Search results

If it helps, the answers on the marking guide are: C B C A D A D C B D A A B C A D C D B B

Thanks for your thoughts. The integral you mention is meaningless, I agree... there is a vertical asymptote somewhere near x \approx 1.75 and integration across a discontinuity is meaningless. It is still clear, though, that the function is positive for all x > e^{-1} \approx 0.368, so a...

A full house (like AAAKK) is neither a pair nor a three-of-a-kind - the terms describing hands do not overlap

It's from the 2023 Western Maths paper

From the area: \begin{align*} A &= \cfrac{1}{2} r^2 \theta \\ 49 &= \cfrac{1}{2} r^2 \theta \\ \theta &= \cfrac{98}{r^2} \end{align*} The perimeter is then \begin{align*} P &= r + r + r\theta \\ &= 2r + r \times \cfrac{98}{r^2} \\ &= 2r + \cfrac{98}{r} \\ &= 2r + 98r^{-1} \end{align*}...

What do you do when you encounter a question during an exam, and the question is flawed and you realise it is flawed? For example, I have just come across the following question: The solutions take the usual approach to a separable DE to get y = k(x + 1)(x - 1) where k = e^C and C is an...

This is definitely (B), an addition polymerisation: n H2C=CRR' ----> -(-H2C-CRR'-)n- with R = CH3 and R'= COOCH3

You are correct, the answer should be V = \pi\int_{\frac{\pi}{4}}^{\frac{\pi}{3}} \tan^2{y} - y^2\ \!dy

As a straight binomial probability, P(X < 9) and P(X \le 8) are the same thing because X \in \{0,\,1,\,2,\,...\,n\}. In taking a normal approximation, a discrete distribution is approximated by a continuous one, which is why the continuity correction is needed. Suppose you toss a fair coin...

Solutions from last year accepted answers both with and without the continuity correction. In this case, though the result changes by a significant amount by the way the solution is constructed, which to me shows that including the correction is the better answer. I wonder, in a case like...

Not Standard 1 - that would be an over-reaction!

Don't the n = 2 AM-GM cases require ab, bc, etc all to be positive? Here, at least one of a, b, c, or d is negative.

It's an application of experimental probability

I agree. It should be: P(X < 9) = P(X \le 8) \approx P(X < 8.5) \text{ after continuity correction}

True, but it took me a while to figure out why your working was valid... it looks like you multiplied by \omega but in fact you didn't... I thought others might have not been sure. :)

It would be quicker to do this as: \begin{align*} \omega^n - 1 &= (\omega - 1)\left(\omega^{n-1} + \omega^{n-2} + .... + \omega + 1\right) \\ \cfrac{\omega^n - 1}{\omega - 1} &= \omega^{n-1} + \omega^{n-2} + .... + \omega + 1 \qquad \text{also provable by summing the GP on the RHS} \\...

A saturated solution of anything involves a solubility equilibrium. An unsaturated solution is not an equilibrium system. It may be difficult to achieve a saturated solution in a specific case. Sodium hydroxide has a very high solubility of around 1 kg/L at 25 oC (according to Wikipedia, and...

Many small droplets of oil / grease, enclosed as micelles and moving through an aqueous phase is more disordered than one big chunk of oil / grease stuck to a surface. Just like an ionic solid dissolving, the process may be enthalpically favourable or disfavourable, but it is entropically...

Re saponification, entropy is also contributing to the grease breaking away from the surface and into micelles / emulsifying in water.

Tywebb posted the questions for the Normanhurst Boys MX1 Trial at https://boredofstudies.org/resources/normanhurst-boys-hs-2023-ext-1-trial.20268/ Here are the solutions to go with it