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We present a study of the mass-metallicity (M-Z) relation and H II regionphysical conditions in a sample of 20 star-forming galaxies at 1.0<z<1.5 drawnfrom the DEEP2 Galaxy Redshift Survey. Our analysis indicates that the zeropoint of the M-Z relationship evolves with redshift, in the sense that galaxiesat fixed stellar mass become more metal-rich at lower redshift. Measurements of[O III]/H-beta and [N II]/H-alpha emission-line ratios show that, on average,objects in the DEEP2 1.0<z<1.5 sample are significantly offset from theexcitation sequence observed in nearby H II regions and SDSS emission-linegalaxies. In order to fully understand the causes of this offset, which is alsoobserved in z~2 star-forming galaxies, we examine in detail the small fractionof SDSS galaxies that have similar diagnostic ratios to those of the DEEP2sample. Some of these galaxies indicate evidence for AGN and/or shock activity,which may give rise to their unusual line ratios, and contribute to Balmeremission lines at the level of ~20%. Others indicate no evidence for AGN orshock excitation, yet are characterized by higher electron densities andtemperatures, and therefore, interstellar gas pressures, than typical SDSSstar-forming galaxies of similar stellar mass. These anomalous objects alsohave higher concentrations and star-formation rate surface densities, which aredirectly connected to higher interstellar pressure. Higher star-formation ratesurface densities, interstellar pressures, and HII region ionization parametersmay also be common at high-redshift. These effects must be taken into accountwhen using strong-line indicators to understand the evolution of heavy elementsin galaxies. When such effects are included, the inferred evolution of the M-Zrelation out to z~2 is more significant than previous estimates. (abridged)

Metallicities and Physical Conditions in Star-forming Galaxies at z~1.0-1.5