This research examined linear and nonlinear (quadratic) relations among general intelligence (g), aptitude tests (SAT, ACT, PSAT), and college GPAs. Test scores and GPAs were obtained from the National Longitudinal Survey of Youth (N = 1950) and the College Board Validity Study (N = 160670). Regressions estimated linear and quadratic relations among g, based on the Armed Services Vocational Aptitude Battery, composite and subtest scores of aptitude tests, and college GPAs. Linear effects explained almost all the variance in relations among variables. In contrast, quadratic effects explained trivial additional variance among variables (less than 1%, on average). The results do not support theories of intelligence (threshold theories or Spearman's Law of Diminishing Returns), which predict that test scores lose predictive power with increases in ability level or at a certain threshold.