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Mathematics: Post your doubts here!
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saimaiftikhar92 said:
Question 1:
You need to get the 2^x terms together. Multiply the denominator over to the other side, bring the 2^x terms together and then use logarithms to find x.
Question 3:
part i) a is acute, so sin and cos are both positive. Use the cos^2 + sin^2 =1 identity to find cos a. Then use the sin(A+B) identity to expand the required expansion, and use your values for cos a and sin a to evaluate.
part ii) Use tan a = (sin a)/(cos a), and then the double angle identity for tan 2a to find that value. Then use tan(3a) = tan(2a + a) and the tan(A+B) identity for the second bit.
Question 4:
part i) M is a stationary point, so dy/dx = 0 at M. Differentiate using the Quotient Rule, then solve your function =0. Remember that you only need to consider the numerator to make it 0.
part ii) M lies between pi and 2pi, so you can use any starting value in that range with the iterative formula, from the graph maybe 3pi/2 would be a decent value. Then use the iterative formula (don't forget to work in radians mode), writing each to 4dp. When they match to 3dp, your 2dp root is correct.
Question 6:
part i) Implicit differentiation to begin, don't forget that you differentiate any term involving y as normal, but then multiply by dy/dx. Then rearrange to get dy/dx on its own.
part ii) Straight lines need a gradient and a point. Use the y coordinate in the original equation to find the value of x. Then use both of these in your dy/dx function to find the gradient. Then use this point and gradient to fin the equation of the tangent.
Hope those hints help,
Cheers,
ASh.
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- Messages
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http://www.xtremepapers.com/CIE/index.p ... _qp_31.pdf QUESTION 8 ...... it is similar but i am not getting the answer
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part 1 or 2?
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both..
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thankyou so much for your help in these 5 , 6 days...... i have maths mock tomorrow ........and I really hope that it goes well......again thankyou so much! :good:
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^^ just press the thank button to thank someone! 
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need solution to question Q8ii and Q9ii both from Mathematics P33 May/June 2011. The questions can be found over here : http://www.xtremepapers.com/CIE/International A And AS Level/9709 - Mathematics/9709_s11_qp_33.pdf. Thanks in advance.
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http://www.xtremepapers.com/CIE/International A And AS Level/9709 - Mathematics/9709_s05_qp_1.pdf
seems a very simple question but still i need its explaination.
Thank You
seems a very simple question but still i need its explaination.
Thank You
XPFMember
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As-salam-o-alaikum!
You forgot to mention the question number!
OH sorry its question number 3
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Here is how:
Part (i)
sin θ + cos θ = 2(sin θ − cos θ)
sin θ + cos θ -2sin θ +2cos θ = 0
3cos θ = sin θ
3= sin θ
.....cos θ
sin θ = tan θ
cos θ
tanθ = 3 (expressed)
Part (ii)
Hence solve the equation sin θ + cos θ = 2(sin θ − cos θ), for 0 ≤ θ ≤ 360
so use the expression fain above:
sin θ + cos θ = 2(sin θ − cos θ)
=
tan θ= 3
θ = tan-1 (3)
= 71.6
tan is positive in first and third quadrant, so:
θ = 71.6, (180 + 71.6)
θ = 71.6° , 251.6°
Part (i)
sin θ + cos θ = 2(sin θ − cos θ)
sin θ + cos θ -2sin θ +2cos θ = 0
3cos θ = sin θ
3= sin θ
.....cos θ
sin θ = tan θ
cos θ
tanθ = 3 (expressed)
Part (ii)
Hence solve the equation sin θ + cos θ = 2(sin θ − cos θ), for 0 ≤ θ ≤ 360
so use the expression fain above:
sin θ + cos θ = 2(sin θ − cos θ)
=
tan θ= 3
θ = tan-1 (3)
= 71.6
tan is positive in first and third quadrant, so:
θ = 71.6, (180 + 71.6)
θ = 71.6° , 251.6°
XPFMember
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As-salam-o-alaikum!
Let me give you a small hint!
Case : 1
If sin and cos are either being added or subtracted, it’ll be possible to rearrange the equation, and hence write it in terms of tan !
Look at this!
2 sin x – 3 cos x = 0
2sin x= 3cos x
sin x /cos x = 3/2
tan x = 3/2
Hence find x
In general, bring all sin x terms to one side, and cos x to the other side, and then change it to tan x as shown above!
For more ways and hints for solving equations, see attached! They are for the whole chapter... for the solving equations help see the last two pages!I am adding it as a zip file, because I don't know why it showed me no option to add the word file :s
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