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  1. 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.
  2. 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...
  3. M

    parametrics question

    Hi, Stuck on this question: convert x=tanx-sinx and y=tanx+sinx to cartesian form. Thanks!
  4. 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...
  5. 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...
  6. 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...
  7. 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)?
  8. M

    BOS 2017 paper

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

    question from terry lee volume

    Was reading volumes by terry lee and it was a trapezoidal solid/frustum and we had to find the volume using similar solids. Mr Lee's answer claimed that the height (h) of the solid is linearly dependent to x which measures the length of the typical slice/cross-section. Is this valid? i mean we...
  10. M

    Indices and Logarithms

    hi, is it safe to assume index laws and logarithmic laws only apply(apply without need to confirm other things...) for positive bases? E.g. for equations like log(base x) 4=2, we only get the answer of 2 and not negative 2 right?
  11. M

    test question

    Ships A and B leave port P at the same time. Ship A sails 4km on a bearing of 40 degrees , then a further 6km on a bearing of 155 degrees to reach destination D. Ship B sails directly from P to the the destination D. In which direction does Ship B sail? I solved this in two ways (sine...
  12. M


    Is the answer to x^(2/3)=4 a) 8 b) 8 or -8?
  13. M

    2014 AMC help

    Hi guys, for those who sat the 2014 AMC, could someone please enlighten me on the last 2 questions. Especially the last question...i dont see any pattern for the primes...
  14. M

    help please

    In circle geometry, when we say an angle is standing on an arc, do we mean it stands on the major arc or the minor arc?
  15. M

    De Moivre's theorem

    I'm confused...MUST you use induction to prove De Moivre's theorem(by the way how do you prove De moivre's theorem for negative integers?)? I mean, isnt zw=r_1 r_2 cis(theta_1+theta_2)? then isnt it obvious that z^n=(r^n)cis(n theta)? so why induction?
  16. M

    A complex number question

    How do one sketch 0< arg(z(1+i)) < pi/2
  17. M

    help please

    Please help
  18. M


    1. Where can you buy 4unit textbook by someone called komoroni 2. How do you sketch y=x/((e^X) -1) without lhopital
  19. M

    2013 trials

    Just wondering if anyone know when the release date for cssa and independent papers for 3/4 unit. Which one tend to be harder?
  20. M

    integration query

    Given I_n=\int_{e^-1}^{1} (1+lnx)^n dx = 1-n(I_(n-1)) and J_n=\int_{e^-1}^{1} (lnx)(1+lnx)^n dx for n=0,1,2,3,... show that J_n=1-(n+2)I_n for n=0,1,2,3,... Sorry for my sloppy latex input PS: is there a way to input latex on this forum?