If you want any help with maths, ask me here

pinkbear

Hi,
I know the leaving cert maths courses pretty well. If anyone wants help with any question, any topic, any level, just post here and I'll answer back as soon as I can.

LLAMAMILK

I have a test on patterns and sequences on Wednesday as part of my report. I'm in Ordinary so apart from Sn and Tn what do I need to know ?

pinkbear

Sequence: A sequence is a list of numbers. E.g. 1,2,3,4,5…
Series: A series is the sum of the terms of a sequence. E.g. 1+2+3+4+5+….

To Find if a Sequence is Linear/Arithmetic, Quadratic, Exponential:
Calculate 1st differences. If they're the same, it's linear/arithmetic.
If they're not calculate 2nd differences. If they're the same, it's quadratic.
If they're not, calculate the ratio between the terms. If they're the same, it's geometric.
If they're not, it could be none of the above, but that's highly unlikely so it's more likely you made a mistake.

Linear / arithmetic: Tn=a+(n-1)d, Sn = n/2 [ 2a + (n – 1)d ] where a is the first term, d is the (1st) difference, and n is the number you sub in.

Quadratic: Tn=an^2 + bn + c, where a=half the 2nd difference
You have to use simultaneous equations to work out b and c. (Example at the bottom)

Geometric: Sn= a(1-r^n) / (1-r), where a is the first term, r is the ratio between one term and the next, n is the number of terms in the series.

These formulas are all in the tables (I think pg 22), except Tn for the quadratic.

E.g. Identify the sequence 1, 5, 13, 25, 41… as linear, quadratic, exponential or none of these. Find Tn and Sn of the series.

Solution:
1st Differences: 4, 8, 12, 16 ….⇒ Not the same ⇒ Not linear
2nd Differences: 4, 4, 4 ….⇒ The same ⇒ Quadratic

Tn = an^2 + bn + c, where a = half the 2nd difference = ½ of 4 = 2
⇒Tn = 2n^2 + bn + c

T1 = 2(1)^2 + b(1) + c = 4 ⇒ 2+ b + c = 1 ⇒ b + c = -1
T2 = 2(2)^2 + b(2) + c = 5 ⇒ 8 + 2b + c = 5 ⇒ 2b + c = -3

Applying simultaneous equations: 2b + c = -3
-b - c = 1
b = -2

Subbing b=-2 into b + c = -1: -2+c = -1 ⇒ c = 1 ⇒Tn = 2n^2 - 2n + 1

Test this: T5=2(52)-2(5)+1 = 2(25) -10+ 1 = 41 ✓

Here's one for you to try:
Q. 13,15,19,25,33 are the first 5 numbers in a pattern.
(i) Follow the pattern to write the next 3 numbers.
(ii) Show that the pattern is quadratic.
(iii) Un=an^2+bn+c. Find the values of a, b, and c.

Oathkeeper

Hi I'm doing higher level maths and I was just wondering how to get good at higher maths in general I usually just barely pass maths so I'm in need of help

pinkbear

Hi Oathkeeper,
There is not just one way to get good at higher maths, but a few points are:
- I would recommend grinds and grinds schools. These can teach you much more efficiently.... you'd probably learn as much in one hours grinds / grinds school as you would in 3 hours on your own. A good grinds teacher should be able to cover almost a full topic in a class.... it might be rushed, but if you get an overview of a full topic, and see 10-12 exam questions done, you'll be in such a better position. (I know they are expensive, so it's not an option for many people, but I think they have a good pay back in terms of extra points).
- You have to start doing the exam questions early. Many teachers, unfortunately, just go by the books and don't look much at exam papers. It's only once you start doing lots and lots of exam papers that you start to see patterns emerging and you can see really quickly what they are looking for in each question.
- When you're doing your homework, if you can't do every question, really focus on the ones you can't get. The ones you got right you can forget about, but do whatever you have to do to get the other ones right. Post here and I'll help you, or send whatsapp messages to your class looking for assistance. If you are going into your leaving cert having got every homework question fully right, you are in a much stronger position.
- Studyclix is great. The paid accounts are even better as you have access to so much material. If you were revising a topic - say trigonometry - rather than wading through your book, I would recommend quickly looking at OL JC questions first to make sure you can do those, then moving onto to HL JC, and OL LC. Looking at those questions shouldn't take too long and will be a great revision of the basics, then should you move onto HL LC. Try to do a question, then click on the Marking Scheme, and so on.
- I read before that the part of the brain that deals with maths doesn't fully develop until about age 26. (I'm over 26). Certainly this was true for me. While I could manage the questions in school, and always did quite well, I didn't really understand them fully. As I got older, I was studying maths in university, but also I could understand concepts with a clarity that I didn't have when I was in school, and I think a lot of it was just due to age. So if anyone is considering studying engineering / maths / anything with a lot of maths in it, I wouldn't let the fact that you find maths difficult now put you off. It will definitely become easier in time.

Hope some of that is of use to you.
PinkBear

EireLemon

How would you go about doing part iii) & iv)? Getting rid of the 5dx in part iii) and 6 in part iv) is causing me issues.

josha1

jinx257

I know how to do calculus, how to apply the formulas etc. But I dont understand it, like where does it come from, whats behind it etc?

pinkbear

jinx257 - Answer on attached pdf.

EireLemon

josha1 wrote: »

Why do you use the differentiation formula instead of the integration formula?

josha1

EireLemon wrote: »

Why do you use the differentiation formula instead of the integration formula?

That is the integration formula. It should be in the log tables under inverse trigonometric formulae for integration.

They're both the same thing really I'm not too sure which one is in the log tables. If you want to use your formula you keep the constant outside the integration sign. The constant with negate the 1/a in front of you formula, so it ends up the same as my formula.

thetalker

Hi if you have any ideas there's a math Q I was wondering how to do.

In a private sweep 100 tickets are sold. A man buys one ticket. A prize is awarded on each draw of a ticket. Assuming replacement of a ticket after each draw, find the least number of prizes which must be awarded so that the probability of the man winning at least one prize is at least 1/4.

I checked the back and the answer is 29 but I have no idea how to approach the Q or how that was found.

pinkbear

I'm getting 28 instead of 29, and don't have time to check it fully, but I'm confident that my method is okay, so you might be able to spot my error (or maybe the back of the book is wrong). Let me know if you spot it!

---

In any particular draw the chance of him winning is 1/100. So for the probability to be 1/4 or greater....

(Chances he wins in first) + (Chances he loses first & wins in 2nd) + (chances he loses first two & wins in 3rd)+ ...... >1/4

1/100 + (99/100)(1/100) + (99/100)(99/100)(1/100) + ..... > 1/4

This is a geometric series that we don't know how many terms are in.

Sn = a (1-r^n)
1 - r
where a = 1/100, r = 99/100

Sn = (1/100) ( 1 - (99/100)^n)

---

1 - 99/100

= (1/100) ( 1 - (99/100)^n) = 1 - (99/100)^n

---

1/100

1 - (99/100)^n > 1/4

1 - (99/100)^n > 1/4
1 - 0.25 > (99/100)^n
0.75 > (99/100)^n
ln 0.75 > ln (0.99)^n

ln 0.75 > n

---

ln 0.99

28.62 > n
n = 28

pinkbear

Basically you're looking for what power of .99 (his chances of not winning) would give a value just under 0.25 but not greater than it.
.99^30=0.7513
.99^29=0.7471

thetalker

Wow thanks for the quick reply, I would never have imagined to do that tbh.

Im a bit confused as to why you're adding the probabilties though. I thought you would only do that for mutually exclusive events. I can see your finding all the possibilities that will add to 1/4 but why is what I don't understand.

I think you pretty much nailed the method though, I think you forgot to flip the inequality sign once you divided by a negative number hence n is actually greater than 28.62 not smaller.

thetalker

Would it not be a geometric sequence where n is the amount of prizes given out/ amount of times game is played and r is 99/100
So Tn=ar^n-1, where a is just 1
Like you posted that would mean were trying to find what power aka n is needed to give
99/100^n-1= 0.75 and then use ln on both sides and then approximate n-1, so that gives 29.62

Or is there a flaw to this method

Paulieniceguy

pinkbear wrote: »

Hi,
I know the leaving cert maths courses pretty well. If anyone wants help with any question, any topic, any level, just post here and I'll answer back as soon as I can.

Fair play to you for offering your help, I will be sure to let my niece know as she is finding higher maths quite difficult

pinkbear

thetalker:
Ah yes, ln .99 is negative, so I was dividing by a negative number but didn't know it! That's where I went wrong.

I'm adding the probabilities because if this line:
(Chances he wins in first) + (Chances he loses first & wins in 2nd) + (chances he loses first two & wins in 3rd)+ ...... >1/4

Winning and losing are mutually exclusive, so you add the probabilities.

Regarding your last post, where you talked about the Tn=an^n-1 method, there is a flaw with this method (I think). You are not looking for which turn has a greater than 1 in 4 chance of winning, you are looking for the sum of them, as you will only get to that turn if you have gone through all the others.

(p.s. I'm not a genius at maths by any means, just more familiar with the course than many! So I do get things wrong.)

thetalker

Ah the thing is I read that line but was confused, you see if you take the probability of winning initially, why do you add the portability of him winning and losing and etc

It feels like if someone was rolling a die to get a 6 and went

1/6 + 1/6(5/6) + 1/6(5/6)^2 etc. to calculate the odds of rolling another 6, it just confuses me because I would understand if it was a series so you had it in a way which was

1/6, 1/6(5/6), 1/6(5/6)^2 etc where we can calculate the odds of getting the the next success or loss based on the sequence.

Tbh we only recently went over this chapter so maybe I'm misunderstanding the theory itself. But I would've thought winning and losing were directly related to each other.

"You are not looking for which turn has a greater than 1 in 4 chance of winning, you are looking for the sum of them, as you will only get to that turn if you have gone through all the others."
But doesn't the term formula do that? since you multiply probabilities to get the next not add them. Looking for the sum feels confusing as like I pointed out I don't think they are exclusive. You have to do the previous one to get to the next after all.

Either way you've been a great help as I was going after the question in the wrong direction!

pinkbear

Ok, hopefully this will clarify it for you, but otherwise maybe ask your teacher.

Where you said ".... where we can calculate the odds of getting the the next success or loss based on the sequence"

the thing to remember is that in ANY go, the chances of success are 1/100. The chances of success are not changing. What is changing is your chances of getting that far in the series (Note... series, not sequence, but I digress).

E.g. if there were loads prizes, sooner or later you're extremely likely to win.

The only way you can be in the 10th draw is if you lost every one of the first 9.

So the total probability of the series is
Chances you win the first OR the second OR the third OR the fourth etc.

But the chances of you winning the second draw means that you also had to lose the first.
And the chances of you winning third draw means that you also had to lose the first and the second.
etc.

thetalker

Hmm I think I'll read over this a few more times to get it, it feels like my brain will eventually click and I'll see why.
I can't really ask for help of the math teacher as these aren't hw Q's and they're busy most days.

Since you already helped I saw a new Q today that I wasn't sure how to do, maybe you can help

"In the equation below, calculate the value of x + y

3^2x - 2^2y = 17 where x and y are natural numbers"

I was trying to use the log rules but couldn't figure out which one. I then thought I could drop the base or something but that doesn't seem possible. Do you have any idea?

pinkbear

I did it this way, as I can't figure out a way to do it neatly with logs either.

Notice that 3^2x - 2^2y is actually a difference of squares.

(3^x)^2 - (2^y)^2 = 17
(3^x - 2^y)(3^x + 2^y) = 17

As 17 is a prime number =>
3^x - 2^y = 1 and 3^x + 2^y = 17

Trying the first few numbers, and we know that x and y can't possibly be very big, we see:
3^2 - 2^3 = 1 and 3^2 + 2^8 = 17

Or by simultaneous equations: 2.3^x = 18
3^x = 9
x = 2

If you were stuck, you could also graph it on desmos or geogebra, and look through the graph until you see a natural number value of x and y.

Keem 'em coming!

Ponguin

In financial maths regarding loans, pensions etc when do you use present value and when do you use future?

pinkbear

Ponguin wrote: »

In financial maths regarding loans, pensions etc when do you use present value and when do you use future?

P means present / before / principal
F means future / after

Use F=P(1+i)^t when you want to find the future value of money, e.g. how much an investment will amount to at some point in the future. E.g. If I invest 10,000 now how much will it be worth in 5 years time? If I put in 400/month in a pension, how much does it amount to?

Use P = F / (1+i)^t when you want to find the present value of a future investment or amount. E.g. how much do I have to invest NOW so that I have 10,000 in 5 years time? If I want to get 1000/month from a pension fund what value has to be in the fund on my retirement date?

Very often the two are combined in a question, e.g. in a pension question. Someone is investing every month into a pension, then withdrawing every month from it. Use the F=.... for the first part, and P=.... for the second part.

thetalker

Ah once again that would never have crossed my mind because I was so focused on the log rules. Guess you really do have to analyze the Q. Anyway since you said keep it coming here's one my teacher couldn't do :P We thought substitution might be what was needed but it didn't seem to work.

"Let x and y have opposite signs and satisy the following equations;

x + y + xy = -2
And
x^2 + y^2 +(xy)^2 = 64

Find the numerical value of x+y"

Oh and here's another like that which also stumped us. I have a feeling we need to apply the same line of thinking as the other though.

x and y are positive integers, if
sqrt x + sqrt Y = sqrt 333, find x+y

These are probably the last Q's I'll be sending here for a while

pinkbear

Hi thetalker,

I haven't had much time, but I haven't been able to solve either of those questions. I can get the first one by popping it into desmos or geogebra or something like that - x=-1.162, y=5.62. But I'm afraid I can't figure out how you could get it mathematically.

PinkBear

DaleyBlind

Question about percentiles.
My maths book is saying two different things. For example, 20 students in a class. If I got the 5th best score on a test what is my percentile. In the example the the book, they say you count the amount that did worse than you, in this case 15. However later on in the problems there are questions on percentiles and the solutions say you count your position, in the case 16th worst.

So in the first case the answer is 1500/20 = 75% and the second is 1600/20 = 80%. Clearly, at least on is wrong. But I'm thinking that the correct thing to do is (15.5/20) x 100, because when calculating percentiles if you get the answer 15, you get the average of 15 and 16, and if you get 15.5 you move it up to 16, so the correct thing to do is put 15.5 into the formula. The inconsistency in the book has slightly confused me and I was just wondering what the correct procedure is. Sorry if anything I said is unclear because I went on for a bit.

thetalker

Thats fine, youve been a great help anyway with the solutions to the other Q's!

pinkbear

DaleyBlind wrote: »

Question about percentiles.
My maths book is saying two different things. For example, 20 students in a class. If I got the 5th best score on a test what is my percentile. In the example the the book, they say you count the amount that did worse than you, in this case 15. However later on in the problems there are questions on percentiles and the solutions say you count your position, in the case 16th worst.

So in the first case the answer is 1500/20 = 75% and the second is 1600/20 = 80%. Clearly, at least on is wrong. But I'm thinking that the correct thing to do is (15.5/20) x 100, because when calculating percentiles if you get the answer 15, you get the average of 15 and 16, and if you get 15.5 you move it up to 16, so the correct thing to do is put 15.5 into the formula. The inconsistency in the book has slightly confused me and I was just wondering what the correct procedure is. Sorry if anything I said is unclear because I went on for a bit.

Hi,

The confusion arises because there isn't an agreed on definition, and the books are inconsistent. E.g. Consise maths doesn't give formula, and active maths says that 75th percentile is upper quartile, but then goes on to say the formula to use to get percentile is:
Percentile = 100x/(total number of values)
Where x is the number of students who had a smaller score than you.
By upper quartile you get 15.5/20 =77.5
By formula you get: (100)(15)/(20) = 75

Either is fine, and unlikely to be asked, as syllabus says that you need to understand about how percentiles relate to relative standing of results only.

DaleyBlind

pinkbear wrote: »

Hi,

The confusion arises because there isn't an agreed on definition, and the books are inconsistent. E.g. Consise maths doesn't give formula, and active maths says that 75th percentile is upper quartile, but then goes on to say the formula to use to get percentile is:
Percentile = 100x/(total number of values)
Where x is the number of students who had a smaller score than you.
By upper quartile you get 15.5/20 =77.5
By formula you get: (100)(15)/(20) = 75

Either is fine, and unlikely to be asked, as syllabus says that you need to understand about how percentiles relate to relative standing of results only.

Thanks a lot! Can't say I'm huge fan of certain parts of statistics, as it doesn't follow basic logic as most of the other chapters in LC maths do. But you definitely cleared that one up for me.

Account Number

Can someone help me with part (ii) prove logbase5 24 = (3a + b) over (1-a)
when a = logbase10 2 and b = log base10 3?? I have up to logbase10 24 over logbase10 5 and am lost cos the change of base doesn't work?? Sorry about the way I laid it out in the post,have no clue where half the buttons are on a laptop keyboard.
https://scontent-fra3-1.xx.fbcdn.net/v/t34.0-0/p280x280/16468846_733399326814859_351788346_n.jpg?oh=143de0052eab1bb6fcc19e4c73f2f89b&oe=589523DD

pinkbear

Account Number wrote: »

Can someone help me with part (ii) prove logbase5 24 = (3a + b) over (1-a)
when a = logbase10 2 and b = log base10 3?? I have up to logbase10 24 over logbase10 5 and am lost cos the change of base doesn't work?? Sorry about the way I laid it out in the post,have no clue where half the buttons are on a laptop keyboard.
https://scontent-fra3-1.xx.fbcdn.net/v/t34.0-0/p280x280/16468846_733399326814859_351788346_n.jpg?oh=143de0052eab1bb6fcc19e4c73f2f89b&oe=589523DD

It's not as difficult as it first looks.

log 24 = log 8 x 3 = log 8 + log 3 = log 2^3 + log 3 = 3log 2 + log 3
log 5 = log 10/2 = log 10 - log 2 = 1 - log 2

Done

Account Number

pinkbear wrote: »

It's not as difficult as it first looks.

log 24 = log 8 x 3 = log 8 + log 3 = log 2^3 + log 3 = 3log 2 + log 3
log 5 = log 10/2 = log 10 - log 2 = 1 - log 2

Done

Sorry,may have phrased my question badly ,but doesn't this just prove log10(24) over log10(5) equals all this? I'm trying to prove the algebra equals log5(24). This is what I have. https://scontent-amt2-1.xx.fbcdn.net/v/t34.0-0/p280x280/16506834_733815803439878_740835441_n.jpg?oh=10710046270c58f6b5d46039d2ec3f86&oe=5896C980

pinkbear

It does prove it (but sorry, I didn't go quite far enough).

Log (base 5) 25 = Log 24 / log 5 = (3log 2 + log 3)/(1 - log 2) = (3a + b)/(1 - a)

Liordi

How does the 'reverse chain rule' work?
Can't seem to make sense of it..

eg a question like this.

pinkbear

Liordi wrote: »

How does the 'reverse chain rule' work?
Can't seem to make sense of it..

eg a question like this.

The reverse chain rule is used when you notice that you have the integral of
(a function) times (something that looks like the derivative of that function).
e.g. Integral of (x^3)(3-2x^4)^6 dx
The function is (3-2x^4)^6
When you differentiate this you get 8x^3. This looks like x^3 so the reverse chain rule can be used in this situation.

I had a quick look on YouTube do see if your exact question is done somewhere, are it would take so many lines to write out, that you'd fall asleep before the end! Luckily Khan Academy have the exact question done here:
https://www.youtube.com/watch?v=7FQWBCeVIJM

Work through it, and I'm happy to answer anything you're confused about (quote the time on the video where you need further clarification).

Take Your Pants Off

Would someone explain to me the difference between the hypothesis testing. In 2 diff books they used diff methods and get diff answers ?!?
Are they used for diff situations or something.
Much appreciated

Take Your Pants Off

A similar situation arises here. I don't know which one to follow or use.

pinkbear

Hopefully this might clarify some of this really tricky topic for you…. but you may still have questions at the end.

Just to start with a few definitions…..

Hypothesis: An assumption made on the basis of limited evidence. It’s used as a starting point for further investigation.
Null hypothesis: The hypothesis that there is no significant difference between specified populations. This is the ‘status quo’, the thing being stated.
Hypothesis testing means testing a hypothesis by comparing it with the null hypothesis. The null hypothesis is only rejected if its probability falls below a predetermined significance level, usually 5%.
Significance level and confidence interval and p value: If your S.I. is 0.05 the corresponding C.I. is 95%. If your P value is less than 0.05 (the S.I.) the hypotheses test is statistically significant. If the C.I. does not contain the null hypothesis value, the results are statistically significant.

There are 3 formulas for hypothesis testing which have increasing complexity and increasing accuracy.

Formula (1)
The simplest one is 1/(square root of n)
This is all that is needed to be know for OL but wouldn’t get full marks at HL.

Formula (2)
The next one is 1.96(sigma)/(square root of n)

Formula (3)
For higher level, my understanding is that the more complex formulas should be known.
Margin of error = 1.96 x (the square root of (p(1-p)/n)

You may have to choose which one to use depending on what you’re given. E.g. In worked example 5.10 & 5.11, you were given information about p and about p(hat). You could be given information about the standard deviation, sigma, in which case you would use formula 2. I think avoid formula 1 if you want to get full marks. That example you show that uses it (the drugs company producing a new pain-relieving drug one)….. is that an ordinary level book? It makes sense if it is. I did it using formula 3, and I got .8+/-0.06272, so it doesn’t change the answer to the question, it just makes the confidence interval ‘tighter’.

For any of the questions that come up, the 3 formulas should give the same answer to the question, but they may have decimal points difference, as they get more accurate.

(Just as an aside…. where does the figure of 1.96 come from?
1.96 is read from the normal distribution table. It is the figure for z is less than or equal 0.9750, as this is the probability of the figure being within 95% of the mean. Look up your z-tables….. find 0.975 and you’ll see that it’s at 1.9 on the y and .06 on the x. 95% confidence is the only one that has ever come up I think, but perhaps other levels could come up. One of your pictures is of 90% confidence. In this case you’re looking for .95 on the z table which you’ll find at 1.6 and between .04 and .05, i.e. 1.645)

pinkbear

Here's a nice challenge for anyone interested.... from last year's mock paper..... I'll put up the answer in a day or two. It's very much based on the curriculum; there are no tricks or anything in it.

Tom has to retrieve a number of stones to put them in a bucket. It takes 5 seconds to retrieve the first stone and place it in the bucket. The time it takes him to place each subsequent stone in the bucket increases by 40%. How many stones can Tom retrieve and place in the bucket in 10 minutes?

Spanish Eyes

Hi folks,

I am not taking any exams anymore but did back in the day.

Was a C grade in maths at a struggle that is, and that was O level.

I have to say I cannot remember where the scenarios outlined above, or Pythagorus' Thereom etc, ever entered my fekkin head after LC.

Where is all that stuff relevant please!

At least with languages and literature there is something to be talked about. But maths. Feck sake. Calculators mean it's all a bit of a joke now surely.

Sorry to the maths nerds.

Take Your Pants Off

pinkbear wrote: »

Hopefully this might clarify some of this really tricky topic for you…. but you may still have questions at the end.

Just to start with a few definitions…..

Hypothesis: An assumption made on the basis of limited evidence. It’s used as a starting point for further investigation.
Null hypothesis: The hypothesis that there is no significant difference between specified populations. This is the ‘status quo’, the thing being stated.
Hypothesis testing means testing a hypothesis by comparing it with the null hypothesis. The null hypothesis is only rejected if its probability falls below a predetermined significance level, usually 5%.
Significance level and confidence interval and p value: If your S.I. is 0.05 the corresponding C.I. is 95%. If your P value is less than 0.05 (the S.I.) the hypotheses test is statistically significant. If the C.I. does not contain the null hypothesis value, the results are statistically significant.

There are 3 formulas for hypothesis testing which have increasing complexity and increasing accuracy.

Formula (1)
The simplest one is 1/(square root of n)
This is all that is needed to be know for OL but wouldn’t get full marks at HL.

Formula (2)
The next one is 1.96(sigma)/(square root of n)

Formula (3)
For higher level, my understanding is that the more complex formulas should be known.
Margin of error = 1.96 x (the square root of (p(1-p)/n)

You may have to choose which one to use depending on what you’re given. E.g. In worked example 5.10 & 5.11, you were given information about p and about p(hat). You could be given information about the standard deviation, sigma, in which case you would use formula 2. I think avoid formula 1 if you want to get full marks. That example you show that uses it (the drugs company producing a new pain-relieving drug one)….. is that an ordinary level book? It makes sense if it is. I did it using formula 3, and I got .8+/-0.06272, so it doesn’t change the answer to the question, it just makes the confidence interval ‘tighter’.

For any of the questions that come up, the 3 formulas should give the same answer to the question, but they may have decimal points difference, as they get more accurate.

(Just as an aside…. where does the figure of 1.96 come from?
1.96 is read from the normal distribution table. It is the figure for z is less than or equal 0.9750, as this is the probability of the figure being within 95% of the mean. Look up your z-tables….. find 0.975 and you’ll see that it’s at 1.9 on the y and .06 on the x. 95% confidence is the only one that has ever come up I think, but perhaps other levels could come up. One of your pictures is of 90% confidence. In this case you’re looking for .95 on the z table which you’ll find at 1.6 and between .04 and .05, i.e. 1.645)

Thanks helped a lot.
I know which one to use going forward now.
The drugs one was from text and test hl. The other one was from the active maths book.
Nevertheless thanks for the help.

pinkbear

Spanish Eyes, I know you’re just trolling, but on the off chance that you actually believe what you said or if anyone else reading does, I will respond.

Studying maths trains your mind in logic, and trains your memory. People who study maths are better at puzzles, and are better able to see the connections between words and concepts. The thought process in working out a maths problem is often similar to that involved in fine your car, setting up a home network, or writing code.

So you asked where this stuff is relevant? Well without maths there would be no technology, no engineering, no computers, no mobile phones, no printing machines, very primitive buildings, no planes, no ships no cars, no statistics, no stock market, no economies, no medicines….. I can provide a more comprehensive list if you with but I’m sure you get the gist.

Calculators don’t do anything other than speed up calculations that would otherwise be tedious, allowing us to focus on the more complicated concepts behind them.

Just as you have never used maths since leaving school, I use it on a daily basis in my job and in my life. I love it, and don’t consider myself a “nerd” in any kind of a derogatory sense…. I have friends and am sociable, and well able to discuss languages and literature as you mentioned, but my favourite subject has always been maths, just as others have a preference for music or business or art. I believe maths has helped greatly develop my logical reasoning, and memory, and I have been able to succeed at a great number of technical challenges over the years thanks to these skills. (Oh yes, not only do I love working with maths, but I earn good money at it too!)

sunny2004

I think pink bear is doing an amazing service to the community here.

That's coming from someone who is not doing any exams, I simply think she/he is very good for giving their time and knowledge.

BRAVO !!!

pinkbear

sunny2004 wrote: »

I think pink bear is doing an amazing service to the community here.

That's coming from someone who is not doing any exams, I simply think she/he is very good for giving their time and knowledge.

BRAVO !!!

Aw, thanks very much for the praise!

jinx257

Matrices...

I always found these easy and was able to do any problems and get full marks.... BUT what are they, what is their use and function? I never understood that...

pinkbear

jinx257 wrote: »

Matrices...

I always found these easy and was able to do any problems and get full marks.... BUT what are they, what is their use and function? I never understood that...

You do know that matrices are completely gone from the course now?

But to answer your question some uses of matrices are:
- in science and industry to track, record and display the results of research.
- In the study of electrical circuits (I've used them in Kirchoff's laws I think, and calculating battery power output)
- In quantum mechanics
- Encryption
- Displaying 3D images
- In robotics to calculate movements

I know this answer is a bit vague, as I'm not sure exactly how they are used in many of these applications, just that they are used and make the calculations much simpler.

evolving_doors

Think of each colour pixel on your TV/ phone screen as being represented by a number.
123
456
789
You can apply preset algorithms to manipulate the picture. A Basic manipulation would be to turn your image upside down or say to rotate from landscape to portrait would make it go to
369
258
147
The code can be found here, its a pretty basic interview question for graphics coders http://techieme.in/matrix-rotation/


Another use is algorithms for page ranking by Google (so you get to the 'top hit' website for your inputted word in the search bar).
Consider each number in the matrix as a probability of going to a certain page (transition matrix)... have a look at the first 4 pictures here for a better explanation http://www.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html
Obviously these matrices would be MASSIVE as there's lots of sites out there with your 'key term' you want explored. But it's just pure numbers... messing with numbers is pretty easy stuff for a computer.

Another one is calculating probabilities as to an eventual outcome (as the number of iterations/ moves increases then a certain outcome is more likely)... markov chains

Strange it's not on the course....

ImaCabbage

Hello, I can't get my head around using "95% confidence intervals", i.e. 2015 P2 Q2/statistics. The notes provided in our book are very vague and the e-xamit solutions give very little guidance as well.

Any strong notes/advice on this specific area?

thetalker

Yeah thats in the supplementery material, I never really liked statistics but there's a formula you can just learn off.

Its 1.96 times the standard error(standard deviation over root n), you then add or subtract that from the mean to get the 95% confidence interval. same idea for a 5% margin of error.

Take Your Pants Off

Quite short pointing out needed, I get everything bar where the 4 came from in the (x^2+jx+4) is it the because you need 20 for the equation to match the 20 in the f(x). So you have 5 and you need to decide what by 5 will give you 20. Might be completely wrong but cannot get my head around it. The rest seems grand to me