Mathematics: Post your doubts here!

[shanky631]

what is the present value of Rupee 1 to be received after 2 years compounded annually at 10%?? can someone plz solve this.

whitecorp

 

[iKhaled]

can someone please explain question 5 of this paper in FULL DETAILS!
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_w06_qp_3.pdf
thank you.

 

[Silent Hunter]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s11_qp_31.pdf

Q9 (i) ...... please solve anybody help ..... i just cant get the trigonometry proving thingy

 

[iKhaled]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_31.pdf

Q9 (i) ...... please solve anybody help ..... i just cant get the trigonometry proving thingy

cos 4θ + 4cos 2θ = 8cos^4 θ -3

cos 4θ = 2cos^2 2θ -1 ( double angle formulae )

2cos^2 2θ - 1 + 4cos 2θ
2 (cos 2θ)(cos2θ) - 1 + 4cos 2θ

use the double angle formula again cos 2θ = 2cos^2 θ -1

2(2cos^2 θ -1)(2cos^2 θ -1 )-1 +4(2cos^2 θ-1)
2(4cos^4 θ -4cos^2 θ +1)-1 +8cos^2θ -4

expand the brackets and cancel stuff u will end up with 8cos^4 θ -3

 

[Silent Hunter]

cos 4θ + 4cos 2θ = 8cos^4 θ -3

cos 4θ = 2cos^2 2θ -1 ( double angle formulae )

2cos^2 2θ - 1 + 4cos 2θ
2 (cos 2θ)(cos2θ) - 1 + 4cos 2θ

use the double angle formula again cos 2θ = 2cos^2 θ -1

2(2cos^2 θ -1)(2cos^2 θ -1 )-1 +4(2cos^2 θ-1)
2(4cos^4 θ -4cos^2 θ +1)-1 +8cos^2θ -4

expand the brackets and cancel stuff u will end up with 8cos^4 θ -3

JazakAllah ... thanks alot..... is there any specific technique for these questions or just trial and error thing? and how much formulae related to trig do we have to remember?

 

[iKhaled]

JazakAllah ... thanks alot..... is there any specific technique for these questions or just trial and error thing? and how much formulae related to trig do we have to remember?

nah there isn't any specific technique u will just need to memorize all the trig formulas u have from ur AS level and A2 level book and practice a lot of questions on prove identity to get experienced in solving them. you only need to memorize the formulas and practice a lot to be experienced how to deal with these questions and which formulas to use.

 

[Silent Hunter]

nah there isn't any specific technique u will just need to memorize all the trig formulas u have from ur AS level and A2 level book and practice a lot of questions on prove identity to get experienced in solving them. you only need to memorize the formulas and practice a lot to be experienced how to deal with these questions and which formulas to use.

but there are some formulae in the booklet too.?

 

[iKhaled]

but there are some formulae in the booklet too.?

i checked the syllabus if thats what u mean then yes these r the formulas also

 

[Silent Hunter]

i checked the syllabus if thats what u mean then yes these r the formulas also

i meant that the formulas mentioned here in syllabus are the only ones?

 

[iKhaled]

i meant that the formulas mentioned here in syllabus are the only ones?

yeah plus u need to know cot = 1/tan or cot = cos/sin and cosec = 1/sin and sec = 1/cos

 

[salvatore]

Please help me solve the question above (I'll appreciate a step-by-step explanation).
Thanks!

 

[Rutzaba]

Please help me solve the question above (I'll appreciate a step-by-step explanation).
Thanks!

1. convert it into this form ... (3x+1)^0.5

2. add 1 to the power... (3x+1)^1.5

3.divide the whole thing with the new power [(3x+1)^1.5] / 1.5

4. differentiate the term inside the bracket. that wud be 3

5. divide the whole term with 3.

6.[ (3x+1)^1.5] divided by [ 1.5 x 3]

7. that would make it [(3x+1)^1.5]
....................................__________ + C

..........................................4.5


8. now you put limits ... put 1 into x then put 0 into x.

then substact the X=0 term from the X=1 term

9. putting 1
[(4^1.5)] ............... [(3(0)+1)^1.5]
_______ _ _________
4.5............................... 4.5

10. (16/9) _ (2/9)

it will give you 14/9 as the final answer

 

[Rutzaba]

1. convert it into this form ... (3x+1)^0.5

2. add 1 to the power... (3x+1)^1.5

3.divide the whole thing with the new power [(3x+1)^1.5] / 1.5

4. differentiate the term inside the bracket. that wud be 3

5. divide the whole term with 3.

6.[ (3x+1)^1.5] divided by [ 1.5 x 3]

7. that would make it [(3x+1)^1.5]
....................................__________ + C

..........................................4.5


8. now you put limits ... put 1 into x then put 0 into x.

then substact the X=0 term from the X=1 term

9. putting 1
[(4^1.5)] ............... [(3(0)+1)^1.5]
_______ _ _________
4.5............................... 4.5

10. (16/9) _ (2/9)

it will give you 14/9 as the final answer

ignore the ......... it is for gap

 

[Rutzaba]

can someone please explain question 5 of this paper in FULL DETAILS!
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_w06_qp_3.pdf
thank you.

this looks tough but is a peice of cake as the numbers given suggest.
i want you to ignore the ....... part. it stands for gap or space ok?

take [(1+x)^0.5] as a
take [(1-x)^0.5] as b

(a+b) (a-b)= (a^2) - (b^2)

putting back the values of a and b
[(1+x)^0.5]^2 - [(1-x)^0.5]^2



that wud give u

(1+x)-(1-x)

simplify this and you will get 2x

 

[Rutzaba]

after that its just a matter of cross multiplication

currently
(a+b)(a-b)=2x

so ..........(1).........................(a-b)
......_______......= ......._______
............ (a+b) ...................... 2x

 

[salvatore]

1. convert it into this form ... (3x+1)^0.5

2. add 1 to the power... (3x+1)^1.5

3.divide the whole thing with the new power [(3x+1)^1.5] / 1.5

4. differentiate the term inside the bracket. that wud be 3

5. divide the whole term with 3.

6.[ (3x+1)^1.5] divided by [ 1.5 x 3]

7. that would make it [(3x+1)^1.5]
....................................__________ + C

..........................................4.5


8. now you put limits ... put 1 into x then put 0 into x.

then substact the X=0 term from the X=1 term

9. putting 1
[(4^1.5)] ............... [(3(0)+1)^1.5]
_______ _ _________
4.5............................... 4.5

10. (16/9) _ (2/9)

it will give you 14/9 as the final answer

Thanks a lot.. ur amazing!

I understood fully till step 3.. but I don't get why you differentiated the term in the bracket and divided the whole term by the answer.
Secondly, in step 6, I don't understand why you multiplied 1.5 by 3.. please explain the steps 4, 5, 6 & 7.

I know I'm bothering you.. but I really need your help since I'm not very good at maths.

Thanks
Waiting for your reply..

 

[Rutzaba]

Thanks a lot.. ur amazing!

I understood fully till step 3.. but I don't get why you differentiated the term in the bracket and divided the whole term by the answer.
Secondly, in step 6, I don't understand why you multiplied 1.5 by 3.. please explain the steps 4, 5, 6 & 7.

I know I'm bothering you.. but I really need your help since I'm not very good at maths.

Thanks
Waiting for your reply..

thats a rule of integration... we add one to the power... divide the term with new power and divide it with the differential of the term

 

[Rutzaba]

Thanks a lot.. ur amazing!

I understood fully till step 3.. but I don't get why you differentiated the term in the bracket and divided the whole term by the answer.
Secondly, in step 6, I don't understand why you multiplied 1.5 by 3.. please explain the steps 4, 5, 6 & 7.

I know I'm bothering you.. but I really need your help since I'm not very good at maths.

Thanks
Waiting for your reply..

in step 6 i multiplied 1.5 by 3 becux

somethng divided by 3 divided by 1.5 can also be written as
something divided by (1.5 x3)

 

[salvatore]

in step 6 i multiplied 1.5 by 3 becux

somethng divided by 3 divided by 1.5 can also be written as
something divided by (1.5 x3)

Thank you for your reply..

I'm still confused
Are we dividing just the denominator by 3 or the whole term?
3/2 divided by 3 = 3/6 !
If you don't mind.. can you please please show the working..

 

[Rutzaba]

Thank you for your reply..

I'm still confused
Are we dividing just the denominator by 3 or the whole term?
3/2 divided by 3 = 3/6 !
If you don't mind.. can you please please show the working..

ok


lets take 9
lets take 9... 9/1.5=6 6/3=2

now the other way 1.5 x3 = 4.5
9/4.5= 2