Mathematics Question Thread

[RuiAce]

What exactly do you mean by 'illegal'?

If it means doing something that is mathematically wrong like dividing by zero on both sides on a equation, or assuming what you are trying to prove, then that's a big no no.

However if you're using theorems, results and formulas that are outside of the syllabus and not taught covered in school, that's a big yes as it shows you have the initiative to learn more than you're expected to.

Not necessarily in the HSC. Concepts such as L'Hopital's rule that used to get abused by students are now strictly forbidden and subject to being penalised.

[anotherworld2b]

I apologize for not being clear about what I  meant by 'illegal'

I was referring to my habit of constantly doing something that is mathematically wrong/not possible.
How do you know what you can and can not do in regards to the trig identities?
Are there particular rules that must be followed when proving trig identities?

[RuiAce]

I apologize for not being clear about what I  meant by 'illegal'

I was referring to my habit of constantly doing something that is mathematically wrong/not possible.
How do you know what you can and can not do in regards to the trig identities?
Are there particular rules that must be followed when proving trig identities?

The rule that everything is not a mathematical mistake or misuse in assumption? Show me an example of where you messed up and did something "illegal" for a better idea.

[wyzard]

Not necessarily in the HSC. Concepts such as L'Hopital's rule that used to get abused by students are now strictly forbidden and subject to being penalised.

Damn didn't realize the use L'Hopital rule got caught on, it's such a useful theorem to use though Yeah I agree with you though, be mindful of what concepts you can't use too.

I apologize for not being clear about what I  meant by 'illegal'

I was referring to my habit of constantly doing something that is mathematically wrong/not possible.
How do you know what you can and can not do in regards to the trig identities?
Are there particular rules that must be followed when proving trig identities?

Unfortunately there's no easy way out of this, the process of learning mathematics is by making mistakes, and learning from them. So the more mistake you make, the better. It's best learned by experience, just jump in there, make many silly "illegal" moves, and study why you can't do that. Over time, you'll become more sensitive to the mistake and you'll avoid them.

[RuiAce]

Damn didn't realize the use L'Hopital rule got caught on, it's such a useful theorem to use though Yeah I agree with you though, be mindful of what concepts you can't use too.

Yep

One of the more minor reasons as to why I wanted to do uni maths already was just to abuse the crap out of L'H

But the HSC is just the way it is. Always try to use what's in the syllabuses. I think one of the most lenient things they do is allow implicit differentiation in Ext 1...when it's really just properly taught in Ext 2.

[jamonwindeyer]

Yep

One of the more minor reasons as to why I wanted to do uni maths already was just to abuse the crap out of L'H

But the HSC is just the way it is. Always try to use what's in the syllabuses. I think one of the most lenient things they do is allow implicit differentiation in Ext 1...when it's really just properly taught in Ext 2.

You'll get marks for the correct answer (if they are available based on the criteria) but not the working  you're totally right, stick to the method taught in that course, no point playing with fire 

Would like to say that L'Hopital was my favourite thing in first year math, now it's probably Cauchy-Goursat's Theorem for use in complex contour integration (beautiful math)  

[conic curve]

Okay so I am having trouble with "quadratic identities"

I don't seem to understand things like x^2+x+1=a(x-1)^2+b(x-1)+c

How is a=1 c=3 b=3 in this case

Same with this case 3x^2-5x-2=a(x-1)^2+b(x+1)+c

How is a=3 c=-6 and b=1

If anyone here is good at explaining clearly then could you please help me

Thanks 

[RuiAce]

Okay so I am having trouble with "quadratic identities"

I don't seem to understand things like x^2+x+1=a(x-1)^2+b(x-1)+c

How is a=1 c=3 b=3 in this case

Same with this case 3x^2-5x-2=a(x-1)^2+b(x+1)+c

How is a=3 c=-6 and b=1

If anyone here is good at explaining clearly then could you please help me

Thanks 

[wyzard]

Would like to say that L'Hopital was my favourite thing in first year math, now it's probably Cauchy-Goursat's Theorem for use in complex contour integration (beautiful math)  

Oh that's such a sweet result I'd say my the Residue Theorem's (again from Complex Analysis) my favorite, and how it can be used to find really nasty integrals and find inverse Laplace Transforms so efficiently.

[jamonwindeyer]

Oh that's such a sweet result I'd say my the Residue Theorem's (again from Complex Analysis) my favorite, and how it can be used to find really nasty integrals and find inverse Laplace Transforms so efficiently.

Definitely up there, love the Residue Theorem, after I learned it I was like "Why did you even bother teaching us Cauchy's Integral Theorem then?"

[conic curve]

Need help with the following questions:

6. A motorbike and car leave a service station at the same time. The motorbike travels on a bearing of 080 degrees and the car travels for 15.7km on a bearing of 108 degrees until the bearing of the motorbike from the car is 310 degrees. How far, correct to 1 decimal place, has the motorbike travelled?

7. A  plane flies from Dubbo on a bearing of 139 degrees for 852 km then turns and flies on a bearing of 285 degrees until it is due west of Dubbo. How far from Dubbo is the place, to the nearest km?

8. Stig leaves home and trave;s on a bearing of 248 degrees for 109.8 km. He then tuens and travels for 271.8 km on a bearing of 143 degrees. Stif then turns and travels home on a bearing of "a"
a. How far does he travel on the final part of his journey?
b. Evaluate a

9. Two cars leave an intersection at the same time, one travelling at 70km/h along one road and he other car travelling at 80 km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection?

[RuiAce]

Need help with the following questions:

6. A motorbike and car leave a service station at the same time. The motorbike travels on a bearing of 080 degrees and the car travels for 15.7km on a bearing of 108 degrees until the bearing of the motorbike from the car is 310 degrees. How far, correct to 1 decimal place, has the motorbike travelled?

7. A  plane flies from Dubbo on a bearing of 139 degrees for 852 km then turns and flies on a bearing of 285 degrees until it is due west of Dubbo. How far from Dubbo is the place, to the nearest km?

8. Stig leaves home and trave;s on a bearing of 248 degrees for 109.8 km. He then tuens and travels for 271.8 km on a bearing of 143 degrees. Stif then turns and travels home on a bearing of "a"
a. How far does he travel on the final part of his journey?
b. Evaluate a

9. Two cars leave an intersection at the same time, one travelling at 70km/h along one road and he other car travelling at 80 km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection?

The others are lecturing right now and I'm afraid I don't have paper on me at this moment. Have you tried drawing diagrams?

If you could upload images of diagram I can tell you if it looks correct, and then just sketch out the method to attempting these questions.

[happy_turtle]

Need help with the following questions:

6. A motorbike and car leave a service station at the same time. The motorbike travels on a bearing of 080 degrees and the car travels for 15.7km on a bearing of 108 degrees until the bearing of the motorbike from the car is 310 degrees. How far, correct to 1 decimal place, has the motorbike travelled?

7. A  plane flies from Dubbo on a bearing of 139 degrees for 852 km then turns and flies on a bearing of 285 degrees until it is due west of Dubbo. How far from Dubbo is the place, to the nearest km?

8. Stig leaves home and trave;s on a bearing of 248 degrees for 109.8 km. He then tuens and travels for 271.8 km on a bearing of 143 degrees. Stif then turns and travels home on a bearing of "a"
a. How far does he travel on the final part of his journey?
b. Evaluate a

9. Two cars leave an intersection at the same time, one travelling at 70km/h along one road and he other car travelling at 80 km/h along the other road. After 2 hours they are 218 km apart. At what angle, to the nearest minute, do the roads meet at the intersection?

I have question 9... I'm not sure about the others though

[RuiAce]

I have question 9... I'm not sure about the others though

This looks correct. I had glanced at Q9 and realised that it would throw some people off because it makes you go back to speed=distance/time, but judging by that you catered it correctly (and the cosine rule does not look incorrectly substituted) it appears correct

[jamonwindeyer]

I have question 9... I'm not sure about the others though

Thanks for that answer happy_turtle, and welcome to the forums!! Absolute legend  conic I'll definitely come and give you an explanation of this style of question tomorrow, just need to finish this lecture series first  I'll run through one besides Question 9