When people of a certain age talk about GCSEs, the conversation may well quickly turn to the old ‘O Level’ qualification, and, more often than
not, how much harder these were than anything 16 year olds are expected to do
today. Part of the problem with these conversations is that few people are in
a position to make a real comparison. Most people have only ever seen one type
of exam, and if it is the O Levels, this was a long time ago. Perhaps for that reason, when I was a teenager (I was a weird teenager) the old
exams had a certain mystique. As somebody who got a little too much of their sense of self
through exam grades, I couldn’t help but wonder how I would have done at them. While I’ll never know the answer to that
question, thanks to the wonders of the internet, it’s certainly possible to
compare the two exams, if you are geeky and obsessive enough to do so. What
follows are the results of that endeavour with the old Maths O Level, and an
attempt to answer that all important question: how much harder was it really?

The first thing to mention is that the O Levels (at least
the exams from the ’50s and ‘60s) feel in many ways like very dated exams. They
are densely printed, long, and in terms of structure feel a lot more like university exams. They have two sections, one of short questions and one of
longer questions of which you choose a few (GCSE Maths papers don’t involve any
choice).

Some of the material is very much from a time when people didn’t
have calculators. There are lots of questions which are clearly testing your
ability to use logarithmic and trigonometric tables and others which ask you to
approximate π as 22/7 (at GCSE you’d either just put it in a calculator and
round, or give your answer as a multiple of π, but it's still a nice approximation to use for rough calculations). There are then arithmetic problems
which require some numerical manipulation to solve, often better thought of
first as algebraic expressions to simplify, such as these ones here:

You can see why there would have been a greater focus on numerical skills before calculators, but I think it’s a bit of a
shame this kind of numerical manipulation isn't taught as much anymore, as it can help children with algebra. Part iii) of this
question is also a reminder of another pesky feature of these exams: old,
imperial units and pre-decimal currency (I couldn't answer part iii without looking up how many shillings there were in a pound!)

That said, there is a lot about the exams that hasn’t
changed at all. The algebra is pretty much the same, both in terms of content
and level of difficulty (if we are comparing the O Level to the Higher Tier
GCSE, after Gove’s reforms. The Foundation is dramatically less challenging,
and prior to Gove’s reforms the GCSEs were considerably less difficult). This
question, for example, taken from a 1962 O Level exam could have come straight
out the GCSE were it not for the font:

There are a few algebra questions in the O Levels which do seem a little more inventive
in terms of what is asked. Question 4 (ii) below, for example, requires students not
to solve for a single unknown but a quotient of two. That said, how difficult
this kind of problem is very much depends on whether you have been taught to do
it before or seen it for the first time, and I haven’t seen enough papers to
know if this was a standard problem.

The section B algebra problems also seem to have required a little
more in terms of initiative and personal input to solve. This one here, for example, I could only solve
easily by introducing two unknowns of my own (I used n for the initial number of items sold and N for the total) which you could then get rid of by rearranging.

The GCSE does require algebraic proof and introducing an unknown to solve numerical problems, but not introducing several unknowns to derive a purely algebraic expression which does not contain the variables you’ve introduced. An example of the type of problem tested at GCSE is here, which you solve by forming a quadratic (e.g by setting the number of green pens as x and blue as x+ 3).

One way in which the O Level was definitely more challenging
was the geometry. GCSE geometry questions tend to provide diagrams, the O Levels
required you to figure out yourself what they would look like based only on worded
descriptions. This question here, for example, could easily be a GCSE question,
but there is no way they would ask you to do it without a diagram provided.

The proof questions were stylistically different, but don’t
seem all that much more challenging. The main difference is volume: the O Level
papers seem to have

*a lot*of geometric proof involved, whereas on the GCSE there will only be a couple of questions. Below, for comparison, are two geometric proof questions, first a 1968 O Level and below that a 2017 GCSE question.
Content wise, the other main difference is that the O Level
was in some ways a narrower exam. In the 1950’s and 60’s papers I didn’t find
any statistics, data handling or probability questions, and very little on
volumes, number properties, primes factor decomposition or surds. Algebra, geometry
and doing long calculations with tables and slide rules seemed to be the
greater focus. That said, the O Level did require knowing some basic calculus,
and apart from the Edexcel IGCSE this isn’t taught until A Level (and even with the IGCSE there is no integration). And one exam
I found from 1957 also had a rather charming third paper on the history of
mathematics. I don’t know if this was a common part of the curriculum or not,
but there is certainly something wonderfully quaint about it.

So, all in all, was the O Level Maths exam more difficult
than the GCSE? Compared to the exams I sat, pre Michael Gove, I regret to say
the answer is certainly yes. Compared to the exams students sit now, I’m less
certain. There are certainly fewer gift questions (even the higher tier GCSE still
has a some very easy questions at the start of the exam, the O Level seemed to
have fewer, and they were less easy). On balance, I would still conclude that the O Levels were a little
more challenging, if nothing else because they required more personal input and
initiative to do start the questions (introducing your own variables, working out
what a geometry problem looks like based on a description). But they aren’t a
million miles away from one another.

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