You can take the exam. Private high school refers to a high school invested by private or private institutions and approved by the local government and education department. Private high schools are also a part of education in China, and they are under the control of the Education Bureau. Therefore, Guangyu private high school in Fengxian can enter the university. College only refers to the general name of schools with higher education, or schools that only offer university courses, or colleges affiliated to a university.