Are there any resources for harder 3 unit? Also, 2 sequences questions (1 Viewer)

[sadpwner]

Inequalities give me the utter most cancer. The same can said to a lesser degree for induction, perms and combs and sequences. Anyway, are there any good resources for these topics?

Anyway, I simply can't do any of part ii. Can any1 help me out

 

[RealiseNothing]

Break it into:



We know , so using this 3 times gets the result.

 

[RealiseNothing]

For the second one, use the substitutions:







Then after simplifying the LHS we have:



But from the first inequality, we know that the thing in brackets above is greater than 6. So the result follows.

 

[sadpwner]

For the second one, use the substitutions:







Then after simplifying the LHS we have:



But from the first inequality, we know that the thing in brackets above is greater than 6. So the result follows.

How did you figure out these substitutions were required? It's not obvious at all.

 

[braintic]

How did you figure out these substitutions were required? It's not obvious at all.

You can get those substitutions by letting a+b=x, b+c=y and a+c=z, then solving simultaneously for a, b and c.

 

[sadpwner]

You can get those substitutions by letting a+b=x, b+c=y and a+c=z, then solving simultaneously for a, b and c.

What is the supposed difficulty of this question. It's only worth 2 marks, which I find absurd. I got it now, but I don't see how these steps are obvious. What gave you the idea to substitute this in then use simultaneous then sub it back into the main eq?

 

[simpleetal]

What is the supposed difficulty of this question. It's only worth 2 marks, which I find absurd. I got it now, but I don't see how these steps are obvious. What gave you the idea to substitute this in then use simultaneous then sub it back into the main eq?

If this question was to come up in a HSC 4u exam, then it would usually appear as the later parts of question 14 (paper of average difficulty), or the early parts of question 15 (if the paper is easy that year).