This paper provides evidence that a short, fully online, well-constructed diagnostic test based on research literature can give teachers information about their students' thinking and strategies that is sufficiently accurate to use for formative assessment purposes. The example is a test for students beginning to learn to solve equations. The main goal is to inform their teacher of the solving strategies each can use. Accuracy data from 3010 students is analysed to judge how well the overall performance of each group matches predictions. Alongside a previous analysis of misconceptions and common errors, we show this test gives teachers a good picture of most students to plan their lessons.