****Leaving Certificate: Higher Level Maths Discussion****

Calvin

MegGustaa wrote: »

P is for Permutations, C is for combinations.

A permutation is an arrangement of objects in a specific order, while a combination is a selection of objects in any order.

7P3 is for when you have 7 objects and want to find out how many ways you can arrange any 3 of them. E.g. how many arrangements of three letters can you make from A, B, C, D, E, F, G?

7C3 is for when you have 7 objects and want to find out how many different selections of 3 objects you can make. E.g. how many different selections of 3 letters can you make from A, B, C, D, E, F, G?

7P3 = 210, 7C3 = 35.
The reason there are so many more permutations is because order is taken into account. In the first instance, the permutation ABC is distinct from CBA so they are counted separately. However, in the second instance ABC and CBA are the same combination of letters, so they are not counted twice.

I hope that makes sense.

Ah, so P is used when there is an order and C is used when there is no order required? So, P could be used when choosing a team and a certain person must be first where as C would be used if any person could be first chosen?

Gcc ct96

Can somone please explain how to prove question 6b on the sec sample 2014 paper 2 would be greatly appreciated thanks

MegGustaa

Calvin Leong wrote: »

Ah, so P is used when there is an order and C is used when there is no order required? So, P could be used when choosing a team and a certain person must be first where as C would be used if any person could be first chosen?

No P is used when the order of the entire group is taken into account.

If you have 10 people (A - J) and need to pick a team of 5, but player B must be picked first, you're essentially saying that you're picking a team of 4 from a group of 9. So it's 9C4. The reason why it's a combination rather than a permutation is because the team made up of BACDE is the same team as BCAED, right? It doesn't matter what order they were picked in, or what order they stand in, etc. They're the same 5 individuals.

P has more to do with selecting objects in a certain order. For example, you want to work out the number of different 4-digit bike lock codes you can make from the numbers 0 - 9, with no repeated digits.
There are 10 possible digits. The order matters because obviously if the code "1234" will open the lock, "2143" will not. It's the same selection of numbers but in a different order. So we're dealing with permutations.

How many distinct codes can be made? 10P4 = 5040.
Or, to work it out by hand: 10x9x8x7 = 5040 (there are 10 choices for the 1st digit, 9 for the 2nd, etc.)

If you could repeat the digits, there would be far more permutations, right?
10x10x10x10 = 10000

Fiske

I've missed a ton of school this year and haven't gotten to revise much at all - I'm pretty sure I got a C on Paper 1 and at this point I'm sure that Maths is going to end up being the subject that isn't counted for me. What are the essentials that I should learn for tomorrow just to get by?

PaleMoonlight

I'm an applied maths student and I just wanted to check, its okay if I use methods I learn in applied maths in normal maths, right? For example I just did 2010 Sec q8 using what I've learned in applied maths. I think I remember my teacher saying its okay but I just want to make sure.

Peregrine

PaleMoonlight wrote: »

I'm an applied maths student and I just wanted to check, its okay if I use methods I learn in applied maths in normal maths, right? For example I just did 2010 Sec q8 using what I've learned in applied maths. I think I remember my teacher saying its okay but I just want to make sure.

2010?

What was the question and what did you use?

Gcc ct96

Anyone know how to prove 2014 sec sAmple 6 B thanks

PaleMoonlight wrote: »

I'm an applied maths student and I just wanted to check, its okay if I use methods I learn in applied maths in normal maths, right? For example I just did 2010 Sec q8 using what I've learned in applied maths. I think I remember my teacher saying its okay but I just want to make sure.

I do applied maths too and all valid methods must be accepted so it's ok as long as you show workings

MegGustaa

Nimrod 7 wrote: »

2010?

What was the question and what did you use?

It was practically lifted off an Applied Maths paper, involving a lighthouse and a ship, where you had to find the shortest distance between them.

2010 was the first year of Project Maths for the pilot schools. I don't know how representative that paper is for subsequent years, to be honest.

booblefoop

Gcc ct96 wrote: »

Anyone know how to prove 2014 sec sAmple 6 B thanks

The one with proving DOC = DEC?

Basically DOEC is a cyclic quadrilateral because ODC and OEC add up to 180, and opposite angles in a cyclic quadrilateral always add up to 180.

That makes DC the arc of a circle, and the points O and E are both on the circle.

Therefore, they must be equal, as angles standing on the same arc are always equal.

little sis...

MegGustaa wrote: »

It was practically lifted off an Applied Maths paper, involving a lighthouse and a ship, where you had to find the shortest distance between them.

2010 was the first year of Project Maths for the pilot schools. I don't know how representative that paper is for subsequent years, to be honest.

Isnt the shortest distance the perpendicular distance from a point to the line? Thats how I did that Q anyway

PaleMoonlight

Gcc ct96 wrote: »

I do applied maths too and all valid methods must be accepted so it's ok as long as you show workings

Thank you

MegGustaa wrote: »

It was practically lifted off an Applied Maths paper, involving a lighthouse and a ship, where you had to find the shortest distance between them.

2010 was the first year of Project Maths for the pilot schools. I don't know how representative that paper is for subsequent years, to be honest.

I rang my applied maths teacher to ask her to know for sure, and she said its fine to use what I know from applied maths. She also mentioned that a lot of applied maths is coming into project maths, like some maths questions have been basically easy applied maths ones. Not really fair for people that don't do the subject.

little sis...

If you are given a set of values say a list of x values and their frequencies, how do you find the upper/lower quartile and the interquartile range? We never really covered that

Calvin

MegGustaa wrote: »

No P is used when the order of the entire group is taken into account.

If you have 10 people (A - J) and need to pick a team of 5, but player B must be picked first, you're essentially saying that you're picking a team of 4 from a group of 9. So it's 9C4. The reason why it's a combination rather than a permutation is because the team made up of BACDE is the same team as BCAED, right? It doesn't matter what order they were picked in, or what order they stand in, etc. They're the same 5 individuals.

P has more to do with selecting objects in a certain order. For example, you want to work out the number of different 4-digit bike lock codes you can make from the numbers 0 - 9, with no repeated digits.
There are 10 possible digits. The order matters because obviously if the code "1234" will open the lock, "2143" will not. It's the same selection of numbers but in a different order. So we're dealing with permutations.

How many distinct codes can be made? 10P4 = 5040.
Or, to work it out by hand: 10x9x8x7 = 5040 (there are 10 choices for the 1st digit, 9 for the 2nd, etc.)

If you could repeat the digits, there would be far more permutations, right?
10x10x10x10 = 10000

Ahhh okay, I understand now. P is used when the order of the entire result matters where as C is used when there can be a repeated result? eg as long as student A is first in line out of 5 spaces, the order of B-G doesn't matter? So for that, it'd be 6C4. 7 options at the start with 5 spaces, but A must be there so it decreases your amount of options and spaces by one.

MegGustaa

Calvin Leong wrote: »

Ahhh okay, I understand now. P is used when the order of the entire result matters where as C is used when there can be a repeated result? eg as long as student A is first in line out of 5 spaces, the order of B-G doesn't matter? So for that, it'd be 6C4. 7 options at the start with 5 spaces, but A must be there so it decreases your amount of options and spaces by one.

Almost completely right, yep, except for the repeated result thing.

You can't use P or C for situations where repeats (or "replacement") occurs.

For example, 9 discs labelled 0 - 9 in a bag. You take one out, note the number, return it to the bag. Then you take out another one, etc. Each time, you have 9 discs to choose from. With straight-forward permutations and combinations, it's assumed you can only select one object once.

Howeller

Did anyone forget to enter their calculator make and model or does anyone know if this is a big issue?

pa95

Howeller wrote: »

Did anyone forget to enter their calculator make and model or does anyone know if this is a big issue?

Yep I did, the superintendents didn't mention anything about it...I'm sure if it were that important the SEC would have instructed them to remind us to do it. Also they shouldn't put it on the sneaky page on the inside, I was quite nervous before the exam and when they told us to start I completely missed that page haha

Howeller

pa95 wrote: »

Yep I did, the superintendents didn't mention anything about it...I'm sure if it were that important the SEC would have instructed them to remind us to do it. Also they shouldn't put it on the sneaky page on the inside, I was quite nervous before the exam and when they told us to start I completely missed that page haha

Yeah did not see that inside page either but I'm sure lots of people forget! Best thing to do might be to leave a nice note saying we forgot it on the paper 2? Our superintendent might have said it but I couldn't hear haha

yoyojc

MegGustaa wrote: »

If I'm understanding you correctly, you're wondering why you can't multiply the 77 by e? Because the e is raised to a power. You can't touch the e until you deal with the exponent (BEMDAS). That's why you divide across by 77 and then get the natural log (ln or log to the base e) of both sides.

Thank you for your response to my awkwardly asked question! This is extremely helpful, believe it or not I'm an A student and never knew this or heard of 'BEMDAS' so it's really great that you've answered my question. So deal with the exponents first, appreciate it!

Calvin

MegGustaa wrote: »

Almost completely right, yep, except for the repeated result thing.

You can't use P or C for situations where repeats (or "replacement") occurs.

For example, 9 discs labelled 0 - 9 in a bag. You take one out, note the number, return it to the bag. Then you take out another one, etc. Each time, you have 9 discs to choose from. With straight-forward permutations and combinations, it's assumed you can only select one object once.

Ahh, I see now. Thank you!

deadpixel

Anyone have the soultions to the deb paper 2? Trying to correct it fully but not sure on one or two questions.. Also for 3 (b) (ii) is the tan ∅ = ± m1 -m2 / 1 + m1m2 formula in the log tables as I can't find it in mine?

booblefoop

WoolyAbyss wrote: »

Oh god, whats the central limit theorem?

I'm probably not going to explain this the best but:

Imagine you have a huge array of data. You take a random sample of size n, and find the mean. You do it again, find a different sample, and find the mean of that.

If you keep doing that until you've exhausted all the possible samples, the means you've found will be normally distributed, even if the original data wasn't.

Peregrine

deadpixel wrote: »

Also for 3 (b) (ii) is the tan ∅ = ± m1 -m2 / 1 + m1m2 formula in the log tables as I can't find it in mine?

Page 19.

deadpixel

Nimrod 7 wrote: »

Page 19.

OK good to know, just circle formulas for page 19 on mine but they may be a little out of date, the ones in there should have it messed up that question trying to remember the right formula on the pre hah.

Peregrine

deadpixel wrote: »

OK good to know, just circle formulas for page 19 on mine but they may be a little out of date, the ones in there should have it messed up that question trying to remember the right formula on the pre hah.

Haha I've had a similar experience.

http://www.examinations.ie/schools/S_92_09_Re_Formulae_and_Tables_Booklet.pdf

This circular says it was added in 2010 so it should be there in the one you get in the exam.

Calvin

Any predictions for the theorems/constructions? Or even just the most important :rolleyes:

PaleMoonlight

Anyone know if we need to be able to prove the twin rule?

aleatorio

This is from the Examcraft mock and I think it's the Central Limit theory?

'400 samples of size 10 are taken from a production line producing jars of gravy. The mean weight of a jar is 200g with a standard deviation of 1.5g. Calculate the limits between which you would expect 95% of the sample mean to lie'

I know the formula for the mean of the sample is the SD divided by the sample size, but is the sample size 10 or 400(10)?

And then it would just be 200+/- 2 standard deviations.. Yeah....?

MegGustaa

aleatorio wrote: »

This is from the Examcraft mock and I think it's the Central Limit theory?

'400 samples of size 10 are taken from a production line producing jars of gravy. The mean weight of a jar is 200g with a standard deviation of 1.5g. Calculate the limits between which you would expect 95% of the sample mean to lie'

I know the formula for the mean of the sample is the SD divided by the sample size, but is the sample size 10 or 400(10)?

And then it would just be 200+/- 2 standard deviations.. Yeah....?

Yep, sample size n = 10, and you use the standard deviation of the means (found by dividing the SD by root n).

The expected mean of all the smaller sample is also 200, by the CLT

plmko

aleatorio wrote: »

This is from the Examcraft mock and I think it's the Central Limit theory?

'400 samples of size 10 are taken from a production line producing jars of gravy. The mean weight of a jar is 200g with a standard deviation of 1.5g. Calculate the limits between which you would expect 95% of the sample mean to lie'

I know the formula for the mean of the sample is the SD divided by the sample size, but is the sample size 10 or 400(10)?

And then it would just be 200+/- 2 standard deviations.. Yeah....?

Sample size is 10
[used 400 in my pre and got it wrong!]

MegGustaa

PaleMoonlight wrote: »

Anyone know if we need to be able to prove the twin rule?

What is that? Never heard of it..