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Can anyone provide the working for below? Tysm

I'm always getting stuck with questions like these, not in standard textbooks i don't think, how can i improve on these, like any books out there or website?(and also if you can shed light on how to solve it plz...) Q: Determine all possible pairs of positive integers such that their sum is 2623...

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?

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...

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?

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?

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

Very stuck on b) and c)...

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...

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?

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...

please see photo

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

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...

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.

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...

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

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...

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...

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...