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Yes

The former is all real numbers, the latter is only the positive ones (sometimes including 0, so you may need to check the convention used by the author).

Try sketching the graph of the cubic. You should be able to do this once you've factorised it.

No

Once you've factorised the cubic, you should be able to sketch its graph and deduce from that the solution to the inequation.

Try and factorise the cubic.

Yes

Re: Help! Question from Maths in Focus Challenge Exercise 6 - Applications of Calculu Note that it asks for the percentage increase, so the answer will be sida1049's answer minus 100%. I.e. it is (P(10) – P_0)/(P_0), where P(10) is the population at time 10 (and then convert this to a...

Write x in terms of y. Square both sides as the first step. And make sure to state the correct domain.

Yeah

Sub. x = 0 into the expression.

Which question? I'll assume Q.12. For the induction step, assume that a k-set (i.e. a k-member set) has 2^k subsets for some particular non-negative integer k. Consider putting in one more element now (call it X) to have a (k+1)-set. What are the subsets of these? Well there are all the 2^k...

You should know the shapes of the graphs of some standard functions. For other ones, you can sketch them with the help of calculus to find turning points and so on. There is a ''curve-sketching recipe'' in some textbooks (like one of the Pender ones) that you can have a look at, or find online.

No mark in any one subject alone would "practically guarantee" 99.9+ ATAR. But you should probably try to get around mid-high 90's in English Standard if you want 99.9+ ATAR.

Practically 0 (even if it was 80 in English Advanced (talking about HSC Mark, not raw mark)).

It is theoretically possible to get 99.95 ATAR while doing Standard English. Just because no-one may have done it before (which I'm not sure if the case, I haven't investigated), it would not imply that it is impossible to get 99.95 ATAR while doing Standard English.

Yes

Correct!

No

Correct!