Old Exam Questions #7

First, my solution to Old Exam Question #6

1966

solna

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:

1918:

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Old Exam Questions #5

First, my solution to Old Exam Question #4

1957

(Click for enlargements)

soln1

soln2

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.

soln3

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

1971

Old Exam Questions #3

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

(Click for enlargements)

PART 1

PART 2

PART 3

PART 4

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:

1974

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