously to get values of a and b.

iii) easiest.. when you got values of a and b ... u would have got some equations in terms of a and b for λ and µ in part (i)
calculate either λ or µ and then substitute that value in either equation of l or m respectively ...

its difficult to understand by reading .. just do it to get it

 

[kiara15]

http://www.ilovemaths.com/3.asp... very useful link

 

[Esme]

from part i) u would have got
y = 70 e^(e^(-3t) -1)

p = mass at time t / initial mass x 100
p = 70 e^(e^(-3t) -1) / 70 x 100
p = e^(e^(-3t)-1)) x 100


now if yu see if t becomes very large the expression e^(-3t) would approach zero .
look at it this way
e^(-3t) = 1/e^(3t)
see if denominator becomes very large the fraction becomes too small i.e. it approaches zero.
thus if e^(-3t) aproaches zero then e^(-3t)-1 approaches -1
thus e^(e^(-3t)-1) approaches e^(-1)

so p = e^(-1) x 100

take yur time reading this post..

Yep understood perfectly ! Thank you soo much !

 

[MustafaMotani]

Oh I Also Did The Same But Might Have Done Smthng Wrong In Algebra Thanku Very Much

Yep understood perfectly ! Thank you soo much !

anytime fellas ..

 

[studen12345]

in Question
9i) just equate both the equations

equation of l : r1 = (3-λ)i + (-2+2λ)j + (1+λ)k
equation of m : r2 = (4 +µa)i + (4 +µb)j + (2-µ)k

since they intersect r1 = r2
(3-λ)i + (-2+2λ)j + (1+λ)k = (4 +µa)i + (4 +µb)j + (2-µ)k
compare the coeficients
and after some substitutions u shall get the desired result .

ii) since they are perpendicular ... dot the direction vector of both the lines and equate it to zero ..
u shall get another eqution with a and b . Solve them simultaneously to get values of a and b.

iii) easiest.. when you got values of a and b ... u would have got some equations in terms of a and b for λ and µ in part (i)
calculate either λ or µ and then substitute that value in either equation of l or m respectively ...

its difficult to understand by reading .. just do it to get it

CAn Not dothefirst Part Have Done Therest I Know Its Silly But Can U Plz Show Da Wrking For Part 1 Iam Trying For So Long THANX

 

[Esme]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_33.pdf
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_ms_33.pdf

Q10 b) i) I've made the diagram. Can someone check and tell me if my shading is right ? If it's wrong please do tell me the correct shading. Also how to do ii) part ?

MustafaMotani
Alice123

or anyone

 

[MustafaMotani]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_ms_33.pdf

Q10 b) i) I've made the diagram. Can someone check and tell me if my shading is right ? If it's wrong please do tell me the correct shading. Also how to do ii) part ?

MustafaMotani
Alice123

or anyone

its okay if yu ask me ..

 

[Esme]

its okay if yu ask me ..

Alright... ii) part please ?

 

[studen12345]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_ms_33.pdf

Q10 b) i) I've made the diagram. Can someone check and tell me if my shading is right ? If it's wrong please do tell me the correct shading. Also how to do ii) part ?

MustafaMotani
Alice123

or anyone

I Also Made It Like This Ithink Its Right