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Mathematics examination paper from 1970

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.

Question 1.JPG

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Reply 1

Mr M

Study Forum Helper

Reply 2

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.. =|

Reply 3

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?

Reply 4

coldfusion

This is pretty tough for A level standard. Guess it really was harder back in the day

Reply 5

Mr M

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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!

Reply 6

around

coldfusion

This is pretty tough for A level standard. Guess it really was harder back in the day

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.

Reply 7

Tallon

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 :colondollar:

Reply 8

Simplicity

2. looks easy

Spoiler

Wait a minute I will post the next one. For all values, looks like they don't want induction. Power series I'm thinking. Yeah, that could work.

Reply 9

Mr M

Study Forum Helper

It doesn't say integer values of x simp.

Reply 10

coldfusion

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

Reply 11

Of the Standard of Taste

Rep to anyone who can answer all them questions!

Reply 12

Simplicity

Yes I did realize that before you said that. :o:

Reply 13

Simplicity

Okay 2. the correct way

Spoiler

Dibs on question 1.

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.

Reply 16

#Limabean1

I wouldn't be able to answer it. I wouldn't be able to answer one from nowadays either.

Reply 17

jj193

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