# Old Exam Questions #7

First, my solution to Old Exam Question #6

I *think* I have a nice proof without words. I’m probably wrong. Incidentally I was wrong with last month’s solution. The corrected version is online now. I put the right angle in the wrong place. Oops.

Aaaanyway, here’s the next one from a Cambridge Maths Exam from 1918:

:

# Concentric Circle Problem

Someone at work showed me this today. I like it!

# Old Exam Questions #6

First, my solution to Old Exam Question #5

(Click to enlarge)

The only annoying part was the counter-intuitive naming of the diagram (OXZY) Supposedly to make it clearer once they throw in the axis.

Did you solve it differently?

Here is the next question, from a 1966 O Level maths exam:

# Old Exam Questions #5

First, my solution to Old Exam Question #4

(Click for enlargements)

You may notice I couldn’t see the wood for the trees in my original solution. I got an idea stuck in my head and ran with it, which is fine (and was fun!), but there was a much, much quicker way to do it (there usually is with maths). Shortcut is below.

And now onto the latest question. This is from an Additional Maths 1971 O Level paper:

# Old Exam Questions #4

First off, here is my solution to Old Exam Question #3

(Click for enlargements)

Did you use a different method? I’m not convinced I’d be awarded full marks, which in itself prompts interesting questions about marking examinations perhaps… perhaps not.

Anyway, this is from an O Level paper written in 1957:

# Old Exam Questions #3

First off, here is my solution to Old Exam Question #2:

(Click for enlargements)

I even stuck to the no calculator rule! Tangent is very slightly out, but if I repeated the algorithm it would be right. I suspect I’d get the mark despite being 0.01 out.

Did you use a different method to Old Exam Question #2 ?

Anyway, onto the next question.

This is from a 1974 O Level Paper:

My solution will be posted with the next question (soon).