OneAndOneIs2

I was in another maths exam today.

There were some rather higher questions in this one. There was real algebra, and geometry, and all sorts.

An example:

Simplify the following:

x^2 - 8x + 15
2x^2 - 7x - 15

Obviously, there were a few who hadn't grasped quadratic equations and algebra to a particularly high extent: They figured that since there were x's high and low, they could cancel them out. And there were 15s on both too! So they wound up with -8/-5

Sigh.

Then there were the ones who actually knew what they were doing. As with any simplification of a fraction, you find a common denominator and remove it. In this case, of course, the only useful factors of 15 are 3 and 5. It's easy enough to get 8 with those, and 7 as well when you have an option of multiplying by two.

So you re-arrange the equations into:

And since (x-5) is common, you remove it and get a final answer of

I saw several correct answers. Maybe there's hope yet?

Well..

There was this other question: Two lines joined to form an acute angle. AKA a V-shape

They had to use ruler and compass to draw a line that bisected the acute angle. It specifically told them this.

And some of them duly place a compass on the point of convergence, used them to place a bisecting curve on each line equidistant from the point, and used those two points to find another point midway between the two lines, which they used to draw the bisecting line.

Fine. No problems there. Good understanding of basic geometry.

But then there were the students who read the question, reached for their rulers, and drew a line joining the two ends of the V-shape to form a triangle.

And this, they think, is a good answer to a question worth three marks that tells them they need to use a compass.

The light at the end of the tunnel just went out..