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In teaching mathematics at my secondary charter school (for 10 years now) it has been necessary to create a curriculum from scratch that covers the material the students never did grasp in earlier grades as well as get them to be reasonably skilled and knowledgeable in the grade-level areas. I have found that the majority of them did not arrive with the skills to perform simple tasks--never mind the skills needed for engineering professions.
These questions are typical of what is covered in my classes and are also typical of the skills they will need for engineering.
You can use the quiz as an instructional guide or as a handout to those who think that they might have an interest in engineering!