x Turn on thread page Beta
 You are Here: Home >< A-levels

# Current Year 13 thread Mark I (2014-2015) watch

1. (Original post by Bude8)
I'm gonna be honest, not exactly sure what a tetrahedron looks like like fudge

Just looked it up, makes a bit more sense now!

Vector product is, but there's a way of remembering it. You still need to look out for minus signs, so many **** ups happen there lol

The way to remember it:

Let's take the term, to get it, write the v and w column vectors next to each other, and cover the first row of it with your finger. Then you make a diagonal 'cross' between v and w, from top left to bottom right. Repeat for the next term - but the order is important; is the x component (first row) of the cross product. Then for the y component (second row), you cover the second row of v and w and make the cross again, remember the order is important!
Don't you mean v1w1.

Sounds like matrices work, covering up with the minds eye
2. (Original post by L'Evil Fish)
Don't you mean v1w1.

Sounds like matrices work, covering up with the minds eye
Yeah, spotted my mistake and already edited it to make the correction!

So many places to mess up when you're doing vectors/planes
3. (Original post by Red Fox)
Long time no see.

(I don't think we've actually talked that much but I just remember the Peppa Pig avatar)
I've been so busy with A2/UCAS

How have you been?
4. (Original post by Bude8)
Yeah, spotted my mistake and already edited it to make the correction!

So many places to mess up when you're doing vectors/planes
Yeah, I couldn't answer a 7 marker on my paper because I didn't know what it was asking

It was annoying because I found out after what they wanted and it was just so easy
I've been so busy with A2/UCAS

How have you been?
I'm good, UCAS is like a distant memory for me now.

Which A2s are you doing?
6. (Original post by L'Evil Fish)
Yeah, I couldn't answer a 7 marker on my paper because I didn't know what it was asking

It was annoying because I found out after what they wanted and it was just so easy
One of the best mathematicians in the year, some Chinese guy, didn't get an A* in A2 Maths (we do A2 in one year if you're doing FM). He made mistakes like reading as derivative and not inverse function
7. (Original post by Bude8)
One of the best mathematicians in the year, some Chinese guy, didn't get an A* in A2 Maths (we do A2 in one year if you're doing FM). He made mistakes like reading as derivative and not inverse function
That's what we do (although I did mine in Year 11, resat C3 in Year 12, and doing all of FM this year)

f'(x) is derivative though wut, how could it be inverse hmm
8. (Original post by L'Evil Fish)
That's what we do (although I did mine in Year 11, resat C3 in Year 12, and doing all of FM this year)

f'(x) is derivative though wut, how could it be inverse hmm
Isn't f'(x) used to denote inverse function sometimes...?
9. (Original post by Bude8)
Isn't f'(x) used to denote inverse function sometimes...?
f^-1(x) would always be the inverse on an A-Level exam.
10. (Original post by Bude8)
Isn't f'(x) used to denote inverse function sometimes...?
Didn't know that haha
11. (Original post by Red Fox)
f^-1(x) would always be the inverse on an A-Level exam.
(Original post by L'Evil Fish)
Didn't know that haha
Ah, see what Red Fox said. That's what I meant - he got the two mixed up lol
12. (Original post by Bude8)
Ok, forgot to tell you this but:

My method for the volume is correct but you need to multiply it by 1/3 as well, not sure where that comes from...
Duuuddee, I need help with proof by induction!

I understand the process of 1. Proving it for one case, 2. Making an assumption say: (n=k and 2k+1 = 2m) and using the induction step (k+1) but how do you PROVE it? Is it supposed to end up looking like the assumption?
13. (Original post by Princepieman)
Duuuddee, I need help with proof by induction!

I understand the process of 1. Proving it for one case, 2. Making an assumption say: (n=k and 2k+1 = 2m) and using the induction step (k+1) but how do you PROVE it? Is it supposed to end up looking like the assumption?
You assume it's true for n=k

Then you add on the next term in the sequence and show that if it's true for n=k then it must be true for n=k+1

You then show it's true for some number (e.g. 1) therefore it must be true for all integers greater than 1.
14. (Original post by Princepieman)
Duuuddee, I need help with proof by induction!

I understand the process of 1. Proving it for one case, 2. Making an assumption say: (n=k and 2k+1 = 2m) and using the induction step (k+1) but how do you PROVE it? Is it supposed to end up looking like the assumption?
Depends on the type

If it's a summation you have what k+1 should look like. Then you prove it by doing k + the next term and show they're equivalent

For a multiple, you show k + next term is divisible as well, or k - term before

So it depends on those
15. (Original post by Red Fox)
I'm good, UCAS is like a distant memory for me now.

Which A2s are you doing?
Econ politics and ICT

You?
16. (Original post by Red Fox)
You assume it's true for n=k

Then you add on the next term in the sequence and show that if it's true for n=k then it must be true for n=k+1

You then show it's true for some number (e.g. 1) therefore it must be true for all integers greater than 1.
I get that. I'm not sure as to how you show it's true for n=k+1. Is it a matter of subbing k+1 into the assumption? Or are you using k+1 to get to the assumption somehow?

I'm sorry if this question is too vague maybe I should use an example from an Advanced Higher past paper?
Econ politics and ICT

You?
Maths, FM, Phys, Chem
(Original post by Princepieman)
I get that. I'm not sure as to how you show it's true for n=k+1. Is it a matter of subbing k+1 into the assumption? Or are you using k+1 to get to the assumption somehow?

I'm sorry if this question is too vague maybe I should use an example from an Advanced Higher past paper?
No you would add on the next term in the sequence and then rearrange it to give the same expression that you originally had but instead of k it now says k+1, feel free to post a question.
18. (Original post by Princepieman)
Duuuddee, I need help with proof by induction!

I understand the process of 1. Proving it for one case, 2. Making an assumption say: (n=k and 2k+1 = 2m) and using the induction step (k+1) but how do you PROVE it? Is it supposed to end up looking like the assumption?
Ok so step one you know, proving for n=1 or n=0 occasionally. Do you understand how the concept of induction works? It's a bit like dominoes - you knock over the first one, it works - you knock over the kth domino and it will still knock over the ones after it, so if you knock over the k+1 th domino it'll still work.

Step 2.
Assume true for n=k where k is some number, so you rewrite what you are trying to prove but substitute n for k. You will need your assumption, or some rearranged form of it in

Step 3.
Prove for n=k+1, substitute k+1 wherever you see n, and try to manipulate it. You will need your previous assumption.

So let's look at a question:

Step 1. Prove for n=1, rather trivial, just show LHS = RHS

Step 2. The assumption:

Step 3. Prove for n=k+1

At this point there should be an obvious substitution to make - then after that you need to try and show LHS = RHS. Give it a go yourself A general hint is to only work on one side of the equation at any time.
19. (Original post by L'Evil Fish)
Depends on the type

If it's a summation you have what k+1 should look like. Then you prove it by doing k + the next term and show they're equivalent

For a multiple, you show k + next term is divisible as well, or k - term before

So it depends on those
Ah right, that makes sense. So you have an idea of what k+1 looks like and you use the next term in the sequence to arrive at what you believe k+1 to be?
20. (Original post by Princepieman)
Ah right, that makes sense. So you have an idea of what k+1 looks like and you use the next term in the sequence to arrive at what you believe k+1 to be?
Yeah so say it's

Prove

Sigma r (from r =1 to n) = 1/2(n)(n+1)

Do for n = 1
Then assume true for n = K and you'll have a statement
Then if true for n =K, assume try for n=k+1 and replace all the ks with k+1

Prove directly:
Do Pk + (k+1)th term and then make it match the Pk+1

And that's it done

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 10, 2015
Today on TSR

### How do I turn down a guy in a club?

What should I do?

Poll

## All the essentials

### Student life: what to expect

What it's really like going to uni

### Essay expert

Learn to write like a pro with our ultimate essay guide.

### Create a study plan

Get your head around what you need to do and when with the study planner tool.

### Resources by subject

Everything from mind maps to class notes.

### Study tips from A* students

Students who got top grades in their A-levels share their secrets