Maths-Ext 1/2 Marks Lost and Hardest Topics (2 Viewers)

Qeru · Jan 20, 2021

Yep I wanted to showcase the 'reverse product rule,'

$\int\sin^{99}(x)\sin(101x)dx$

$=\int\sin^{99}(x)\sin(100x+x)dx$

$\int\sin^{99}(x) \sin(100x) \cos{x}+\sin^{100}(x)\cos(100x) dx$

$\text{Now notice how:}\quad\frac{d}{dx}\sin^{100}(x)=100\sin^{99}(x)\cos{x} \quad\text{and}\quad\frac{d}{dx}\sin(100x)=100\cos(100x)$

SO our integral is in the form: $\int uv'+vu' dx$ but off by a constant of $\frac{1}{100}$

$\therefore \int\sin^{99}(x)\sin(101x)dx=\frac{1}{100}\sin^{100}(x)\sin(100x)+C$

Qeru · Jan 20, 2021

Nacseo said:
Jeez my head hurt just by looking at these equations, I'm also gonna apply for Ext 1 Maths, but now when I see this I'm like, sh*t, SH*T.

This is extension 2 so don't worry haha.

Nacseo · Jan 20, 2021

Qeru said:
This is extension 2 so don't worry haha.

Oh thank god, I was abouta jump off a microwave for a sec

tito981 · Jan 20, 2021

Qeru said:
Yep I wanted to showcase the 'reverse product rule,'

$\int\sin^{99}(x)\sin(101x)dx$

$=\int\sin^{99}(x)\sin(100x+x)dx$

$\int\sin^{99}(x) \sin(100x) \cos{x}+\sin^{100}(x)\cos(100x) dx$

$\text{Now notice how:}\quad\frac{d}{dx}\sin^{100}(x)=100\sin^{99}(x)\cos{x} \quad\text{and}\quad\frac{d}{dx}\sin(100x)=100\cos(100x)$

SO our integral is in the form: $\int uv'+vu' dx$ but off by a constant of $\frac{1}{100}$

$\therefore \int\sin^{99}(x)\sin(101x)dx=\frac{1}{100}\sin^{100}(x)\sin(100x)+C$

ye when i watched the mit integration bee i felt it was an easy expansion + reverse pro rule, iirc neither of the contestants got it right.

Trebla · Jan 20, 2021

Reverse product/quotient rule is literally equivalent to integration by parts in the same way that reverse chain rule is equivalent to substitution.

Qeru · Jan 20, 2021

Yes you can also do IBP on the first integral from the third line: $I=\int\sin^{99}(x) \sin(100x) \cos{x}dx+\int\sin^{100}(x)\cos(100x) dx$ to get

$I=\frac{1}{100}\sin^{100}(x)\sin(100x)-\int\sin^{100}(x)\cos(100x) dx+\int\sin^{100}(x)\cos(100x) dx$
Which is the same thing.

Jojofelyx · Jan 24, 2021

What do you guys reckon the hardest papers are from the last 10 years in order (for ext 2 and 1)?

idkkdi · Jan 24, 2021

Jojofelyx said:
What do you guys reckon the hardest papers are from the last 10 years in order (for ext 2 and 1)?

anything more than 10 years ago.

Drdusk · Jan 24, 2021

Jojofelyx said:
What do you guys reckon the hardest papers are from the last 10 years in order (for ext 2 and 1)?

Last 10 years?? Maybe 2010? 2010 had a pretty nice final question.

vernburn · Jan 24, 2021

Not really related but I remember reading that 1989 (especially the last question) is considered the hardest 4U paper ever written. As for the last 10 years I’d say 2010.

black.mamba · Jan 24, 2021

Jojofelyx said:
What do you guys reckon the hardest papers are from the last 10 years in order (for ext 2 and 1)?

easiest ext 2 2020 lol

Qeru · Jan 24, 2021

black.mamba said:
easiest ext 2 2020 lol

they really shouldnt have removed harder 3U.

vernburn · Jan 24, 2021

Qeru said:
they really shouldnt have removed harder 3U.

Couldn’t agree more!

idkkdi · Jan 24, 2021

vernburn said:
Couldn’t agree more!

maybe u would have state ranked with harder ext 1

idkkdi · Jan 24, 2021

vernburn said:
Not really related but I remember reading that 1989 (especially the last question) is considered the hardest 4U paper ever written. As for the last 10 years I’d say 2010.

i also heard 1989 last q is very hard.

CM_Tutor · Jan 29, 2021

1989 last question was too hard, which was bad because that doesn't help in creating a ranking order, leaving aside how it makes the candidates feel.

Having removed 'harder 3u', the place with the opportunity for really challenging materials (IMO) is proof. The recent thread on second-order recursion illustrates one way the proof topic can be used to make challenging questions.

idkkdi · Jan 29, 2021

CM_Tutor said:
1989 last question was too hard, which was bad because that doesn't help in creating a ranking order, leaving aside how it makes the candidates feel.

Having removed 'harder 3u', the place with the opportunity for really challenging materials (IMO) is proof. The recent thread on second-order recursion illustrates one way the proof topic can be used to make challenging questions.

Mech is hard lol can’t do algebra

Maths-Ext 1/2 Marks Lost and Hardest Topics (2 Viewers)

Qeru

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