Shout here for any general help on Pure Maths stuff from Y12 or Y13…
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Pure MathsShout here for any general help on Pure Maths stuff from Y12 or Y13… 123 comments to Pure Maths |
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Copyright © 2012 The Sydenham High School Mathematics Department Blog - All Rights Reserved |
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I can’t do 7f, 16aiii and 16b! I’ve gone through a million different ways and still don’t know what to do.
Hi Deola,
16a part iii
The tan of 45deg is 1 so you can replace some of the 1s with tan45 to get the format of tan(A-B)
16b
Start by expanding the bracket on the right and using the values you know for cos and sin 60. See where that leads.
Tea Lady
thanx
next question?
how do you find the maximum when it involves sin, because i can do it with cos, as cos(0)=1 or something like that
Hi Deola,
Think about the sine curve: max value of sine = 1, min value = -1
i’m stuck on two questions, i thought i could do them but i cant get the answer and i don’t know why
1.given that cotx = -1.5 and that x is obtuse, find the exact value of cosecx
i can get the value right, but i cant get the sign right, in the answers it says cosecx = – (root 13)/ 2, but if its obtuse and tan is negative it has to be in the second quadrant and therefore shouldn’t sinx be positive?
2. find the exact value of cos(arcsin(-1/3)) -pie/2 (< and equal to) arcsinx (< and equal to) pie/2
when i did it i got root 2/3 but the answer says 2root2/3, i'm confused
also does (tan-b)=tanb?
megan
Hi Megan,
I agree with you on the first one.
Last bit: tan(-b) = – tan b.
I’ll come back on the other one when I’ve worked it out!
JT
Hi Megan,
Do your Pythagoras triangle: sine is 1 over 3 which makes the third side root8. Root 8 is 2root3.
JT
thankyou
i’m getting kind of confused with inverse’s
when you have arcsin (-1/3) doesnt that equal pie/6
when you have cos/tan/sin with arc does that go to the angle or the side as in is it like pie/4 or like 1/3? if that makes sense lol
also my calculator broke today, so i got a new one, but because i’m not that used to it, do you have an old style one that i could take in the exam aswell incase i cant work out how to do something on the newer one?
Hi Megan, don’t confuse 1/3 with 1/root3 which is the TAN of 30deg.
Remember, you can always check them on your calculator – does it do surd form?
The answer to arc-anything is an angle.
eg arcsin0.5
Read it as ‘the angle whose sine is 0.5′
Yes, you can borrow my calculator.
JT
thanks that helps alot.
where will you be around 12.30, 1ish, so i can come get the calculator?
With a combined function fg(x) how do you know the domain of x or the range? Are you supposed to know?
In one question, for f(x) x was bigger than 1, but in g(x) x was an element of the real numbers. Then what is the domain for fg(x)?
Thanks
Megan – depends if any year 13s are around. C7 or lunch!!
Emily, the range of the function you do first becomes the domain for the second function.
Ok so in fg(x) the range of g(x) becomes the domain for fg(x)?
thanks see you tommorow
sorry last question, when you do the change of sign rule does it have to be in radians?
Emily – yes.
Megan – have no idea what you’re talking about lol! Ask me tomorrow – go to bed now!
thank you
i cant do question 2 in the ex5k.
Hi Deola,
Do you have my C4? The one you asked me for for Mr Atkins?
You have a and b (sorry can’t bold or underline them)
so you can find vector AB = b – a
Double that to get vector AP
then AP = p – a
JT
omg!! lol sorry mrs T that’s what i was meant to say when i left my first message. I completely forgot to see mr Atkins after i left your classroom.
why do u need to double AB because AP is double BP?
Also their answer was (-i-2j-5k)?
ALSO, i dont know how to go about question 4?
Deola, draw it! If you draw AB then keep going till AP is double BP, then B is the midpoint of your line.
You need to find p not AP so are you ATQing?
Q4 How do you find the mod of a vector? Square both sides and you’re there.
Good job I managed to find a spare C4 in school today then, wasn’t it?!!
JT
i drew it and AP was 2/3 of AB. The problem is that i dont understand any of these questions tbh.
But i still don’t understand because i don’t know how to use the position vectors they have given.
q4….but they asked for the point of intersection so don’t i need to create 2 vector equations?
Deola,
Q2 RTQ It says P is on AB produced ie extended, not AB itself.
Q4 Sorry – was looking at wrong exercise.
You need the vectors of the 2 lines
Call points A B C D for example
then AB = b – a
CD = d – c
then you can do their dot product to find the angle between them.
The vectors AB and CD will be your direction vectors for finding the point of intersection. See example 33.
i didnt know that produced meant extened sorry
okay i’ll try q4 again and see how it goes
yet again im stuck, i cant do part 2 of q7?
Find vector AB
AC is 2/3 of that
AC = c-a
I think you need to revise position vectors, in particular the general result that
vector PQ = q-p
Going out now so you’re on your own till later tonight.
i’m stuck on ex6c 3a – how do you intergrate cos2xcosx?
megan
Hi Megan,
It’s one of those P+Q, P-Q thingies!
Have a look at the trig in your C3 notes for the one with the cos cos format.
Good luck
Hi Megan,
Have you found it?
It’s the format for the sum of two cosines.
To get the first one, add your angles; to get the second one, subtract.
Therefore 2 cos2x cosx = cos(2x+x) + cos(2x-x) = cos3x + cosx
and these are functions which you know how to integrate.
JT
o i get it Thankyou.
you cant add cos3x and cosx to get cos4x can you?
megan
NOOOOOOOOOOOOO!
Integrate them separately.
Whenever you wonder about something like that, try putting in some numbers eg does cos75cos25 = cos90?
Hey Mrs Tibble
Was wondering if it’d be ok to look at some questions from C3 Ex6F tomorrow?
Thank you
Hi Mel,
OK. Will bring my C3 book then.
JT
im doing exercise 3c, page 28 question 1 (d). i have been trying to work it out but i cant seem to work out what the end result is, help?
hannah
Hi Hannah,
(4.5, 4.5) and (6,3)
Answers are in the back of the book!!
JT
Hannah,
Rearrange eqn1 to give x=(9-y)
Sub into other eqn twice to replace the x-squared and the x in the 2nd term.
Multiply out all the brackets. Be careful of the 2nd one: there’s a double negative.
Tidy up.
Divide by 3 to make life easier.
Factorise and solve.
thank you. i was trying to work it out but my answer was completely different to the book but i will try that. Thanks again!
Hannah
I am completely stuck on the logarithm homework – could you help me with question 1 :/?
“Find the possible values of x for which 2^2x+1 = 3(2^x)-1.”
Thank you
Hi Katja,
I’m not sure from the way you’ve typed it, what the right hand side is. Please can you clarify as i don’t have a C2 here.
Thanks
What do you mean by the right hand side?
The right hand side of the equation!!!!!!!!!!
Give me a page number instead as I’ve found the disc.
Sorry I was confused :S
It’s page 46
Thank You
Do it the same way as Example 9.
Aaah Thank you
hi Mrs T
doing ex 5H and dont know how to do qu 2? its probs really easy but could you help me just get started!
Thank You,
H
Hi Hannah,
The equations in parts a, b, c are the general equations for each of the lines.
When you use t=1, then this becomes the position vector of point P.
When you use t=5 you get the position vector of point Q.
You can then do vector PQ = q – p
so you’ll have the vector that goes from P to Q.
The distance between P and Q is the magnitude of the vector, so do the modulus (Pythagoras it) and you’re there.
Does that help?
Tea Lady (did you manage to finish that bucketful?)
oh ok i get it thanks!
erm i nearly did i only wasted a tiny bit of it, i dont think that bucket will be coming to our lesson again any time soon
Thanks again & see you tomorrow,
H
I am having a bit of an issue with vectors- every question is asking to prove that a point lies on the line and I can’t find an example anywhere.
What topic does it come under? and how do I prove this?
Thank you!