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In your example, the free radical on carbon #1 takes a hydrogen from carbon #5, turning carbon 1 from CH2. to CH3 and turning carbon 2 from CH2 to CH.

The data provided here are deeply dodgy. If the pH of the acetic acid solution is 3.8 without any base having been added, then the acetic acid solution has a concentration of something like 0.002 mol/L.

Another derivation: Solving the equations of the circle (x - x_0)^2 + (y - y_0)^2 = r^2 and the line Ax + By + C = 0 simultaneously should yield a quadratic equation, which has only one solution if the line is a tangent to the circle. By setting the discriminant to zero, the result should...

For the last part, it proves that the midpoint of the hypoteneuse of a right-angled triangle is equidistant from all three vertices.

The perpendicular distance formula gives the shortest distance from a point P\left(x_0,\ \!y_0\right) to the line Ax + By + C = 0, which is d_{\perp} = \cfrac{\left|Ax_0 + By_0 + C\right|}{\sqrt{A^2 + B^2}} It was a part of the 2 unit syllabus until the change in 2020. Now the only way is to...

Firstly, I agree that using your own ideas in more than one response is fine, so long as they are relevant to the question to which you are responding. Secondly, even if a single marker does see both responses, what are the chances that they remember that it is from the same student? Yes, the...

The headings identify the courses for each paper, so you could take "Standard 2 Maths", "Advanced Maths", etc., out of each separate entry in the lists. That would save quite a few characters.

You had P( z < 3.125). If z is less than 3.125 then it can't be 3.13 to 2 decimal places, is my point.

Being picky about it, Is there any number that is less than 3.125 that rounds to 3.13 (2 dec. pl.)? Alternatively, one could argue that the answer is 0.99910 < P < 0.99913 and so P must be 0.9991 (4 sig. fig.)

Grove (Maths in Focus), Yr 11 Advanced, ,Chapter 10 Cambridge Yr 11 (Advanced), Chapter 11 Cambridge Year 11 (Extension 1), Chapter 13

For Module 8 spectroscopy, there are only three or four isotopic distributions that matter: Cl and Br as 3:1 and 1:1, as noted above C being mostly 12C but some 13C matters for mass spec - to explain the peaks at m / z = M + 1, where M is the molar mass of the parent ion 13C NMR - to explain...

All of the content you have quoted appears in various texts and trial papers, though without the detail. The last image may sound unfamiliar but I'd bet you've done examples of it by drawing a tree diagram for selections without replacement. Suppose you toss a bag has 6 red balls and 4 green...

Those apply to a binomial distribution, and you are correct that they will work for the example that I gave (as it is binomial). However, I am talking about a method applicable to any discrete probability distribution, and all of this was covered in Year 11 Advanced content, and is extended to...

Suppose you toss a fair coin three times. You get a probability distribution where P(0 heads) = 1 / 8 P(1 head) = 3 / 8 P(2 heads) = 3 / 8 P(3 heads) = 1 / 8 E(X) = add up X values times their probabilities: E(X) = 0 \times \cfrac{1}{8} + 1 \times \cfrac{3}{8} + 2 \times \cfrac{3}{8} + 3...

The first one is the standard formula used to find the variance: Var(X) = E(X2) - [E(X)]2 ...but rearranged to make E(X2) the subject. The others are results you could be asked to prove, but should still know... E(aX + b) = aE(X) + b which means if I take a set of data, multiple each data...

Definitely need to be aware that 35Cl : 37Cl is approximately 3 : 1 and that 79Br : 81Br is approximately 1:1.

The curves y = f(x) and y = g(x) meet only when f(x) = g(x), or f(x) - g(x) = 0. We know this equation is a degree four polynomial as the degree of f(x) is 4 and the degree of g(x) is 2. We also know that this equation has only two solutions (as two points of contact) and in each case the...

\begin{align*} \text{A first order DE is linear in $y$ if it can be written as} \qquad f(x) \times \cfrac{dy}{dx} + g(x) \times y &= h(x) \qquad \text{where $f(x)$, $g(x)$, and $h(x)$ are not restricted as to degree} \\ \\ \text{Option (A) can be written as} \qquad 1 \times \cfrac{dy}{dx} + 0...

I have uploaded a version where the questions match the solutions to the resources.

There are two versions of the North Sydney Girls High School 2023 Maths Extension 2 paper circulating, with similar questions. The version presented here is the one that matches with the solutions attached to it. I don't know which version was the one actually used by the school, and which is...