Can I purchase a Sycamore High School (Cincinnati, Ohio) certificate in the USA? How much to buy an SHS degree? Sycamore High School (SHS) is a four-year public high school in the northeast suburbs of Cincinnati, Ohio. It is the only high school in the Sycamore Community School District. Sycamore High School offers more than 223 courses including six global languages, more than 20 AP course offerings, and post-AP level classes.