Help with a maths test!

Eccentric Toast

Hi All,

Have a maths test tomorrow morning but the lecture wont tell me what topics are on it and wont open his notes for me. It is a repeat of a test I missed earlier in the year due to personal circumstances. I have the previous paper here (See attachment) but don't know how to do the majority of it. Any help at all would be extremely appreciated.

Thanks

.E_C_K_S.

For Q4, the composition of a function is given by (f ∘ g)(x) = f(g(x)).
So you have your g(x)=2x+1.
so sub x=2x+1 into the following f(x)=(x+1)^2 and you get f(g(x)).
Just use this for the other two,it should not be too hard.

Sorry about the rest, wouldn't know much about it maybe others will help ya good luck!

Eccentric Toast

Every little helps!
Thanks!

TouchingVirus

Looks very much like the sort of thing you'd see on a computer science course


Q5
If A and B are two independent events, the probably of both occuring is equal to the product of the possibility of A occuring and B occuring i.e. P(A).P(b)

The probability of at least A or B hitting the target is P(a)+P(b). But that's only because it said at least one of them hitting the target. If it said the probability of only 1 hitting the target then that's P(a)+P(b) - P(A and . I might be wrong on this one, been a while since I did probability


Q6
The degree of a vertex is the number of edges it has attached to it. So the degree of a is 4, b is 3 etc. I don't know the handshaking theorem to test if you are right, google is your friend

Q7
A graph has an Euler trail/path if you can visit each edge exactly once (so no doubling back). Picture it like this: If I gave you a pencil, and told you to make it touch paper only once and never re-draw over the same line, can you draw this graph? If you can then it has an Euler path. An Euler cycle is where a graph has an Euler path and you can start and end on the same vertex. So if a graph has an Euler cycle it has an Euler trail/path, but not all graphs with trails/paths have a cycle (because you must end on the same vertex). Help yourself, google Euler Trails and Cycles to see how to figure out if a graph has one (you're not expected to try every way to draw a graph i.e. an exhaustive test) I'll give you a hint - it's something to do with the degree of each vertex

Q9
A bipartite graph is a graph where you can split the vertices into two sets, where each vertex is set 1 is only connected to a vertex (or vertices) in set 2. So no vertex in set 1 can connect to another in set 1, and no vertex in set 2 can connect to another in set 2.

Again, google this for further understanding, it's all out there and none of it is incredibly complex

Eccentric Toast

Exactly the sort of thing you would see on a computer science course!

TouchingVirus

Eccentric Toast wrote: »

Exactly the sort of thing you would see on a computer science course!

You should have went to more lectures :P Updated my previous post with some tips

.E_C_K_S.

Ok maybe for Q1:
( cardinality is just the NUMBER OF numbers in a set)
i) I won't have a go for the first part
ii){1,2},{1,3},{2,3} are all subsets of {1,2,3}
iii)(a,b) could = (2,3),(3,2),(4,1),(1,4)

I think I'm right anways?!:p