How strict are HSC Markers? (1 Viewer)

[coyney]

Does anyone know how strict HSC markers are for Mathematical Induction Proof, more specifically the wording part.

For example would this be acceptable

Q) Prove 2^(3n) - 3^n is divisible by 5 for n>= 1

Let n = 1
2^3 - 3 = 5M
5 = 5M
1 = M
Therefore true for n=1

Let n=k
2^(3k) - 3^k = 5Q
3^k = 2^(3k) - 5Q

Let n = k+1
2^(3k+3) - 3^(k+1) = 5P
...
... rest of working out
...
5[2^(3k)] + 15Q = 5P
2^(3k) + 3Q = P

Therefore since 2^(3n) - 3^n is divisible by 5 for n=1, n=k, n=k+1
Then 2^(3n) - 3^n is divisible by 5 for n>=1

 

[asianese]

Does anyone know how strict HSC markers are for Mathematical Induction Proof, more specifically the wording part.

For example would this be acceptable

Q) Prove 2^(3n) - 3^n is divisible by 5 for n>= 1

Let n = 1
2^3 - 3 = 5M
5 = 5M
1 = M
Therefore true for n=1

Let n=k
2^(3k) - 3^k = 5Q
3^k = 2^(3k) - 5Q

Let n = k+1
2^(3k+3) - 3^(k+1) = 5P
...
... rest of working out
...
5[2^(3k)] + 15Q = 5P
2^(3k) + 3Q = P

Therefore since 2^(3n) - 3^n is divisible by 5 for n=1, n=k, n=k+1
Then 2^(3n) - 3^n is divisible by 5 for n>=1

Some of your working is incorrectly worded or deduced.

You should say:

LHS = 2^(3) - 3 = 8-3 = 5, which is divisible by 5, so the statement is true for n=1. By writing 5M immediately you are assuming that the left hand side is divisible by 5, you must deduce this - the fact that M=1 is irrelevant here.


Then you should say that Q is an integer, whilst saying: we assume the result for some n=k (or something to that degree).

For the next bolded bit, 5(2^(3k)) + 15Q = 5(2^(3k)+5Q) which is divisible by 5 since 2^(3k)+5Q is an integer.

For the conclusion, say:

Hence proved true by (mathematical) induction for n>=1.

 

[pheelx3]

Well... im not too sure about that question, but from the science teachers that I've asked, and they do HSC marking...
They say in trials they are as harsh as possible so that you can differentiate between shit and good students but in the HSC you try be as lenient as possible.
Or well that's what i've heard so yeah.