Automated Generation of Geometry Questions for High School Mathematics
We describe a framework that combines a combinatorial approach, pattern matching and automated deduction 
 
to generate and solve geometry problems for high school mathematics. Such a system would help teachers 
 
to quickly generate large numbers of questions on a geometry topic. Students can explore and revise specific 
 
topics covered in classes and textbooks based on generated questions. The system can act as a personalized 
 
instructor - it can generate problems that meet users specific weaknesses. This system may also help standardize 
 
tests such as GMAT and SAT. Our novel methodology uses (i) a combinatorial approach for generating 
 
geometric figures (ii) a pattern matching approach for generating questions and (iii) automated deduction to 
 
generate new questions and solutions. By combining these methods, we are able to generate questions involving 
 
finding or proving relationships between geometric objects based on a specification of the geometry 
 
objects, concepts and theorems to be covered by the questions. Experimental results show that a large number 
 
of questions can be generated in a short time. We have tested our generated questions on an existing geometry 
 
question solving software JGEX, verifying the validity of the generated questions.