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There is also a middle ground where students don't show work but can't work
back from answers: the last handful of questions in each SAT section are
"student produced responses". The students have to bubble in the numeric
answers. There can be more than one right answer. In that format, I think
you could require algebra:
The line through the points (2,5) and (7, -1) is expressed in the form Ax +
By = C where A, B and C are integers. Find a possible value of C. [1]
I think you would have to do the algebra. Or be so familiar with this kind
of algebra that you can skip a bunch of steps -- but that's not the same
thing as evading the algebra entirely.
But this raises another question in my mind: this format has been around
for a while on the SAT -- more than a decade. But they rarely choose to
use it to make students do algebra. I suspect that somewhere in the inner
core of where SAT policy is created, there are still some people
who like the fact that the test rewards clever work-arounds.