Algebra and moderation

Here is a simple way to assess students' understanding of algebraic functions. Suppose you gave a test and you are about to return them the paper. Ask them this:

Let's say your marks for this paper is x, and you are giving a choice to change your makes by using a certain function. Which function will you choose? You are only given one choice!

1. x+5
2. max(60, x+10)
3. 100-x
4. 10sqrt(x)
5. 20ln(x)

Which one would you choose and in what situation would you choose each of them?

Of course you can extend this problem into a two variable function. Suppose paper 1 is x and paper 2 is y. Which one would you choose as your marks?

1. (x+y)/2
2. sqrt(x^2+y^2)
3. sqrt(xy)
4. max(x , y)

You can come up with many other functions to assess the students' higher order thinking skills.