Edexcel A2 C3 Mathematics 12th June 2015

Original post by adorablegirl1202

https://07a69ccf283966549a9350d1a66951a7bc96e2dc.googledrive.com/host/0B1ZiqBksUHNYZ0JQM1NRcmdHdXM/June%202014%20QP%20-%20C3%20Edexcel.pdf

For 9b, I made a mistake I thought that because it's 3theta that means sin(3theta - 1.1071) = 3 not 1, can someone explain to me?

and for c I thought the min value would be -1 for the sin bit

Sin has a range of -1 and 1.

For min value questions you usually think 'oh, it's going to be -1', but in the equation H(theta), if your sin function outputs -1, what does H(theta) equal? So is it a minimum? (By sin function outputting one I mean sin(3theta-a) = -1, so that's without R and the other stuff.

Reply 1182

mat1996

Hi, could someone help me on this question
"Given that 2 sin(θ + 30)° = cos(θ + 60)°, find the exact value of tan θ °."

This is the answer
2sin(θ + 30)° = cos(θ + 60)°
2sinθ°cos30° + 2cosθ°sin30° = cosθ°cos60° – sinθ° sin60°
2root3/2 sinθ° +2/2cosθ° =1/2 cosθ° – root3/2 sinθ°
Finding tanθ°, tanθ° = – 1/3root3 or equiva.

I don't understand how you get the last bit of the answer, could someone help me please :confused:

Reply 1183

Original post by Ripper Phoenix

how do you get range of functions that look like this:

1/(x+1)(x-1) or 2x/(3x+5)

like also how do i know when to say y is not equal to 0 as part of the range answer

help?

One rule of thumb is to compare the leading term of the numerator and your denominator (the term with the highest power of x) and look at the ratio of your coefficients.

So for your first one, it's 1/(x^2-1). When x is large, it becomes 1/a very large number, so it seems to be going to 0. I suspect that you can't have a number a such that 1/a = 0, so y won't be equal to 0. (One way of thinking about it is that because x is large, x^2 is large, so the -1 is of little consequence, so you're left with 1/x^2. If you think about x = 1000, then f(x) = 1/((1000^2)-1), which is probably very close to 1/(1000^2).

If you have 2x/3x+5 and x becomes large, so that +5 becomes of little consequence, what do you think it will converge to?

(edited 8 years ago)

Reply 1184

TeeEm

19

Original post by mat1996

Hi, could someone help me on this question
"Given that 2 sin(θ + 30)° = cos(θ + 60)°, find the exact value of tan θ °."

This is the answer
2sin(θ + 30)° = cos(θ + 60)°
2sinθ°cos30° + 2cosθ°sin30° = cosθ°cos60° – sinθ° sin60°
2root3/2 sinθ° +2/2cosθ° =1/2 cosθ° – root3/2 sinθ°
Finding tanθ°, tanθ° = – 1/3root3 or equiva.

I don't understand how you get the last bit of the answer, could someone help me please :confused:

equation has been divided by cosθ

Reply 1185

TheRaspberry

9

Do we need to know about counter examples then?

Reply 1186

BioAgent

10

For the domain and range sometimes the mark scheme doesn't include x/f(x) is equal to all real numbers. I f you do include it do you loose marks?

Reply 1187

TheRaspberry

9

I am really confused when solving these mod equations; for the 2nd solution, how do you know which side to put the minus on, because I am pretty sure there have been questions where it has been required for it to be put on alternate sides (e.g the minus on the mod equation side, and then on the non-mod side (not on the same question!!))

Sorry if this is confusing, but any help would be really appreciated. If anyone could just talk me through part b, to determine on which side you would put the minus, the question being from the June 2014 (R) paper that would also be much appreciated. :smile:

Reply 1188

mat1996

Original post by TeeEm

equation has been divided by cosθ

OMG, I can't believe i didn't see that. Thank you so much for your help :smile:

but you know when I do it on the calculator it gives me -root3/9. Would examiners know this is equivalent or should i change it to the other answer (and how would I know this in the exam)

Reply 1189

adorablegirl1202

Original post by SeanFM

Sin has a range of -1 and 1.

For min value questions you usually think 'oh, it's going to be -1', but in the equation H(theta), if your sin function outputs -1, what does H(theta) equal? So is it a minimum? (By sin function outputting one I mean sin(3theta-a) = -1, so that's without R and the other stuff.

ok thanks! so basically even if it's 3theta 4theta or whatever theta sin and cos will always be within -1 to 1 their usual range, got it!
Another thing, I was sketching |8-2x| and got my line extending a bit into the second quadrant but I did the mod bit correct by reflecting what's in the negative x axis above, but in the markscheme they don't have the line extending, so i was wondering if you could explain??

Reply 1190

Original post by adorablegirl1202

ok thanks! so basically even if it's 3theta 4theta or whatever theta sin and cos will always be within -1 to 1 their usual range, got it!
Another thing, I was sketching |8-2x| and got my line extending a bit into the second quadrant but I did the mod bit correct by reflecting what's in the negative x axis above, but in the markscheme they don't have the line extending, so i was wondering if you could explain??

I'm not 100% sure what you mean, from what points to what points is it extending on your sketch?

Reply 1191

danlocke

Original post by Maham88

which solomon paper is this from ?

F and L IIRC.

Reply 1192

danlocke

Whats the general consensus on Solomon vs Elmwood? Which is harder? I've finished all the Solomon papers so far and have just done the first Elmwood- it seemed easier to me...

Reply 1193

it's a me, mario

Is it possible to put something like

3sinx + 2cosx in the form Rsin(x-alpha) ?

Or is it always Rsin(x+alpha) ?

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Reply 1194

adorablegirl1202

Original post by SeanFM

I'm not 100% sure what you mean, from what points to what points is it extending on your sketch?

As in it from the y axis at 8 but the graph in the markscheme just has it start from 8

Reply 1195

it's a me, mario

Do we need to know how to solve inequalities involving modulus stuff? :eek:

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Reply 1196