4U Maths Question Thread

[RuiAce]

Hey, how would I do this question?

Cheers

A and D are integrals of odd functions so they are exactly equal to 0.

On the other hand B and C are integrals of even functions. But if we sketch the function being integrated in C we will find that the region is entirely BELOW the x-axis, so the integral is negative.

If you sketch the one for B, that one will always be above the x-axis. Hence that is the correct answer, as the integral will be positive as a consequence of this.

[chelseam]

Hi! Could someone please show me how to prove the triangle inequality? I'm confused about both the geometric and algebraic approaches! Thank you so much

[RuiAce]

Hi! Could someone please show me how to prove the triangle inequality? I'm confused about both the geometric and algebraic approaches! Thank you so much

I'm fairly sure there is no algebraic proof that you're expected to know of in 4U. The first time I proved it algebraically was in first year uni after doing some linear algebra in advance. The only thing that can be proven algebraically is the generalised triangle inequality, and even then you have to assume that it's true for 2 complex numbers before you can prove it for n complex numbers.

[chelseam]

I'm fairly sure there is no algebraic proof that you're expected to know of in 4U. The first time I proved it algebraically was in first year uni after doing some linear algebra in advance. The only thing that can be proven algebraically is the generalised triangle inequality, and even then you have to assume that it's true for 2 complex numbers before you can prove it for n complex numbers.

Thanks so much Rui!

[statues]

2001 HSC 5
(c) A class of 22 students is to be divided into four groups consisting of 4, 5, 6 and
7 students.
(i) In how many ways can this be done? Leave your answer in unsimplified
form.

The answer my book gives is 22C4x18C5x13C16
What I don't understand is why this isn't divided by 4! on account of the ways that the same groups can be selected in different orders, but still essentially be the same.
Many Thanks

[Ali_Abbas]

Hi! Could someone please show me how to prove the triangle inequality? I'm confused about both the geometric and algebraic approaches! Thank you so much

Algebraic proof of the triangle inequality can be done in two ways.

[RuiAce]

2001 HSC 5
(c) A class of 22 students is to be divided into four groups consisting of 4, 5, 6 and
7 students.
(i) In how many ways can this be done? Leave your answer in unsimplified
form.

The answer my book gives is 22C4x18C5x13C16
What I don't understand is why this isn't divided by 4! on account of the ways that the same groups can be selected in different orders, but still essentially be the same.
Many Thanks

This is basically when to not use the identical groups problem I covered in my trial survival lectures.


Selecting the groups in another order was not what caused the problem; it was the actual groups themselves.

[Shlomo314]

Hi,
When finding the eccentricity for a conjugate hyperbola (y^2/b^2-x^2/a^2=1), is it e^2=1+a^2/b^2 or is it e^2=1+b^2/a^2
Thankyou

[RuiAce]

Hi,
When finding the eccentricity for a conjugate hyperbola (y^2/b^2-x^2/a^2=1), is it e^2=1+a^2/b^2 or is it e^2=1+b^2/a^2
Thankyou

I always memorised it as this (because textbooks can use multiple conventions and it gets annoying)

So for \(\frac{y^2}{b^2}-\frac{x^2}{a^2} = 1\) it would be \( a^2=b^2(e^2-1) \)

[Shlomo314]

Hey Rui

For the 2016 question 9, I dont understand how you did h/4=x/6 with similar triangle method (I saw the 6 from finding the difference of the two lengths but how did you use similar triangles and got 6)?

Thanks

[RuiAce]

Hey Rui

For the 2016 question 9, I dont understand how you did h/4=x/6 with similar triangle method (I saw the 6 from finding the difference of the two lengths but how did you use similar triangles and got 6)?

Thanks

The front view is basically the trapezium itself, and by drawing in that blue line you get triangles and parallelograms appearing. Then, the proportional sides on similar triangles are useful to us. (We know that the triangles are similar as they are equiangular by inspection.)

This is a pretty fairly common technique that I wrote in my book

[Shlomo314]

Hey,
In the mechanics section, more specifically F=ma, how do you know when to include the 'm' when integrating? Is there a difference between 'Resistance' and 'Retardation' where you leave the m or take the m out of the equation?

Thanks

[chelseam]

Algebraic proof of the triangle inequality can be done in two ways.

Thank you so much!

[RuiAce]

Hey,
In the mechanics section, more specifically F=ma, how do you know when to include the 'm' when integrating? Is there a difference between 'Resistance' and 'Retardation' where you leave the m or take the m out of the equation?

Thanks

Retardation is negative acceleration. Resistance is negative force.

As for the 'm' problem, many textbooks are full of confusion but the HSC usually clears up any disambiguity with whether or not the m is necessary. They will either say "proportional to the velocity/square of the velocity" or "proportional to the mass times the velocity/square of the velocity". So you will know what to do when that happens.

Besides, when in doubt, just look at what they want you to prove. If the m disappears, then the resistive force should be something like mkv. If the m stays, the resistive force should be something like kv.

[beau77bro]

HELPPP, i can't work out this question. and i am struggling with my reasoning. i have all the principles for Probability, but i can't apply them and im struggling, like in the last question how i didn't see how you didnt arrange them, well it was because it was an arrangement and was set. but now im sturggling with a lot of probability and was wondering how i could brush up or revise - like just arranging things properly or knowing when not to, or when it's just repeats or basic stuff i am over complicating.


i cant do the first part, i would like to attempt the second after you guys give me hints, thankyou.