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Pure Maths

Shout here for any general help on Pure Maths stuff from Y12 or Y13…

28 comments to Pure Maths

  • DEOLA

    I can’t do 7f, 16aiii and 16b! I’ve gone through a million different ways and still don’t know what to do.

  • Mrs Tibble

    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

  • DEOLA

    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

  • Mrs Tibble

    Hi Deola,
    Think about the sine curve: max value of sine = 1, min value = -1

  • Megan Conway

    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

  • Mrs Tibble

    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

  • Mrs Tibble

    Hi Megan,
    Do your Pythagoras triangle: sine is 1 over 3 which makes the third side root8. Root 8 is 2root3.
    JT

  • Megan Conway

    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?

  • Mrs Tibble

    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?

  • Mrs Tibble

    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

  • Megan Conway

    thanks that helps alot.
    where will you be around 12.30, 1ish, so i can come get the calculator?

  • Emily Boyce

    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

  • Mrs Tibble

    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.

  • Emily Boyce

    Ok so in fg(x) the range of g(x) becomes the domain for fg(x)?

  • Megan Conway

    thanks see you tommorow

  • Megan Conway

    sorry last question, when you do the change of sign rule does it have to be in radians?

  • Mrs Tibble

    Emily – yes.

    Megan – have no idea what you’re talking about lol! Ask me tomorrow – go to bed now!

  • Emily Boyce

    thank you :)

  • DEOLA

    i cant do question 2 in the ex5k.

  • Mrs Tibble

    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

  • DEOLA

    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. :P

    why do u need to double AB because AP is double BP?
    Also their answer was (-i-2j-5k)?

  • DEOLA

    ALSO, i dont know how to go about question 4?

  • Mrs Tibble

    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

  • DEOLA

    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?

  • Mrs Tibble

    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.

  • Mrs Tibble

    The vectors AB and CD will be your direction vectors for finding the point of intersection. See example 33.

  • DEOLA

    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?

  • Mrs Tibble

    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.

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