Mathematics Question Thread

[Shadowxo]

other parts
it was the second part of
differentiate y=x^2e^x

what a legend ruiace! thank gosh i took 2u

Using the product rule for this question,
dy/dx = 2xe^x + x²e^x
= e^x(2x+x²) which can be rewritten as
e^xx(2+x)
so the integral for e^xx(2+x) is just x²e^x (the function we differentiated) +c!

[RuiAce]

other parts
it was the second part of
differentiate y=x^2e^x

what a legend ruiace! thank gosh i took 2u

[katnisschung]

thanks! yeah i realised that after i expanded it...

another q do i need to know how to integrate 5^x for 2u

[RuiAce]

thanks! yeah i realised that after i expanded it...

another q do i need to know how to integrate 5^x for 2u

[katnisschung]

stuck on another q

[RuiAce]

stuck on another q

[12070]

Okay, so I got (64)/5 but apparently you need two volumes or something. I'm so confused. Please help

[RuiAce]

Okay, so I got (64)/5 but apparently you need two volumes or something. I'm so confused. Please help

[katnisschung]

too lazy to check the syllabus..
2u don't have to know how to integrate by parts correct?

example attached

[jamonwindeyer]

too lazy to check the syllabus..
2u don't have to know how to integrate by parts correct?

example attached

Correct but you don't need to integrate that one by parts:

[Arisa_90]

Can i have help with these questions please?

[anotherworld2b]

I am not sure how to antidifferentiate these questions. Can I please have help?

[katnisschung]

stuck on a)

i got
pi/2+3/4

[Shadowxo]

I am not sure how to antidifferentiate these questions. Can I please have help?

For those questions, you have to use substitution. For g), you know that the derivative of e^-x is -e^-x.
So use u=1+e^-x, du/dx = -e^-x
So you end up with
You can see that there's a function, and the derivative of that function in each question. So let u = the number to a power / more complicated part then find the derivative of u, and use that to substitute in to antidiff with respect to u.

stuck on a)

i got
pi/2+3/4

For a)
You can divide it up into 5 sections, I'll call them 1,2,3,4,5.
Section 3 and 4 cancel out as they're equal in area and opposite signs
Area 1 = positive 1/4 * π * 1² = π/4
Area 2 = negative 1/2 *(1*1) = -1/2
Area 5 = positive 1/4 * π * 1² = π/4
Area 1 + Area 2 + Area 5 = π/2 - 1/2

Edit: this is for b)
Area from 0-1 is positive, areas from 1-2 and 2-3 cancel out as one's positive and one's negative and they're equal, and area from 3-4 is negative
Area 1 = positive (1-1/4*π)
Area 4 = negative (1/4*π)
Area 1 + Area 4 = 1-1/4*π-1/4*π = 1-π/2

[Ellie__]

When you are using past papers to study, how are you managing your time?

Simply knowing content will not be enough for mathematics. You need to keep doing past papers so that you can constantly adapt to different types of questions that you may see on the day. And speeding up is another thing that comes with practice, which you need to do a lot of.

When doing the past paper, you should not be overanalysing questions until potentially the last few. With practice comes the ability to generate ideas more quickly. Reading time is the first instance where ideas can be generated. During reading time, you don't have to expect your ideas to actually work, but you should already have a brief idea about what to do. Come writing time, you start putting it to the test. The thing about maths is that if you have an idea that you're confident about, it's usually the right way to go about it. So write it down quickly. And whilst recklessness is common with calculators, there is no need to be too slow with punching in numbers either.

Whilst English was more stressful with continuously writing, maths was (potentially surprisingly) second to it. It's easy to run out of time in maths, so you need to develop quick handwriting abilities for it also.

And as always, follow typical exam guidelines. Get all the marks you can guarantee that you will get first, before moving on to the harder questions that require more thought. Never spend too long on a question and always check the clock if you feel you've just been staring the whole time.

Ah thankyou Rui Ace!!

That makes sense, yeah I'm spending at least 10 mins on some 2-3 markers, so I'll give that a go