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  1. M

    A general question for limits

    Was just trying out a few things with first principles and got stuck at one point: \lim_{x\to 0} \cfrac{\sqrt{x^2+x^3}}{x} can someone help?
  2. M

    help for proofs

    I am fine for the first part, not sure how to do the HENCE part...it could have been easily done with letting f(x)=e^x-1-a^2 and showing its always positive...but the HENCE...
  3. M

    Implicit Differentiation

    I saw on page 591 in Cambridge 3unit year 12 textbook for example 25, they used implicit differentiation to solve the question, is this examinable under the new syllabus?
  4. M

    Is implicit differentiation still in the syllabus?

    I saw on page 591 in Cambridge for example 25, they used implicit differentiation to solve the question, is this examinable under the new syllabus?
  5. M


    Does anyone have any vectors worksheet they can share, i don't have anything to practice with other than the textbook(which i guess is the only thing most of us has at the moment...), so was wondering if people from selective schools can share some useful harder questions
  6. M

    Help with complex

    Very stuck on b) and c)...
  7. M

    help with problem solving

    Trying to find help with the following 2 questions: 1) Terry has a solid shape that has four triangular faces. Three of these faces are at right angles to each other, while the fourth face has side lengths 11, 20 and 21. What is the...
  8. M

    Logic - negation

    Just wonering if we want to find the negation of an implication, is it wrong to add in the word "IF", and if so why? For example, the negation of "If A, then B" should be "A and not B", but why can't we say "IF A and not B" or are these both correct?
  9. M

    pigeon hole principle help!

    Consider a 3cmX3cm grid, made of nine 1X1cm squares. If you are to put a stamp in the squares, what is the maximum number of stamps you can make without having 3 stamps diagonally, vertically or horizontally? Obviously the answer is 6 by intuition, but how can you use pigeon hole principle to...
  10. M

    Help with Network/minimum cut theorem

    please see photo
  11. M

    help on abstract perms and combs

    Given 50 cards with the integers 1, 2, 3, ... 50 printed on them, how many ways are there to select 9 distinct cards, such that no two cards have consecutive numbers printed on them? Detailed explanation appreciated! Thanks
  12. M

    Perms and combs help

    Twelve people sit around two tables labelled A(5 seats) and B(7 seats), how many ways can this be done. The solution says 12C5*4!*6! which i understand works. I was thinking doing 1*11*10*9*8* 1*6*5*4*3*2*1 which gives a different answer. My logic is, the first person that sits down on table A...
  13. M

    pls help

    Question: Sugar is dissolved in water in the ratio 1:3 to form sugar syrup. This sugar syrup is further diluted with the addition of water so that the ratio of the sugar syrup to the additional water is 5:7. FInd the ratio of sugar to water in the final mixture.
  14. M

    AMC practice

    Hi can anyone explain the following? Two identical coins are placed one inside and one outside a thin circular wire, which has twice the diameter of each coin. Each coin is rolled, without slipping, around the wire until it returns to its starting point. If the direction of rotation does not...
  15. M

    parametrics question

    Hi, Stuck on this question: convert x=tanx-sinx and y=tanx+sinx to cartesian form. Thanks!
  16. M

    sketching reciprocal function

    Hi, 1) Just wondering what happens when you reciprocate a vertical asymptote. For example if you are given the graph y=1/x and asked to reciprocate it, will the origin be an open circle or closed circle. 2) If you are NOT given the equation of y=1/x but given something that looks similar...
  17. M

    BOS trial

    Was stuck on a question: Sketch the locus defined by arg(z^2+z)=pi/3, stating its equation. Obviously this will turn into the hyperbola with the positive branch, but how do we find the equation? Also, anyone know when the bored of studies trial will be held this year, of is it held already...
  18. M

    function notation

    Hi, A bit confused with the use of the notation y=f(x). If we have the circle x^2+y^2=1, we can obviously rearrange and make y the subject which gives y=+-(1-x^2)^0.5. Is it wrong to write f(x)=+-(1-x^2)^0.5 since this is not a function hence we can't use f(x)? If so, does that also mean...
  19. M

    integration by substitution

    Consider the integral of sin(2x+1). I note the normal method would be to let u=2x+1(if you are asked to use substitution). But can someone explain the following method: integral (sin(2x+1)dx)=integral(sin(2x+1) d(2x+1)/2)?
  20. M

    BOS 2017 paper

    Does anyone know if BOS is making a 2017 paper and if so when? Would like to sit it.