Focus On The Solution

One of the best approaches to writing high-quality parametized questions is to focus on the solution to the problem and work backwards to the question. The simultaneous equation question in the previous section demonstrated this approach.

$ax - y = $b

$cx + y = $d

Parameters:

$a=range(2,9)

$c=range(2,9)

$x=range(1,20)

$y=range(1,20)

$b=$a*$x-$y

$d=$c*$x+$y

In this question, we have created parameters for $x and $y which represent the solution to the question. Being parametized, we have full control over the possible solutions. In this example, the solutions will all be positive integers between 1 and 20. This makes it much easier to create consistently difficult questions.

Focusing on the solution means that we have to calculate parts of the question definition. This can  be done as expression parameters as shown above.

$b=$a*$x-$y

$d=$c*$x+$y

These two lines use $a and $c as well as our solution to create the appropriate values for our question. This guarantees that the question will always "work".

Focussing on the solution is not always possible or necessary, but is always worth considering.