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This article has been accepted for publication in Monthly notices of the Royal Astronomical Society Journal © 2013 RAS. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. AH-C and AA-H acknowledge funding by the Universidad de Cantabria Augusto González Linares program. We acknowledge support from the Spanish Programa Nacional de Astronomía y Astrofísica under grants AYA2009-07723-E and AYA2009-10368. SHARDS has been funded by the Spanish MICINN/MINECO under the Consolider-Ingenio 2010 Program grant CSD2006-00070: First Science with the GTC. This work has made use of the Rainbow Cosmological Surveys Database, which is operated by the Universidad Complutense de Madrid (UCM). Based on observations made with the GTC, installed at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, in the island of La Palma. We thank all the GTC Staff for their support and enthusiasm with the SHARDS project, and we would like to especially acknowledge the help from Antonio Cabrera and Rene Rutten. We also thank the anonymous referee for their useful comments that helped to improve this paper., We report on results from the analysis of a stellar mass-selected (log (M-*/M-circle dot) >= 9.0) sample of 1644 galaxies at 0.65 < z < 1.1 with ultradeep (m(AB) < 26.5) optical medium-band (R similar to 50) photometry from the Survey for High-z Absorption Red and Dead Sources (SHARDS). The spectral resolution of SHARDS allows us to consistently measure the strength of the 4000 A spectral break [D-n(4000), an excellent age indicator for the stellar populations of quiescent galaxies] for all galaxies at z similar to 0.9 down to log (M-*/M-circle dot) similar to 9. The D-n(4000) index cannot be resolved from broad-band photometry, and measurements from optical spectroscopic surveys are typically limited to galaxies at least 10 times more massive. When combined with the rest-frame U - V colour, (U - V)(r), D-n(4000) provides a powerful diagnostic of the extinction affecting the stellar population that is relatively insensitive to degeneracies with age, metallicity or star formation history. We use this novel approach to estimate de-reddened colours and light-weighted stellar ages for individual sources. We explore the relationships linking stellar mass, (U - V)(r), and D-n(4000) for the sources in the sample, and compare them to those found in local galaxies. The main results are: (a) both D-n(4000) and (U - V)(r) correlate with M-*. The dispersion in D-n(4000) values at a given M-* increases with M-*, while the dispersion for (U - V)(r) decreases due to the higher average extinction prevalent in massive star-forming galaxies. (b) For massive galaxies, we find a smooth transition between the blue cloud and red sequence in the intrinsic U - V colour, in contrast with other recent results. (c) At a fixed stellar age, we find a positive correlation between extinction and stellar mass. (d) The fraction of sources with declining or halted star formation increases steeply with the stellar mass, from similar to 5 per cent at log (M-*/M-circle dot) = 9.0-9.5 to similar to 80 p, Universidad de Cantabria Augusto Gonzalez Linares program, Spanish Programa Nacional de Astronomia y Astrofisica, Spanish MICINN/MINECO under the Consolider-Ingenio Program, Depto. de Física de la Tierra y Astrofísica, Fac. de Ciencias Físicas, TRUE, pub