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# Mathematics examination paper from 1970 watch

1. I thought some of you might enjoy having a go at the A Level Special Paper from 1970. This was the equivalent of the AEA and was designed for the top 15% of A Level candidates. You had to answer 8 questions out of 10 in 3 hours.

2. Wow, thanks for posting.

Really does show how the syllabus has changed. Sure, A level Maths can be difficult. But compared to 1970, its been dumbed down greatly.. =|
3. Wow nice nice post dude,
sure a lot of people will be interested in this!

Think i might give it a go see what i get, you get mark scheme?
4. This is pretty tough for A level standard. Guess it really was harder back in the day
5. (Original post by gummers)
Wow nice nice post dude,
sure a lot of people will be interested in this!

Think i might give it a go see what i get, you get mark scheme?
No mark scheme I'm afraid. I'm sure the TSR team can create one. Use spoilers though!
6. (Original post by coldfusion)
This is pretty tough for A level standard. Guess it really was harder back in the day
(Original post by Shayke)
Wow, thanks for posting.

Really does show how the syllabus has changed. Sure, A level Maths can be difficult. But compared to 1970, its been dumbed down greatly.. =|
This isn't a-level standard, this is more comparable to STEP.
7. mark schemes?

edit: oh well. I would post what I think are the correct answers to the ones I can do but I don't want to get them wrong and look stupid lol
8. 2. looks easy
Spoiler:
Show
Base case 1=1

Inductive hypothesis n=k

to deduce n=k+1
(multiplying by e, and using obvious facts like e>2)

Wait a minute I will post the next one. For all values, looks like they don't want induction, gay. Power series I'm thinking. Yeah, that could work.
9. It doesn't say integer values of x simp.
10. (Original post by around)
This isn't a-level standard, this is more comparable to STEP.
Yeah looking at it now it does seem like STEP II standard
11. Rep to anyone who can answer all them questions!
12. Yes I did realize that before you said that.
13. Okay 2. the correct way
Spoiler:
Show

then

which is obvious because I said so

Well, when x=0 then 0=0 as required

if x>0 then cleary, the sum of positive numbers must be positive

if x<0 ?
14. Dibs on question 1.
15. Question 1 the first part, looks weird. Maybe, I should read about depressed cubes.

Although, the next part seems to be able to be done by just using the old sum of roots method.
16. I wouldn't be able to answer it. I wouldn't be able to answer one from nowadays either.
17. 2
a)
e^x >/= x+1
sketch y=x+1
sketch y=e^x
intercept at (0,1) since e^0 = 0+1
for x<0 d(e^x)/dx < 1 hence for all x<0 e^x is always grater than y=x+1
for x>0 d(e^x)/dx >1 hence for all x>0 e^x is always greater than y=x+1

don't know if it counts as proof...?
same idea for part B)
but again, will only suffice if my method of 'proof' counts

for ii
a = 3-2*(epsilon)
b = c = epsilon
so for maxima: (a^2+b^2+c^2) < 9
and for minima: (1+1+1) = 3
so 3<or=(a^2+b^2+c^2)<9
I'm geussing that derivatives must be used to show that these are the maxima/minima but I cba
something like that methinks
18. (Original post by Simplicity)
Okay 2. the correct way
Spoiler:
Show

then

which is obvious because I said so

Well, when x=0 then 0=0 as required

if x>0 then cleary, the sum of positive numbers must be positive

if x<0 ?
taylor/maclauren series aren't on A-Level...
19. (Original post by jj193)
taylor/maclauren series aren't on A-Level...
they were back then! but that isn't the approach expected ... i looked at gradients too

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