Dear Uncle Colin, I have to prove that, if $a > b \ge 2$, then $ab > a + b$. I can see it must be true, but I can’t prove it! Any ideas? Questioning Everything Done Hi, QED, and thanks for your message! There are several ways to go

Ask Uncle Colin: Greatest Common Divisor (with Polynomials)

Dear Uncle Colin, I have to find the greatest common divisor of $x^4 - 5x^3 + 8x^2 - 10x + 12$ and $x^4 + x^2 - 2$. How do I go about that? - Extremely Unhappy, Clueless Learner In Distress Hi, EUCLID, and thanks for your message! Before we try

Dear Uncle Colin, I’m told that $f(x) = \frac{5x-7}{(x-1)(x-2)}, x\ne 1, x\ne 2$, and need to express it in partial fractions. My usual method would be to write it as $\frac{A}{x-1} + \frac{B}{x-2}$, multiply by $(x-1)(x-2)$ and substitute $x=1$ and $x=2$ to find $A$ and $B$ - but the definition

Ask Uncle Colin: An Exponential Limit

Dear Uncle Colin, I need to work out the limit of $\frac{2^{3x} - 1}{3^{2x}-1}$ as $x \to 0$, and I don’t have any ideas at all. Do you? - Fractions Rotten, Exponents Generally Excellent Hi, FREGE, and thanks for your message! There are a couple of ways to approach this:

Ask Uncle Colin: How many draws?

Dear Uncle Colin, I’m trying to figure out how many possible draws there are for the Champions’ League quarter-finals. There are eight teams involved, and let’s assume first leg home advantage doesn’t matter (so A vs B is the same as B vs A) and there’s no restriction on which

Dear Uncle Colin, I’m told that 70% of the aircraft that go missing in a certain country are subsequently rediscovered. Of those that are recovered, 60% have an emergency locator, and 90% of those that aren’t recovered, don’t have a locator. Supposing an aircraft has disappeared, what’s the probability it

Dear Uncle Colin, I’m given that a curve has equation $y = ax^3 + bx^2 + cx + 1$. It has a turning point at $\left( -1, \frac{11}{3} \right)$ and an inflexion point when $x=2$. How do I find the missing constants? - I’m Not Feeling Like Evaluating Constants, Thanks

Ask Uncle Colin: A Partition Enigma

Dear Uncle Colin, In reading Sir Dermot Turing’s XY&Z, he states that the number of species of cycle is 101 - and after a bit of thought, I figured out that that’s the number of partitions of the number 13. However, I couldn’t work out how to get 101! Can

Dear Uncle Colin, I have a probability question that involves a weird place where every family has three children, and every child is either a girl or a boy. 50-50. Independent of each other. If I take a random family, and choose at random one of the children, I have

Ask Uncle Colin: The Timeless SUVAT Equation

Dear Uncle Colin, I can derive the timeless SUVAT equation $v^2 = u^2 + 2as$, but I can’t intuitively see where it comes from. Any clues? - Everyone Needs Explanations, Really Get Yours Hi, ENERGY, and thanks for your message! This is one that I never really picked up on