There is substantial evidence of the potential for class bias in the use of standardized tests to evaluate college applicants, yet little comparable inquiry considers the written essays typically required of applicants to selective US colleges and universities. We utilize a corpus of 240,000 admissions essays submitted by 60,000 applicants to the University of California in November 2016 to measure the relationship between the content of application essays, reported household income, and standardized test scores (SAT) at scale. We quantify essay content using correlated topic modeling (CTM) and the Linguistic Inquiry and Word Count (LIWC) software package. Results show that essays have a stronger correlation to reported household income than SAT scores. Essay content also explains much of the variance in SAT scores, suggesting that essays encode some of the same information as the SAT, though this relationship attenuates as household income increases. Efforts to realize more equitable college admissions protocols can be informed by attending to how social class is encoded in non-numerical components of applications.