If you want any help with maths, ask me here

Take Your Pants Off

I cannot wrap my head around the 2nd part of 6b. Ok i get the part where u use your answer from above, which i got, but after that no clue. Whats up with dy/dx(dx) ? And the minus stuff. I know ms. Soloutions are not always the best so if theres a more breakdown soloution that someone could provide for this step by step. Would immensly help.

Thar_Cian

Take Your Pants Off wrote: »

I cannot wrap my head around the 2nd part of 6b.

I hope this helps. If you know integration by substitution, you can use that to go from the third-to-last line to the penultimate, or else just remember that you're dividing by the number in the argument (work backwards by differentiating to see how it works).

Take Your Pants Off

Thar_Cian wrote: »

I hope this helps. If you know integration by substitution, you can use that to go from the third-to-last line to the penultimate, or else just remember that you're dividing by the number in the argument (work backwards by differentiating to see how it works).

Thank you !!

thetalker

hey back to this thread after a bit of a break since I wasn't focusing math. But I was brushing up on statistics and was wondering if anyone could explain why something about z-scores is answered the way it is on the marking scheme.

So for Q9 p2 2016 exam part ii deals with z-scores and I think I'm struggling to get the logic.

Were asked to find the income level of the lowest 10% so I assumed that P(z<z1)=0.8 i.e 80% of people fall within z1 standard deviations of the mean. But the marking scheme gives it as P(z<z1)= 0.9
Is there something I'm missing here? I only just thought I was starting to get z scores as well...

Ponguin

Does anyone know if a proof has to come up every year and if so what is the most likely one, trigonometric?

Ponguin

Sorry i just can't find the answers to my questions anywhere so if anyone knows please give me a shout.
Regarding the first Image of a marking scheme from a few years back, does anyone know whether this method of integration is still on the course? As I've never had to use du before in integration (or integrated two products for that matter).
The same goes for the second pic, is there any way of doing this without integrating by parts as I don't think this is on the course anymore.
Lastly in the pic at the end how would one go about getting the average velocity? Would you have to get the average value of each separate function of v(t) 😕😕😫

A97

Ponguin wrote: »

Sorry i just can't find the answers to my questions anywhere so if anyone knows please give me a shout.
Regarding the first Image of a marking scheme from a few years back, does anyone know whether this method of integration is still on the course? As I've never had to use du before in integration (or integrated two products for that matter).
The same goes for the second pic, is there any way of doing this without integrating by parts as I don't think this is on the course anymore.
Lastly in the pic at the end how would one go about getting the average velocity? Would you have to get the average value of each separate function of v(t) 😕😕😫

Substitution isn't on the course anymore, so I'm pretty sure you won't be asked anything like that.

For the second one, the most Leaving Cert friendly way to do the question is to be a bit clever with how you write out the question. If you say that x = x + 3 - 3, you can split your fraction up into (x + 3) / (x + 3) and -3 / (x + 3), very similarly to saying that 2 / 3 = (1 + 1) / 3 = 1 / 3 + 1 / 3.

For the third question, you want to get the average value over the whole function. Since integration is basically adding up a bunch of tiny rectangles, to get the average size of those rectangles, you add them up and then divide by their combined length. That might be a bit unclear so I'll try to explain it differently.

You don't want to get the average value of each separate function since you will then have five different averages representing different things. If this makes sense to you, you could then take a weighted average of these values, where say v(t) between 11 and 14 is counted 6 times for every time v(t) between 0 and 0.5 is counted since its range is 6 times bigger. This should give you the correct answer, but there is an easier way.

You could simply integrate all five functions and then divide by the overall limits i.e. 14 - 0 = 14. This essentially does all of the above paragraph in less steps, since the fact that some parts of the piecewise functions are bigger than others are automatically taken into account this way. This means that the region between 11 and 14 for example contributes more to the average value than the 0 to 0.5 region.

I've written out most of those explanations by hand as it might be a bit easier to understand. You should be able to finish the questions from there, remembering that the definite integral of 1 / (x + a) is ln|x + a| evaluated between its limits, where a is any real number, like 3, pi, -72.76 etc.

thetalker

Ponguin wrote: »

Does anyone know if a proof has to come up every year and if so what is the most likely one, trigonometric?

Idk if its mandatory but a friend says he went to grinds and a big suspect i that de moivre proof will be asked. As well as one of the trig theorem proofs like number 12 or 13

Btw does anyone know if they can ask something like this. I dont remember ever learning it. its from a sample paper, question 2b.
http://www.mathsdojo.ie/pdf/EP_LCH_P1_2015_Sample.pdf

heres the way they solve it, I dont really know how or whats going on.
http://www.mathsdojo.ie/pdf/MS_LCH_P2_2015_Sample.pdf

carefulnowted

Seems like a pretty standard question to me, thetalker - it's just a 95% confidence interval for a sample proportion, which should be in your book. Is there something specific that's confusing you?

aon1998

I think statistics was the last strand of the course to fully change, those questions were only examinable from 2015 onwards so yes there is an extremely high chance that we're going to get a long question on them.

It may not be in your book depending on when it was printed.

carefulnowted

Is the De Moivre's Proof the "prove by induction" one, or one of the "prove this trig identity using De Moivre's" ones?

thetalker

carefulnowted wrote: »

Seems like a pretty standard question to me, thetalker - it's just a 95% confidence interval for a sample proportion, which should be in your book. Is there something specific that's confusing you?

I'm talking about Q2 btw cause in the marking scheme I posted they don't have a 95% confidence interval in part a, they use z scores instead.

And b appears to be relating to something in the supplementary material. Im not sure what exactly it is they've done. Maybe I just need to find the pages that deal with it.

And yeah the proof by induction one is whats been predicted apparently.

edit; I see b is using a confidence interval, I've only see them as 1.96 times the standard error so I amn't familiar with how theyr're doing it. I assume that thats how you do confidence intervals for populations and I only learnt for mean?

carefulnowted

I tried looking online there for the supplementary material from Folens about that bit of stats but I can't seem to find anything about populations.

There's not much to it really - it's just that when you're doing a confidence interval for a proportion you use the "standard error of the proportion" (i.e. the big square root with all the p's underneath it), which is in the log tables so you don't have to remember it. Multiply that by 1.96 and away you go.

thetalker

Ah thanks, I've gotten a friend to send me a picture from the booklet for Active Math which mentions the formula as well as how to get the confidence intervals. Glad to have statistics sorted out at least, better be sure by doing a few questions though!

Take Your Pants Off

Has anyone done edco sample c p1 qs3.
Im not getting the correct values at all.

Take Your Pants Off

Cant seem to attatch either.
But the qs is p(b)= -80b^2+69000b-9300000
Give in the form p(b)=r(b-h)^2+k

I am getting so far
-80((b^2+862.5b+185976.56)-302226.56)

The answer at back is:
-80(b-431.25)^2+5578125

skippy1977

Think you just made a sign mistake. When you factorise the -80 I think you left a -116250 instead of a +116250

Ponguin

A97 wrote: »

I've written out most of those explanations by hand as it might be a bit easier to understand. You should be able to finish the questions from there, remembering that the definite integral of 1 / (x + a) is ln|x + a| evaluated between its limits, where a is any real number, like 3, pi, -72.76 etc.

Sorry only getting around to replying now but thanks a million! That trick for x/x+3 is great it really simplifies things, you must be amazing at maths :P

A97

Ponguin wrote: »

Sorry only getting around to replying now but thanks a million! That trick for x/x+3 is great it really simplifies things, you must be amazing at maths :P

Happy to help. Coming up with something like that on the spot can be quite difficult but at least now you and some of the others on here would be prepared if something like that comes up. It's a bit like those limit questions where you're trying to get something in the form of sin(x) / x by multiplying the numerator and demonimator by the same number.

Another similar line of thinking for integration questions would be used trying to solve something like (x + 3) / 2x². Splitting that up into x / 2x² + 3 / 2x² and then 0.5 / x + 1.5x⁻² makes the integration much handier.

Take Your Pants Off

I swear this is the last time. But I cannot stress how helpful the posters in this group have been to everyone's questions.
I never found trig graphs the most appealing and still dont.
I got the amplitute as 8 and vertical shift as 8.
But i cant get to know the period or the coordinates

A97

See the attachments for my solution. I gave ~4 ways to get C. You only need one, and the second one is probably the easiest. But the others may be useful in certain situations as they are a bit more mathematically rigorous, and if they end up mixing trigonometry with calculus on your exam, they might ask you to use derivatives etc. Let me know if anything is confusing/wrong.

Also, I was a bit surprised to see the x axis in degrees instead of radians, which explains my doodles at the top of the first page. I always find it useful to draw standard sin(x) and/or cos(x) functions and then see what changes from it. Also, the calculator is your friend with these types of questions, since you can check your answers and plug in various angles if you need to.

Take Your Pants Off

A97 wrote: »

See the attachments for my solution. I gave ~4 ways to get C. You only need one, and the second one is probably the easiest. But the others may be useful in certain situations as they are a bit more mathematically rigorous, and if they end up mixing trigonometry with calculus on your exam, they might ask you to use derivatives etc. Let me know if anything is confusing/wrong.

Also, I was a bit surprised to see the x axis in degrees instead of radians, which explains my doodles at the top of the first page. I always find it useful to draw standard sin(x) and/or cos(x) functions and then see what changes from it. Also, the calculator is your friend with these types of questions, since you can check your answers and plug in various angles if you need to.

THANK YOU SOOO MUCH !!!

daraghwal

Could someone do out sin^-1(7/4x) or sine inverse of 7 divided by 4x. I have done it out using the formula on pg 25 of the log tables but wolfram alpha gives back a different solution. I am doing something wrong when multiplying by the bracket differentiated.

Also if someone could show me the steps on integrating ((t^2) + 2t)(e^t). It is equal to (t^2)(e^t) + c but I don't know how it comes to that. It is an example on pg 402 of active maths 4 book 1. Worked example 15.5. Thanks in advance

A97

You can't use the formula on page 25 since the x needs to be in the denominator to use it. You should use the chain rule to differentiate the inner expression too. I've attached a solution. The first page gets the derivative. The second is me trying to simplify the expression a bit. You may or may not need to do this.

I'll do the integration now. Let me know if anything is confusing you.

EDIT: That integral in itself is too difficult for what is taught at LC level. But the example in the book has a previous part, where you differentiate an expression. Essentially, all that part is testing of you is knowing that integration is the reverse of differentiation. So the indefinite integral of any function f'(x) is just f(x) + C. Don't forget your constant of integration! See attachments for further explanation.

daraghwal

A97 wrote: »

You can't use the formula on page 25 since the x needs to be in the denominator to use it. You should use the chain rule to differentiate the inner expression too. I've attached a solution. The first page gets the derivative. The second is me trying to simplify the expression a bit. You may or may not need to do this.

I'll do the integration now. Let me know if anything is confusing you.

EDIT: That integral in itself is too difficult for what is taught at LC level. But the example in the book has a previous part, where you differentiate an expression. Essentially, all that part is testing of you is knowing that integration is the reverse of differentiation. So the indefinite integral of any function f'(x) is just f(x) + C. Don't forget your constant of integration! See attachments for further explanation.

Thank you! Had a bit of a heart attack this morning when I thought I didn't know how to integrate something with Es in it like that. :eek:

A97

daraghwal wrote: »

Thank you! Had a bit of a heart attack this morning when I thought I didn't know how to integrate something with Es in it like that. :eek:

No worries. I'm pretty sure that you wouldn't be asked to integrate an exponential that is multiplied by the variable and is raised to the variable too e.g. xe^x, unless it was asked in a manner like that example was. Just be sure that you can integrate any type e raised to a variable such as:

e^-x dx
e^(3t+5) dt

As you probably know, differentiate the exponent, and divide by that derivative. Add a constant of integration if needed. Sines and cosines are very similar, in which you differentiate what you're taking the sine or cosine of and then divide by that. Make sure you integrate the sin and cos bit too.

e.g.

∫sin(5x + 2) dx = -(cos(5x + 2) / 5) + C
∫cos(-πx - 2) dx = (sin(-πx - 2) / -π) + C = -(sin(-πx - 2) / π) + C
∫-sin(2t + 1) dt = (cos(2t + 1) / 2) + C
∫-cos(3π - r) dr = -(sin(3π - r)/ -1) + C = sin(3π - r) + C (Incidentally you can further simplify this to sin(r) + C using the 5th trig identity on page 14)

That's probably the very hardest basic trig integral you would be likely to see tomorrow.

roisiny

Hi there,
Meant to ask my teacher this in blocks but couldn't get round to it.
In financial math, sometimes the formula is written
Sn=
a(r^n - 1)

---

r - 1
while other times it's

Sn=
a(1-r^n)

---

1 - r

The differences when using the two are probably like 40€ in 100,000, but is there any reason for using the first over the ones used in log tables? Thanks

daraghwal

roisiny wrote: »

Hi there,
Meant to ask my teacher this in blocks but couldn't get round to it.
In financial math, sometimes the formula is written
Sn=
a(r^n - 1)

---

r - 1
while other times it's

Sn=
a(1-r^n)

---

1 - r

The differences when using the two are probably like 40€ in 100,000, but is there any reason for using the first over the ones used in log tables? Thanks

I've never noticed this before and I am repeating! I have always used to one in the tables. Can you give an example of where it is? Thanks

roisiny

daraghwal wrote: »

I've never noticed this before and I am repeating! I have always used to one in the tables. Can you give an example of where it is? Thanks

All the Less Stress More Success questions use this, believe the 2011 SEC paper uses it in its solutions. Both of these are pre the newest course but thought be safer to check ☺️

TheBody

Both formula are the same.

Just mulitply top and bottom of one by -1 to get the other.