All of these I consider to be relatively difficult questions and some I got stuck on, please answer these questions and show working.
Thank you everyone!
C2 24th May 2012 REVISION THREAD
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okay, q.6:
a) complete the square:
(x3)^2 9 + (y+2)^2 4 =12
(x3)^2 + (y+2)^2 =25
centre at (3,2)
radius is root25 = 5 (+ve value because it's a length)
b) P at (1,1) and Q at (7,5)
midpoint PQ should be (3,2) if a diameter
midpoint= (71/2, 51/2) = (3,2)
c) I'm not really sure how you'd do this. There's a rightangled triangle between RPQ and you can draw the whole thing onto a set of axes but although R is (0,y), I'm not sure how you'd find the y coordinate 
Offline0ReputationRep:(Original post by jameshewitt)
All of these I consider to be relatively difficult questions and some I got stuck on, please answer these questions and show working.
Thank you everyone!
4sinx=3tanx
For this question you have to know the trigonometric identity that tanx is equal to sinx/cosx. So we substitute tanx for sinx/cosx, which transforms the equation into:
4sinx = 3(sinx/cosx)
We then multiply both sides by cosx:
4sinx(cosx) = 3 sinx
There is sinx on both sides so we can cancel them out so the equation becomes:
4cosx = 3
Then we use our calculator to find the value of x so this becomes:
x = 41.4 (1 decimal place)
Then I think there are various ways to do this next step, but I use a CAST graph. I could draw it out if you want me to, but I'm assuming you know what this is/know what to do as this stage.
So the answer is 41.4 and 318.6 degrees.
If you have any queries, quote me. 
Offline0ReputationRep:(Original post by jameshewitt)
All of these I consider to be relatively difficult questions and some I got stuck on, please answer these questions and show working.
Thank you everyone!
Part a:
You have to know the log rule:
log_{a}n = x is the same as a^{x} = n
So if we apply this rule to log_{2}y = 3 then this becomes:
2^{3}=y
Work out 2^{3} and we get the value for y and hence the answer to this question.
The value of y = 0.125
Part b:
Firstly, I would multiply both sides by log_{2}x to get rid of that fraction so the equation becomes:
log_{2}32 + log_{2}16 = (log_{2}x)^{2}
For this question you will have to know the log multiplication rule: log_{a}x + log_{a}y = log_{a}xy
So the equation becomes:
log_{2}(32*16) = (log_{2}x)^{2}
Simplifying it:
log_{2}(512) = (log_{2}x)^{2}
We then square root both sides. You can find the square root of log_{2}(512) on your calculator, which equals 3 and 3 so the equation becomes:
3 = log_{2}x and 3 = log_{2}x
We can then apply the rule from part a: log_{a}n = x is the same as a^{x} = n
So the equation then becomes:
2^{3} = x and 2^{3} = x
And the final answer:
x = 8 and x = 1/8
Note that you can check if your answers are correct by substituting your answer back into the equation. 
Offline1ReputationRep:(Original post by MrJames16)
For the third question, question 8 about logs:
Part a:
You have to know the log rule:
log_{a}n = x is the same as a^{x} = n
So if we apply this rule to log_{2}y = 3 then this becomes:
2^{3}=y
Work out 2^{3} and we get the value for y and hence the answer to this question.
The value of y = 0.125
Part b:
Firstly, I would multiply both sides by log_{2}x to get rid of that fraction so the equation becomes:
log_{2}32 + log_{2}16 = (log_{2}x)^{2}
For this question you will have to know the log multiplication rule: log_{a}x + log_{a}y = log_{a}xy
So the equation becomes:
log_{2}(32*16) = (log_{2}x)^{2}
Simplifying it:
log_{2}(512) = (log_{2}x)^{2}
We then square root both sides. You can find the square root of log_{2}(512) on your calculator, which equals 3 so the equation becomes:
3 = log_{2}x
We can then apply the rule from part a: log_{a}n = x is the same as a^{x} = n
So the equation then becomes:
2^{3} = x
And the final answer:
x = 8
Note that you can check if your answers are correct by substituting your answer back into the equation.
I will do it in this way,
gives
gives
So 
Offline0ReputationRep:(Original post by raheem94)
There are two answers to the 2nd part,
I will do it in this way,
gives
gives
So
Damn, I always forget about the negative solution when square rooting lol. Thanks for that 
Offline1ReputationRep:(Original post by jameshewitt)
All of these I consider to be relatively difficult questions and some I got stuck on, please answer these questions and show working.
Thank you everyone!(Original post by ohtasha)
okay, q.6:
a) complete the square:
(x3)^2 9 + (y+2)^2 4 =12
(x3)^2 + (y+2)^2 =25
centre at (3,2)
radius is root25 = 5 (+ve value because it's a length)
b) P at (1,1) and Q at (7,5)
midpoint PQ should be (3,2) if a diameter
midpoint= (71/2, 51/2) = (3,2)
c) I'm not really sure how you'd do this. There's a rightangled triangle between RPQ and you can draw the whole thing onto a set of axes but although R is (0,y), I'm not sure how you'd find the y coordinate
Here is the diagram:
As it is a right angled triangle, so applying Pythagoras theorem gives, 
 Thread Starter
Offline0ReputationRep:(Original post by MrJames16)
For the second question, the (ii):
4sinx=3tanx
For this question you have to know the trigonometric identity that tanx is equal to sinx/cosx. So we substitute tanx for sinx/cosx, which transforms the equation into:
4sinx = 3(sinx/cosx)
We then multiply both sides by cosx:
4sinx(cosx) = 3 sinx
There is sinx on both sides so we can cancel them out so the equation becomes:
4cosx = 3
Then we use our calculator to find the value of x so this becomes:
x = 41.4 (1 decimal place)
Then I think there are various ways to do this next step, but I use a CAST graph. I could draw it out if you want me to, but I'm assuming you know what this is/know what to do as this stage.
So the answer is 41.4 and 318.6 degrees.
If you have any queries, quote me. 
 Thread Starter
Offline0ReputationRep:(Original post by MrJames16)
For the third question, question 8 about logs:
Part a:
You have to know the log rule:
log_{a}n = x is the same as a^{x} = n
So if we apply this rule to log_{2}y = 3 then this becomes:
2^{3}=y
Work out 2^{3} and we get the value for y and hence the answer to this question.
The value of y = 0.125
Part b:
Firstly, I would multiply both sides by log_{2}x to get rid of that fraction so the equation becomes:
log_{2}32 + log_{2}16 = (log_{2}x)^{2}
For this question you will have to know the log multiplication rule: log_{a}x + log_{a}y = log_{a}xy
So the equation becomes:
log_{2}(32*16) = (log_{2}x)^{2}
Simplifying it:
log_{2}(512) = (log_{2}x)^{2}
We then square root both sides. You can find the square root of log_{2}(512) on your calculator, which equals 3 and 3 so the equation becomes:
3 = log_{2}x and 3 = log_{2}x
We can then apply the rule from part a: log_{a}n = x is the same as a^{x} = n
So the equation then becomes:
2^{3} = x and 2^{3} = x
And the final answer:
x = 8 and x = 1/8
Note that you can check if your answers are correct by substituting your answer back into the equation. 
 Thread Starter
Offline0ReputationRep:(Original post by raheem94)
For the last part, draw a diagram.
Here is the diagram:
As it is a right angled triangle, so applying Pythagoras theorem gives, 
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Offline0ReputationRep:Also please help

Offline1ReputationRep:(Original post by jameshewitt)
Also please help
We know the coordinates of P, Q and R.
Sub in P,
Sub in Q,
Sub in R,
(3)  (2) gives,
Sub 'a=2' in (1), you will get, 
 Thread Starter
Offline0ReputationRep:(Original post by raheem94)
We know the coordinates of P, Q and R.
Sub in P,
Sub in Q,
Sub in R,
(3)  (2) gives,
Sub 'a=2' in (1), you will get, 
Offline1ReputationRep:(Original post by jameshewitt)
All makes sense now! Thank you, hopefully i'll remember to apply this on Thursday 
Offline0ReputationRep:(Original post by MrJames16)
For the second question, the (ii):
4sinx=3tanx
For this question you have to know the trigonometric identity that tanx is equal to sinx/cosx. So we substitute tanx for sinx/cosx, which transforms the equation into:
4sinx = 3(sinx/cosx)
We then multiply both sides by cosx:
4sinx(cosx) = 3 sinx
There is sinx on both sides so we can cancel them out so the equation becomes:
4cosx = 3
Then we use our calculator to find the value of x so this becomes:
x = 41.4 (1 decimal place)
Then I think there are various ways to do this next step, but I use a CAST graph. I could draw it out if you want me to, but I'm assuming you know what this is/know what to do as this stage.
So the answer is 41.4 and 318.6 degrees.
If you have any queries, quote me.
4sin(x) = 3tan(x) which is the same as:
4sin(x) = 3sin(x) / cos(x)
Multiply by cos(x) which gives: 4sin(x)cos(x) = 3sin(x)
Subtract the 3sin(x), this gives: 4sin(x)cos(x)  3sin(x) = 0
Simplify by collecting the sin's together: sin(x)(4cos(x)3) = 0
Now use CAST or the graph method to work it out so..
Sin(x) = 0 is 0 so the answers for this are 0 degrees and 180 degrees (its also 360, 360 and 180 but these are outside the range they ask for).
Then solve this part of the equation: 4cos(x)3 = 0
Cos(x) = 3/4 is 41.4 degrees and the answers that fit the range are 41.4 and 318.6.
So all my answers are: 0, 41.4, 180 and 318.6.
I understand why you divided the sin(x) as that's what I used to do until I looked at my revision book. So does anyone know which is correct? 
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Guys you can't discuss the exam yet!!!!!!!
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Offline2ReputationRep:(Original post by Bantersaurus Rexx)
Guys you can't discuss the exam yet!!!!!!!
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