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Hi all I am after as many 2020 trial papers (actual papers sat by students in 2020) with schemes/solutions that I can get a hold of, 2U,3U and 4U. If I get enough I will set up a grid where you pick off particular topics in prep for the HSC and to assist others in the future. Are they already...

Find all n and k such that (n choose k) is the sum of (13 choose 6) and (13 choose 5).

Suppose that PQR is an equilateral triangle with an interior point X. Let angle PXR = s and angle QXR = t. Find (in terms of s and t) the three angles of any triangle with side lengths equal to PX, QX and RX.

Let x>0.. x^2=x+x+\dots+x \qquad where the sum on the right has x terms. For example if x=4 we have 4^2=4+4+4+4. Differentiating \qquad x^2=x+x+\dots+x \qquad we have 2x=1+1+\dots 1 \qquad where the sum on the right still has x terms. Thus 2x=x and hence 2=1.

Is it possible for a function to be defined over the entire real line and to have only one point on the graph where a tangent exists (corrected)

Is it possible for a function to be defined over the entire real line and yet to have no tangents to its graph?

Here's an odd one! Define f to be the piecemeal function f(x)=x^2 for x>=0 and f(x) =-(x^2) for x<=0 The graph of f is then sort of like x^3 Does f have a point of inflection at the origin?

Quite some time ago there was a question in the two unit paper that involved AP's and stacking logs? It became famous due to the confusion that was generated over the word "log". Does anyone know the year?? Thanks

Here's a strange one! a) A 4 letter word is to be constructed using the 8 characters EEEEEEGG. In how many ways can this be done? b) How many of the words in a) begin and end with an E? c) What is the probability that a 4 letter word constructed from the 8 characters EEEEEEGG begins...

Here is a spooky little question for everyone preparing for the trials. In how many different ways can six identical black marbles and six idententical white marbles be arranged in a circle? Think carefully abvout your answer

Prove that if z ranges over a fixed circle in the complex plane (not containing 0) then the locus of 1/z is also a circle

Prove that y=x^3 is an increasing function over the entire real line.