Hey there! Sign in to join this conversationNew here? Join for free
    Offline

    22
    ReputationRep:
    (Original post by LelouchViRuge)
    Anyone want to have a go at these?

    Meh, might as well do some easy maths. Getting a bit frustrated by the problem I'm currently on.

    Question 1
    Spoiler:
    Show
    Base case: a_1 = \frac{13+1}{2} = 7 (by the way, you really don't need moduli signs there...

    Assume a_n = \frac{13(7^{n-1}) + 1}{2} then a_{n+1} = \frac{13(7^n) + 7}{2} - \frac{6}{2} = \frac{13(7^n) + 1}{2} and we are done.
    Question 2
    Spoiler:
    Show
    Parabola. Gradient function is 2yy' = 4 \Righattow y' = \frac{2}{y} so tangent at P is y - 2p = \frac{1}{p}(x-p^2) and re-labelling gets us the tangent at Q.

    This means that they intersect at yp - p^2 = yq - q^2 \Rightarrow y(p-q) = p^2 - q^2 = (p-q)(p+q), since p \neq q then y = p+q and x=pq follows trivially.
    Question 3
    Spoiler:
    Show
    PQ has equation y - 2p= \frac{2(p-q)}{(p-q)(p+q)}(x-p^2) \iff y = 2p + \frac{2}{p+q}(x-p^2).

    At (1,0) - we have: 0 = p + \frac{1-p^2}{p+q} \iff p^2 - 1 = p^2 + pq \iff  pq = -1

    The normal has equation y - 2p = -p(x-p^2) and this intersects the other normal when:

    \displaystyle

\begin{align*}2p -p(x-p^2) = 2q -q(x-q^2) & \iff 2(p-q) + p^3 - q^3= x(p-q)  \\ & \iff  2 + (p^2 + qp + q^2) =  p^2 + q^2 + 1 = x \end{align*} from the fact that pq=-1.

    Bonus
    Spoiler:
    Show
    Blah blah gradients blah blah too bored
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    ....
    Sweet, those were not actually mod signs lol. They were [ .... ]

    The second question was actually STEP 1. They have a lot of nice parabola questions which are easily accessible to people without C3/C4 knowledge
    Offline

    22
    ReputationRep:
    (Original post by LelouchViRuge)
    The second question was actually STEP 1. They have a lot of nice parabola questions which are easily accessible to people without C3/C4 knowledge
    Yeah, I know. STEP I, Q2, 2005, right? :lol:
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Zacken)
    Yeah, I know. STEP I, Q2, 2005, right? :lol:
    Did you just remember that on the spot? o.O

    I'm guessing the first time you met that question, she made it a day you'd never forget?
    Offline

    22
    ReputationRep:
    (Original post by LelouchViRuge)
    Did you just remember that on the spot? o.O

    I'm guessing the first time you met that question, she made it a day you'd never forget?
    Nah, I seem to remember all the questions I've done. :lol: Each STEP question has that distinct 'flavour' that sticks. If you want some more accessible STEP I questions, try these:

    STEP I, 2012, Q4
    STEP I, 2009, Q8
    Offline

    3
    ReputationRep:
    (Original post by aymanzayedmannan)
    It's not on spec for the UK syllabus since you don't need to know how to turn it about any given angle.

    However, the matrix \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin\theta & \cos\theta \end{pmatrix} is the matrix which rotates any matrix through an angle \theta about O. You'd use this matrix to find \mathbf{Q}.
    Thanks
    Offline

    2
    ReputationRep:
    LelouchViRuge
    have you finished learning the content for the FP1 one exam?
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Acrux)
    LelouchViRuge
    have you finished learning the content for the FP1 one exam?
    Yup, finished it about a week or two ago

    Wbu bud?
    Offline

    2
    ReputationRep:
    (Original post by LelouchViRuge)
    Yup, finished it about a week or two ago

    Wbu bud?
    That's Brilliant
    Unfortunately i'm about halfway through should i be worried
    Have you Completed all your other modules
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Acrux)
    That's Brilliant
    Unfortunately i'm about halfway through should i be worried
    Have you Completed all your other modules
    Lol, nope, I still have 3 modules to cover. I started taking A levels seriously and started working around early March.

    If you are not in my position, I'd say you are doing fine.
    Offline

    2
    ReputationRep:

    how do you get 2n(n+1) ?
    is there a rule i'm missing?
    what do you do when you get n instead of r in brackets?
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by Yua)

    how do you get 2n(n+1) ?
    is there a rule i'm missing?
    what do you do when you get n instead of r in brackets?
    Consider when  r = 0 then you have  2n+1 but you also sum up  2n+1 from  r = 1 to  n , so you sum up  (2n+1) (n+1) I asked this question earlier and Zacken answered.
    Offline

    3
    ReputationRep:
    (Original post by NotNotBatman)
    Consider when  r = 0 then you have  2n+1 but you also sum up  2n+1 from  r = 1 to  n , so you sum up  (2n+1) (n+1) I asked this question earlier and Zacken answered.
    I've also answered this on the first couple of posts on this thread. :lol: Pretty popular question.
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by aymanzayedmannan)
    I've also answered this on the first couple of posts on this thread. :lol: Pretty popular question.
    Oh yeah, I remember repping that, and it was a pretty popular question in my FM class last week. I don't recall seeing any questions of that type in the textbook and It's only been in an R paper.
    Offline

    14
    ReputationRep:
    (Original post by NotNotBatman)
    Oh yeah, I remember repping that, and it was a pretty popular question in my FM class last week. I don't recall seeing any questions of that type in the textbook and It's only been in an R paper.
    So make sure that you work through the R papers (and the appropriate questions on the IAL papers).
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by tiny hobbit)
    So make sure that you work through the R papers (and the appropriate questions on the IAL papers).
    Definitely, I'm going to do an IAL paper today in fact.
    Offline

    14
    ReputationRep:
    (Original post by NotNotBatman)
    Definitely, I'm going to do an IAL paper today in fact.
    Leave out the question on each F1 paper about alpha and beta.
    • Community Assistant
    Offline

    18
    ReputationRep:
    Community Assistant
    (Original post by tiny hobbit)
    Leave out the question on each F1 paper about alpha and beta.
    This was actually the only way my teacher has taught it, although I do know how to use other methods, so it should be fine.
    Offline

    14
    ReputationRep:
    (Original post by NotNotBatman)
    This was actually the only way my teacher has taught it, although I do know how to use other methods, so it should be fine.
    Has taught what? Are you doing IAL or "ordinary" A level?
    Offline

    8
    ReputationRep:
    I thought the edexcel FP1 book teaches Alpha and Beta way to work out the quadratic equation when given two complex roots?
    Or are you guys talking about something else
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.