The theorem, the roots it needs, and the line that grade 9 starts from.
The answer key prints on a separate page.
Eighth grade is the year before algebra, and the three sections here are the three things algebra assumes on day one. The Pythagorean theorem is the geometry, and it fails on the same step every time — using it as an addition when the hypotenuse is the side already given. Roots are its arithmetic, and they are here on their own because a child who is slow at them is slow at every Pythagoras question for a reason that has nothing to do with triangles.
Slope closes the paper because it is the idea grade 9 is built on. Rise over run is one division; what is being tested is whether a child can read a line as a rate of change rather than as a picture, and that reading is what makes linear functions make sense next year.
