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Re: MATH1131 help thread For b), the pmf has to sum to 1 when summed from k = 1 to n. The sum is telescopic (factoring out alpha). The sum is: alpha*(1- r^n). So alpha = 1/(1 – r^n). In terms of what values r can be, note p_k = alpha*r^(k-1) * (1-r). The pmf is such that p_k is non-negative...

Not to mention most HSC-style Conics Q's are just messy/tedious algebra.

Re: MATH1131 help thread Note it is clear that det(A) is a non-zero integer. (Non-zero 'cos it's invertible and integer as seen by the fact the determinant expansion contains all integer terms as A has only integer entries; one way to see this via Laplace expansion and an induction on the size...

Oh sorry. I thought you were referring to those who did 3U but not 4U.

This would only explain why a certain common subject must count to the ATAR. It doesn't explain why English must count to the ATAR.

Re: MATH1131 help thread Note that the first component of every vector in plane P is 2. So one way to guarantee we don't intersect with P is to make sure vectors in our new plane never have first component 2. And one way to do this is to make the first component of both direction vectors 0...

What if 4U students wanted to do Statistics too?

Re: MATH1131 help thread $\noindent 2. We can derive these similarly to the trig. ones. We can do it via either differentiation, or integration. Here it is done via integration. Let $x>0$ be fixed. Recall $\cosh t > 1$ for all $t>0$, so integrating this inequality from $0$ to $x$ gives $\sinh...

Re: MATH1131 help thread $\noindent 1. a) It's a line in $\mathbb{R}^2$. The curve is a function of two variables equated to a constant, something like how $x^2 + y^2 = 1$ is just a curve in 2D. So the tangent line is tangent to a curve in 2D, so the line is in 2-space.$ $\noindent b) Note...

Apparently HSC 3 Unit Physics (and Chemistry) is planning on being introduced soon by BOSTES. Will these be helpful in preparing students for real science, or are they likely to still be inadequate (haven't looked into them too closely)?

Median means middle when the array is sorted so the numbers are in ascending order (taking average of two middle I case of even no. of elements). E.g. What is the median of 2,6,2,8,7? When sorted, the numbers are 2,2,6,7,8, so the median is 6 (middle number). (...

It's not necessarily ordered from lowest to highest.

You accidentally wrote the general solution for sin rather than cos (when you did the 180n degrees at the end, that's the general solution to sin X = 0 rather than cos, which is what we needed).

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Assume a, b real. $\noindent Since the roots are real, this is equivalent to saying the discriminant is \emph{greater than or equal to} 0, so $a^2 - 8(b+3)\geq 0$. Thus $a^2 \geq 8(b+3)$. So to minimise $a^2+b^2$, whatever...

We'd need to know what it is to do the Q. I guess just assume it's 0 so that you can get practice by doing the Q.

$\noindent You can use either. One choice may be nicer depending on the signs of the coefficients involved.$ $\noindent If you want to memorise one form, you can memorise $a\cos \theta + b\sin \theta = R \cos \left(\theta - \varphi\right)$, where $R =\sqrt{a^2 + b^2}$ (modulus of the complex...

0/0, since numerator goes to ln(1) = 0.

Re: Multivariable Calculus They're integrating the derivative of a function, so they used FTC. (The 1/2 coming out due to reverse chain rule basically.) Note that (∂/∂v)(g(v+2t)) = g'(v+2t), where g' just means the derivative of the function g. E.g. if g(y) was cos(y), we'd have ∂/∂v...

You could probably also find a derivation online with the help of a search engine.

Yeah.