HSC Stuff > HSC Mathematics Extension 2
4U Maths Question Thread
shekhar.patel:
--- Quote from: fun_jirachi on February 12, 2020, 09:59:17 pm ---Hey there!
One of the ideas that was stressed to me as a student was 'look at what you're working towards'. It's become a really handy hint - note that in the result, the logarithm does not use 'n', rather, it uses '1/n'. Since we know the integral of a linear function is a logarithm, and we can directly see the connection between the given result and the result we're working towards (particularly in the middle term), it makes sense to try out 1/n as an upper limit. As a result of this, this means the right hand side will become 1/n, meaning everything will be multiplied by n, leaving a power on the logarithm. This kind of foresight often reduces the amount of work that needs to be done trialling different limits amongst other things - attempt to use it wherever you can.
Hope this helps :)
--- End quote ---
Ok thanks.
RuiAce:
--- Quote from: milie10 on February 15, 2020, 01:11:59 am ---Hi!
Another vector question I'm struggling with:
"Find the shortest distance between the line through the points (1, 3, 1) and (1, 5, -1) and the line through the points (0, 2, 1) and (1, 2, -3)"
how do you find the equations using vector methods? what would the subsequent steps be?
Thanks!!!
--- End quote ---
This is actually an extremely demanding question given the scope of MX2. The shortest distance between two lines usually requires knowledge of planes in 3D space or the cross product, both of which aren’t in the syllabus. What is the source of this question?
milie10:
--- Quote from: RuiAce on February 16, 2020, 05:49:00 pm ---This is actually an extremely demanding question given the scope of MX2. The shortest distance between two lines usually requires knowledge of planes in 3D space or the cross product, both of which aren’t in the syllabus. What is the source of this question?
--- End quote ---
I think my coaching taught us some out of syllabus content for vectors- they said that for completeness of this topic, learning the cross product is necessary. I'd still love to know how it would be done though, but I'm not too fussed about it since it won't be tested :)
Also, could someone explain this proofs question: Q10d from the cambridge textbook? I've forgotten how roots work- am I meant to use the sum and product of roots?
thanks so much :D
fun_jirachi:
I'll leave the vector question for a more competent user while I continue getting accustomed to them myself, but I'll answer your second question :)
There are a few ways to prove to yourself this is true:
- You can prove to yourself that they are one and the same by doing the sum of roots and product of roots of both those quadratics
- You can also consider the roots as per the quadratic equation for each quadratic, inverting them and rationalising the denominator
- Also, consider what happens when you have \(f(\alpha)\) in the first quadratic, and factor out \(\alpha ^2\), and vice versa
Hopefully this will start to make sense! :)
milie10:
--- Quote from: fun_jirachi on February 17, 2020, 09:26:26 pm ---I'll leave the vector question for a more competent user while I continue getting accustomed to them myself, but I'll answer your second question :)
There are a few ways to prove to yourself this is true:
- You can prove to yourself that they are one and the same by doing the sum of roots and product of roots of both those quadratics
- You can also consider the roots as per the quadratic equation for each quadratic, inverting them and rationalising the denominator
- Also, consider what happens when you have \(f(\alpha)\) in the first quadratic, and factor out \(\alpha ^2\), and vice versa
Hopefully this will start to make sense! :)
--- End quote ---
Thank you so much!!
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