I don’t know of any of the standardized tests that will have explicit diagramming, although I haven’t done the CAT. Diagramming is a very useful tool, especially for visual learners, but it isn’t the only way to get the job done. Very few public schools teach diagramming anymore, which makes me wonder if it is commonly covered on the standardized tests I have not seen or used yet, like the CAT. I do teach it, and I have used the Mary Daly book listed above, and also the grammar book I use in middle school years teaches it (Our Mother Tongue) And since I’m weird, we often pick hard or long sentences we encounter and diagram them for fun. 🙂 I especially like diagramming to help students “get” how the parts of a sentence relate to each other; this can be especially useful when studying other languages. And I find that diagramming is a part of grammar that my boys enjoy; it’s like a puzzle. Irresistible. 🙂 But any way you can find to teach how words relate to each other in a sentence will work well; I know of methods that use colored index cards, etc.