Immediately upon receipt of a petition submitted pursuant to Section 16078 the board shall cause the clerk of the district to examine and verify the signatures, and to certify the result to the board within 10 days. If the petition is found insufficient, the clerk shall certify to the number of additional signatures of qualified electors required to make the petition sufficient, and the petition may be amended by a supplemental petition filed within 10 days from the date of the certificate.