The multiple-choice section of the final examination for the first-year Advanced Physics I course at the University of Newcastle, Australia between 2010 and 2018 was investigated for gender bias. A Mantel-Haenszel analysis revealed that approximately 20% of the multiple-choice questions exhibited statistically significant gender bias. A schema for characterizing the multiple-choice questions was proposed and used to analyze the entire question set. Male bias questions showed moderate to large bias and tended to include characteristics related to visualization, though not images. Several questions exhibited a moderate bias in favor of females and were characterized by requiring a numerical calculation involving a simple one-step equation. These results indicate that with continued development, gender bias analysis of physics questions based on a characterization schema may be used as a routine tool for testing for the presence and origin of gender gaps in student performance.