HSC Stuff > HSC Mathematics Extension 2
4 unit maths questions
deeian:
--- Quote from: deeian on March 01, 2016, 09:49:55 am ---how do you sketch h(root x) for question 5?
--- End quote ---
i'm actually a year 11 student starting 4 unit maths early and i haven't learnt most of 3 unit so i may need extra guidance.
Deeian
jamonwindeyer:
--- Quote from: deeian on March 01, 2016, 09:49:55 am ---how do you sketch h(root x) for question 5?
--- End quote ---
Let's break it down. For x<0, the function will have no value, since the square root of a negative number has no real value in the real domain. So we can disregard that completely.
Now, the current function has roots at x=0, x=2, x=4, x=6 etc. This will remain true, however, it is now the square root of x which must equal these values! So:
So the intercepts will be in these locations. Essentially, what is happening here is that the triangular wave is being stretched out more and more with larger values of x. The further up you go, the further apart the intercepts. This is easiest to see if you look at the graph over a large domain.
To get a clue as to the shape itself, consider x=0 to x=1. In this region, we can model the behaviour of the curve with the function:
Since in the original, the function in this domain was equivalent to y=x. What this (and probably plotting a few points would help if you are unsure) tells us is that while the triangular shape is still present, it is now slightly curved. The square root sign, beyond stretching out the waveform, is also adding the curved shape that we see in the graph of y equals the square root of x.
The graph looks like this. This is an extremely difficult question, although I suspect there might be some 4 Unit processes that eliminate the more intuitive approach I have taken. I am unsure exactly what you've covered, so I stuck with intuition ;D
jakesilove:
--- Quote from: jamonwindeyer on March 01, 2016, 10:49:27 am ---Let's break it down. For x<0, the function will have no value, since the square root of a negative number has no real value in the real domain. So we can disregard that completely.
Now, the current function has roots at x=0, x=2, x=4, x=6 etc. This will remain true, however, it is now the square root of x which must equal these values! So:
So the intercepts will be in these locations. Essentially, what is happening here is that the triangular wave is being stretched out more and more with larger values of x. The further up you go, the further apart the intercepts. This is easiest to see if you look at the graph over a large domain.
To get a clue as to the shape itself, consider x=0 to x=1. In this region, we can model the behaviour of the curve with the function:
Since in the original, the function in this domain was equivalent to y=x. What this (and probably plotting a few points would help if you are unsure) tells us is that while the triangular shape is still present, it is now slightly curved. The square root sign, beyond stretching out the waveform, is also adding the curved shape that we see in the graph of y equals the square root of x.
The graph looks like this. This is an extremely difficult question, although I suspect there might be some 4 Unit processes that eliminate the more intuitive approach I have taken. I am unsure exactly what you've covered, so I stuck with intuition ;D
(Image removed from quote.)
--- End quote ---
Just wanted to quickly jump in here to throw my support behind Jamon: 4U Graph sketching is literally all about intuition. The method is always the same: Look for sensible points to test, and sensible limits to take, in order to get an idea of what the new graph should look like! There isn't any "real" maths going on: just pure intuition. Plotting points is always the easiest way to get a general idea of what the graph should look like. If you're not sure what to do, just transform some points and make something up.
Jake
jamonwindeyer:
--- Quote from: deeian on March 01, 2016, 09:56:21 am ---i'm actually a year 11 student starting 4 unit maths early and i haven't learnt most of 3 unit so i may need extra guidance.
Deeian
--- End quote ---
Extension 2 is an extremely difficult course, I'd argue one of the hardest Secondary subjects in Australia in terms of the level of thinking required. You absolutely MUST know the more basic content first. Doing 4 Unit, half a term into Year 11 is bloody difficult, you are a trooper! Now don't get me wrong, we are so super happy helping you, but if you are struggling with the majority of questions in this paper then it is a sign that the paper is beyond what you can handle for the moment.
I'd strongly recommend that you get a grasp of 2/3 unit content first. Try some Extension 1 papers to get your head around the concepts, before you tackle 4 Unit Difficulty questions. I consider these difficult as a university student, so of course they are going to be hard for you.
Again, totally not discouraging you. Keep asking questions and getting help! I'm just looking out for your best interests, and if you need complete guidance through a 4 Unit Paper, it is a sign you should probably tackle some of the easier stuff first. It is nay impossible to explain 4 Unit questions properly unless you have an extremely solid knowledge of 2 Unit and Extension 1.
Could I ask why you decided to tackle 4U early? Surely your school isn't mandating it? :D
Happy Physics Land:
--- Quote from: jamonwindeyer on March 01, 2016, 10:57:28 am ---Extension 2 is an extremely difficult course, I'd argue one of the hardest Secondary subjects in Australia in terms of the level of thinking required. You absolutely MUST know the more basic content first. Doing 4 Unit, half a term into Year 11 is bloody difficult, you are a trooper! Now don't get me wrong, we are so super happy helping you, but if you are struggling with the majority of questions in this paper then it is a sign that the paper is beyond what you can handle for the moment.
I'd strongly recommend that you get a grasp of 2/3 unit content first. Try some Extension 1 papers to get your head around the concepts, before you tackle 4 Unit Difficulty questions. I consider these difficult as a university student, so of course they are going to be hard for you.
Again, totally not discouraging you. Keep asking questions and getting help! I'm just looking out for your best interests, and if you need complete guidance through a 4 Unit Paper, it is a sign you should probably tackle some of the easier stuff first. It is nay impossible to explain 4 Unit questions properly unless you have an extremely solid knowledge of 2 Unit and Extension 1.
Could I ask why you decided to tackle 4U early? Surely your school isn't mandating it? :D
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Yeah umm I guess I can solve your curiosity jamon. In Ngo and Sons, which is a tutoring facility, they have accelerated mathematics classes for top-end students. In year 10 they will be sitting 2unit and 3unit HSC exams so that by the time of year 12 they would have done it twice already and this ensures a higher band 6 success rate. Some especially talented year 10 students would even sit the 4u HSC exam to prepare for exam in year 12. So I guess deeian is in the same process of learning 4unit maths in year 11 and sitting the HSC exam for 4u so that he would have done the exam once before the official HSC 4u exam in year 12.
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