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http://advancedmathematics.com.au/Resources/2020%20Ext1.pdf

Have a look at Example 4 too. That is also not a pdf. \text{Example 4} \text{For a particular Infant Welfare Centre the probability density function of the age of the children (}x\text{ years) brought to the centre is given by:} f(x) = \begin{cases}\frac{4}{5}x(2-x),&0\le x\le2...

Terry Lee solutions: http://advancedmathematics.com.au/Resources/2020%20Ext2.pdf

If this was an exam question it would be completely invalid. An exam might ask you to verify that a function qualifies as a probability density function, in which case you show that it satisfies both conditions. The authors of this textbook thought that it was an example of a probability...

That means that the function is NOT a probability density function. If you find P(X ≤ 0.1) then you get a negative answer. So it is NOT a probability. You can turn it into a probability density function so that it satisfies both conditions by replacing -3(x-1)2+2 with -6(x-0.5)2+1.5.

OK. Here is hint 4: \text{For a function }f(x)\text{ to be a probability density function:} \bullet f(x)\ge0\text{ for all values of }x \bullet\int_{-\infty}^\infty f(x)\ dx=1,\text{ i.e., the area enclosed by the graph }y=f(x)\text{ and the }x\text{-axis is equal to 1.} Do you think these...

There is something wrong with this example from New Senior Mathematics Advanced on pages 561-562. Can you see what it is? (Hint 1: there is nothing wrong with the calculation.) \text{Example 2} \text{A particular continuous random variable has the following probability density function:}...

This is finally coming out October 23rd. This is on MANSW's website now: This is 3 days before the HSC exam. So you'll have 3 days to work through the whole book.

Howard seems to be updating the 1000 questions quite frequently. Here is version 4: http://howardmathematics.com/wp-content/uploads/2020/09/1000-Extension-2-Revision-Questions-v4-September-10-2020.pdf

Version 3 for 1000 questions: http://howardmathematics.com/wp-content/uploads/2020/09/1000-Extension-2-Revision-Questions-v3-September-8-2020.pdf

Both Howard books were updated yesterday: Text: http://howardmathematics.com/wp-content/uploads/2020/09/HSC-Mathematics-Extension-2-Textbook-v6-2020-09-06-1.pdf (version 6) 1000 questions...

Steve Howard has now finished the 1000 Extension 2 Revision Questions: http://howardmathematics.com/wp-content/uploads/2020/09/1000-Extension-2-Revision-Questions-Exercises-September-12-2020.pdf

There are also the older leaving certificate papers which go back to 1916. For example http://4unitmaths.com/1916.pdf That's pretty good considering that this is effectively a year 11 exam (there was no year 12 till 1967). Before that there were the university entrance exams dating back to to...

200 added - 150 to go: http://howardmathematics.com/wp-content/uploads/2020/08/1000-Extension-2-Revision-Questions-Exercises-1-to-8-August-12-2020.pdf

150 added (for chapter 7) - 350 to go: http://howardmathematics.com/wp-content/uploads/2020/07/1000-Extension-2-Revision-Questions-Exercises-1-to-7-July-29-2020.pdf

Another 100 have been added (for Ch.6): http://howardmathematics.com/wp-content/uploads/2020/07/1000-Extension-2-Revision-Questions-inc-Ch-1-6-2020-7-17.pdf so 500 to go.

Next 200 revision questions from Steve Howard are available now at http://howardmathematics.com/wp-content/uploads/2020/07/1000-Extension-2-Revision-Questions-inc-Ch-1-5-2020-7-11.pdf This adds to the previous 200. So now there are 400 and counting. Eventually it will be 1000. Check...

Now there is a new one by Steve Howard: This is a digital textbook which was up to version 5 on 17.6.2020. It may get updated again in the future too so sometimes check the website howardmathematics.com for updates. I think the first complete version was on 11.6.2020 (version 4). Prior to...

Chapter 1 Development solutions and Chapter Review Exercise 1H solutions are now available: 1A Q10, 11, 12, 13, 14, 15, 16 1B Q5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 1C Q6, 7, 8, 9, 10, 11, 12, 13, 14 1D Q11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 1E Q7, 8, 9, 10, 11, 12, 13, 14, 15...

See thread https://community.boredofstudies.org/threads/new-advice-from-bill-pender-if-you-use-cambridge.390412/ to download the file. It is applicable to Ext. 1 too but more appropriate in that thread.