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hi markosheehan

For part 2:

As you want dA/dt I would work with dV/dt = dV/dA . dA /dt

As D = 2 when H = 2. => r = 0.5h.

Express both V and A in terms of h and eliminate h to get V in terms of A.

Differentiate that.

Bob

hi Migael

Welcome to the forum.

I have added

`[math] tags[/math]`

to post 1 so it shows as a matrix equation.

As the 'vectors' are 2 by 1 this means that T is a transformation matrix 2 by 2.

Only knowing how one vector is mapped is insufficient to determine the four elements of T.

Bob

hi Mandy,

I have started the process of registering as a teacher for the functional skills test. It will take a few days for this to complete. I'll let you know when you can have a go at the test.

Bob

hi Mandy

Mandy wrote:

so which one do you or Steven B think I should do then ?

I wish I knew the answer to this. but I don't Have a look at each course and see what existing students are saying. Decide what features you think are important (eg. good tutor support) and view some sample materials. When you think you're ready to sign up to a course, post here first so that the MIF community can look in detail at that course and give a view on whether it is worth it.

Bob

hi numquester

Think about how you would add two fractions.

This is what you have done:

This isn't correct. You have to put both fractions over a common denominator and then just add the tops:

So in the formula multiply the first fraction top and bottom by 4a

Hopefully you can see how this works now.

Bob

hi Mandy,

Do you mean a course of instruction that you pay for with an tutor and assignments etc? I cannot recommend any because I have never used them. I taught GCSE maths for many years and if I encountered a maths topic that I didn't know, I would get a book and teach myself. Steve thinks you have tried ICS learn in the past. If so, how did you find it?

I used google to search for courses. My search term was "review of on-line maths learning courses UK". That will give you a long list of possible courses. Maybe there is one amongst them that will suit you.

I spoke to my school's exam officer. She said the school does not add any extra charge on top of the exam board's charge for external candidates. She thought it would be difficult to get extra consideration for special needs as you have no 'paperwork' from a teacher that shows your difficulties.

She also recommended having a look at EdExcel's **Functional Skills** course. There are two levels of test and these can be taken on-line. She said these are more suited to post 16 students. Here is a link to the page :

http://qualifications.pearson.com/en/qu … kills.html

There is a pre-course assessment that might be useful to do. I tried to do it myself but you have to have a teacher register a 'class' first. I should be able to do that if you are interested.

Are you going to try the questions that SteveB and I have set or have we wasted our time?

Bob

hi Mandy Jane,

Steve and I have been making up questions ourselves, based on what we know of GCSE foundation. It sounds like you would prefer actual past exam papers. I have every paper June and November from 2004 to 2009 so I have plenty for you to try. The specification has changed but it's not going to alter what sort of questions you are asked.

So, would you like me to email you a paper to try? You would need to print it and then you can write your answers straight on the paper. There will be bits you can do and get correct and some that you try but get wrong. There may also be bits that you don't know how to do. But it will identify what you need to be taught.

I don't know of a good on-line course that you pay for. They may exist but I'm not aware of any. If you track one down, don't commit to any payments before posting to us what course you're interested in. There are some that are a waste of money and I wouldn't like you throw away money on this.

Post back or email if you want a paper to try.

Bob

hi Mandy and others following this thread.

So we can keep better track of the questions set, I have changed the numbering of Steve's question as follows:

G1 means it is from the G1 section of the specification. G1A means it is the first question set by anybody on this topic. AS it has 4 parts I have called them G1A1, G1A2, G1A3 and G1A4. Hope that is not too complicated.

Now for some from me:

G1B. Draw a line exactly 6 cm long. Label one end point P and the other Q (PQ = 6 cm). Use a protractor to make an angle of 90 degrees at Q and mark a point R so that QR = 8 cm and angle PQR = 90.

Join P to R to make a triangle PQR with vertices P, Q, and R.

Measure the length of PR. Measure the size of angle RPQ. Post back your answers.

G1C. Draw a circle, centre C, with radius 5 cm. Mark any point on the circumference and label it L. Keep the compass set at 5cm; put the point of the compass at L and draw two arcs**, to cut the circumference at M and N. Check that LM = 5 cm and LN = 5cm. Now move the compass point to M and draw an arc, cutting the circumference at J. Check that MJ = 5 cm. Now move the point of the compass to J and make an arc that cuts the circumference at K. With the compass point at K make an arc that cuts the circumference at G. You should now have six points around the circle, L, M, J, K, G, N. They should be equal distances apart. (Check this.) Join them to make a polygon LMJKGN. What is the name of this polygon? Measure angle CLM. Now angle JCK. How long is the line JN? How long is the line JG? What is the special name for triangle CGN. Please post all your answers.

Bob

** The word arc isn't on the list but you'll need it anyway. It means a curved line that is just part of a circle. Circumference is the name a curved line that goes round in a circle. You could also call it the edge of the circle or even its perimeter.

hi Mandy,

Mathegocart has given you a link to EdExcel's entry charges for 2016. It was £16.50 for maths GCSE. It'll probably be more by 2018. You don't have to pay anything now; when you put in your entry you pay at that stage. As an external candidate the school may also make a charge for handling your entry and the extra admin costs for them. I'll try to find out and let you know soon.

There are two other GCSE exam boards in the UK. As there is keen competition between them charges won't differ much.

At this stage don't worry about entry costs. Let's get going with the work. You haven't replied to my post about G1 geometry yet. Look again at post number 1877.

Take care that you don't miss posts on this thread. After you make a post there may be several replies. You need to scroll back and read them all.

Bob

Hi Mandy

I've copied the EdExcel content list for foundation level into a word document. I'll attach it to an email for you. There are 94 separate topics under 6 headings: number; algebra; ratio; geometry; probability; statistics. Each topic is given a code such as N1, S3 and so on. Between today and June 1st 2018 there are 511 days so that works out at about 5 days to do each topic allowing a bit of spare time for holidays etc. That's quite a pace for you and you can see there's no room for slacking.

You need to decide for yourself what time of day and which days you are going to spend on this. If you post back with when you'd like to do lessons on-line I'll see if I can meet that. In the past we made best progress when we were on-line at the same time and therefore able to have a post to-and-fro.

These content lists always seem to start with 'number' and we seem to get bogged down in some tricky calculations. How about starting with something else such as geometry? There'll still be some sums; that's inevitable with maths; but at least you'll be getting some pictures to go with the work and that may help. And it'll help to give you some early success.

The first geometry topic, G1, is 'use conventional terms and notation: points, lines, vertices, edges, planes,

parallel lines, perpendicular lines, right angles, polygons, regular polygons

and polygons with reflection and/or rotation symmetries; use the standard

conventions for labelling and referring to the sides and angles of triangles;

draw diagrams from written description

You'll need a sharp pencil, a ruler, a compass and a protractor plus some plain A4 size paper.

Have a look at that list and post back with any of those words that you don't know. Then I'll set you some drawing exercises.

Bob

ps. I see you have posted while I was typing this. I'll have a look on Amazon and post again.

hi Mandy Jane,

Happy New Year!

In the past you started with great determination but after a few weeks stopped posting and so progress ground to a halt. As you know there's a lot to learn. Pupils between 15 and 16 typically get 3 lessons a week and 2 homeworks over a 2 year period. I think you'll need more than that as you've been out of touch with school for so long.

The exam structure changed yet again in 2015. Here's a link to the latest specification from EdExcel

http://qualifications.pearson.com/conte … cation.pdf

There are two levels (higher and foundation). It used to be the case that the maximum grade achievable from foundation was a 'C'. They seem to have dropped letters for grades and substituted numbers. It looks like the old grade C is now called grade 5. The space for grade descriptions is empty at the moment so I'll have to do some more checking about this. Assuming I've got it right then the level to go for is foundation. There are 3 exam papers.

The spec. lists everything you have to know for both levels with the harder stuff in bold print. I don't think there is much difference between the courses offered by the three exams boards because they are restricted by the National Curriculum and by the exam quality control watchdog.

To take an exam you have to register at an exam centre. Secondary schools are always centres but usually only with one exam board. They will charge to register you as an external candidate. If we can prove you have learning difficulties then some extra facilities are available eg. large print papers, coloured overlays, even extra time and a writer if you have difficulty with reading and writing. But you have to be able to prove that any of these things is justified. The school where I taught has a very strong special needs department and I did speak to them last time about this for you so there would be some advantage registering with them. It's no further in travel terms than the place where you were registered when you last had a go at the exams.

This thread is full of study suggestions and help with topics. As bobbym has said it would be a good idea to go over all of that first. I will try to help you with this, but I would like a promise from you that you'll maintain your efforts and not give up after a few posts.

Best wishes,

Bob

hi popotamian

Welcome to the forum.

Mathematicians have a symbol for infinity and use it in certain topics but have found it is best not to regard it as a number, as it doesn't obey the usual rules. Your question is a good demonstration of this. Here's some more:

∞ +1 = ∞

∞ x 5 = ∞

∞ x 7 = ∞

∞ /∞ = ????

Bob

Use the theorem to write down the first three terms of the expansion. Show that term two is independent of n and that later terms are sufficiently small that they will only affect the fourth decimal place and beyond. So you will have an approximation for the expression that is valid to 3dp.

Bob

Here we go......

Then you can use the general binomial theorem https://en.wikipedia.org/wiki/Binomial_ … al_theorem

Bob

hi

I did a quick 'experiment' with n = 1,2,3 ...10 and found the result always had a whole numbered part that is easy to compute from n, and the same decimal digits for the first three places. [bobbym: I did some EM. Hope you arte proud of me.]

So an answer is easy to calculate. But how to prove it? Working on it .......

Bob

hi markosheehan

Normally you might expect the probability of flipping a head to be 1/2. If it is biased, that means the coin doesn't behave like this, but, rather, has a probability of a head that is not 1/2. eg it might be P(head) = 0.75 and P(tail) = 0.25.

We are told to use 'p' for this probability.

For each head the probability is p, so for m heads we need p^m and (1-p)^(n-m) for all the tails. In addition, there are many sequences that give these results. eg. If n = 5 and m = 2 then we could get HHTTT or HTHTT or HTTHT or HTTTH or THHTT or THTHT or THTTH or TTHHT or TTHTH or TTTHH. That's ten ways altogether. You can get this number without writing out all the possibilities by calculating 5C2 = 5!/(2!.3!) = (5 x 4)/(2 x 1) = 10.

You'll find some analysis of this here: http://www.mathsisfun.com/data/binomial … ution.html but you'll have to use P(head) = p not 0.5

Bob

hi They,

Welcome to the forum.

I've thought about this since I read it this morning and I had a look on a physics forum. Work done is defined as force x distance moved. For the up move that's the same as gain in potential energy and is given by the formula mgh = mass x acceleration due to gravity x height. The horizontal movement is much more complex. As the velocity is constant there's no force of acceleration and friction between the ground and the man's shoes has no movement and so is zero. That might suggest that no work is being done.

But that cannot be correct or we'd all be able to walk for ever. Every muscle involved is doing work, moving tendons and thence bones. Also walking requires an increased heart and breathing rate so more work there. The amount of work is impossible to calculate. I suspect that even with a treadmill and a mask to measure oxygen intake only a rough approximation is possible.

Try this; walk normally for a while. Then repeat but this time raise your knees as high as you can for each step and swing your arms wildly. Feeling any different? The second involves much more work, but how would you compute this?

If this is homework ask your teacher about the man's build. leg length, muscle tone, fitness regime etc etc. That should keep them happy.

Bob

ps. I've looked at your other post but I cannot understand what the first question is asking for. Something odd about the notation when I view it. Sorry.

??? Why is the bit about Eratosthenes 'insane'? If the Earth is a sphere down is towards the centre of the Earth. So all that water is being pulled down equally. There is no point on the canal that is 'lower' than any other. Here's a non scaled picture:

Where would anyone put the locks?

As for the angle: 100/24000 times 360 degrees = 1.5 degrees at the centre. That is also the angle between a tangent at one end of the canal and a tangent at the other.

Bob

Sorry but I do not know what you want to be proved. What question?

Have a look at this page: http://www.mathsisfun.com/data/function-grapher-old.php

Enter a function (say 2x) and a second function, x/2. Try out different pairs such as 5x and x/5; x^2 and sqrt(x); sin(x) and asin(x).

What do you notice?

Bob

hi JadeH

If the Earth is a sphere then the gravitational pull is towards the centre. So the canal could be curved and yet not experience any adverse flow towards the end points. Try thinking of the Atlantic and Pacific oceans as the end points of a 'canal' at Cape Horn. No locks there.

Bob

ps. Eratosthenes worked out the curvature of the Earth in 3rd century BC https://en.wikipedia.org/wiki/Eratosthe … cumference

It is how an inverse function is defined. Say the function does this:

Domain Range

3 ------------------------> 7

8 ------------------------> 2

9 ------------------------> 0

Then the inverse function will be:

Domain Range

7 ------------------------> 3

2 ------------------------> 8

0 ------------------------> 9

So you just have to look at which number maps onto which and reverse the direction of the mapping.

Please post a question and hopefully it will become clearer.

Bob

hi

It is a second function that maps each element in the codomain back to the element in the domain.

eg. If f(x) = 2x then the inverse function is x/2

eg. If g(x) = sin(x) then the inverse is asin(x) or sometimes written arcsin(x)

Bob

hi iamaditya

**Welcome to the forum.**

MIF created the forum and is its administrator. bobbym was given administrator status by him, as he wanted help dealing with some problems with running the forum. Moderators can do some things to help too, such as remove people who abuse the forum.

When I first joined there were other categories of member. After a certain number of posts you were automatically 'promoted' to the next category. This encouraged members to make loads of posts just to 'improve' their status. Personally, I'm glad that has been dropped from the new forum as I think it's the quality that counts not the quantity.

A while back there were lots of spammers and trolls who joined the forum and that's when I was made a moderator to help with removing them. After bobbym was made an administrator this problem began to go away because he had some clever computer tricks to prevent it. Nowadays the problem seems to be a lot less so it's unlikely MIF will want to make any new moderators. I hope I'm not tempting fate

Bob

hi Zeeshan 01

Q1. I think this question is asking for the definition of a function. You have the answer in your other post http://www.mathisfunforum.com/viewtopic.php?id=23613

I'll try to answer that question here. You already have met the word domain. X is the domain. And Y is the codomain (or range). The rule tells you what to do to any 'x' in order to get 'y'. eg the rule could be 'square x' or find the 'sine of x'.

Q2. I'm not sure what word is expected here. If you look here: http://www.mathsisfun.com/sets/function.html you'll see that y could be called the output of the function. But you'll see, further down the page, other possible answers: 'range element', 'dependent variable', 'value of the function'. I have also heard it called the 'image' of x.

Q3. I f you go to this page: http://www.mathsisfun.com/data/function-grapher.php, you'll find a function grapher. Choose values for 'a', 'b' and 'c' and you'll get a graph with either a maximum value or a minimum value (n shaped or U shaped curve). Experiment with different values and you should be able to find that changing just one of the values switches the graph from maximum to minimum.

Q4. Here the value of y never changes whatever you choose for x. I'd call that a 'constant' function.

Hope that helps,

Bob